100 results found for "radical republicanism" in Class 10.
चीनी उन्नीस सौ ग्यारह क्रांति में राष्ट्रवाद और गणतंत्रवाद का संबंध क्या था?
What was the relation between nationalism and republicanism in the Chinese Revolution of 1911?
#world history
#revolutions
#xinhai revolution
#nationalism republicanism
A राष्ट्रवाद ने छिंग शासन और विदेशी प्रभाव का विरोध किया जबकि गणतंत्रवाद ने राजवंशीय शासन को चुनौती दी / Nationalism opposed Qing rule and foreign influence while republicanism challenged dynastic rule
B राष्ट्रवाद ने केवल शोगुनत को बचाया / Nationalism only saved the Shogunate
C गणतंत्रवाद ने सम्राटीय शासन बढ़ाया / Republicanism increased imperial rule
D दोनों का राजनीति से कोई संबंध नहीं था / Both had no relation with politics
Explanation opens after your attempt
Correct Answer
A. राष्ट्रवाद ने छिंग शासन और विदेशी प्रभाव का विरोध किया जबकि गणतंत्रवाद ने राजवंशीय शासन को चुनौती दी / Nationalism opposed Qing rule and foreign influence while republicanism challenged dynastic rule
Explanation
Simple Explanation
दोनों विचार चीन को नई राजनीतिक दिशा देने से जुड़े थे। परीक्षा में विचारधारा को शासन परिवर्तन से जोड़ें। / Both ideas were linked with giving China a new political direction. For exams connect ideology with regime change.
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सुन यात सेन किस देश में गणतंत्रवाद से जुड़े थे?
Sun Yat sen was associated with republicanism in which country?
#world_history
#famous_leaders
#sun_yat_sen
A जापान / Japan
B चीन / China
C कोरिया / Korea
D थाईलैंड / Thailand
Explanation opens after your attempt
Correct Answer
B. चीन / China
Explanation
Simple Explanation
सुन यात सेन चीन में गणतंत्रवादी आंदोलन के प्रमुख नेता थे। परीक्षा में उन्हें आधुनिक चीन के आरंभ से जोड़ें। / Sun Yat sen was a major leader of republicanism in China. Exam tip: connect him with the beginning of modern China.
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अमेरिकी क्रांति में रिपब्लिकनिज्म का विचार किस बात पर जोर देता था?
What did the idea of republicanism emphasize in the American Revolution?
#world-history
#revolutions
#american-revolution
A नागरिक सद्गुण प्रतिनिधि शासन और वंशानुगत राजसत्ता का विरोध / Civic virtue representative government and opposition to hereditary monarchy
B राजा के दैवी अधिकार का समर्थन / Support for divine right of kings
C उपनिवेशों में स्थायी ब्रिटिश सेना का विस्तार / Expansion of permanent British army in colonies
D चर्च को सभी राजनीतिक अधिकार देना / Giving all political rights to the Church
Explanation opens after your attempt
Correct Answer
A. नागरिक सद्गुण प्रतिनिधि शासन और वंशानुगत राजसत्ता का विरोध / Civic virtue representative government and opposition to hereditary monarchy
Explanation
Simple Explanation
रिपब्लिकनिज्म ने नागरिक भागीदारी और प्रतिनिधि शासन को महत्व दिया। परीक्षा में इसे राजतंत्र विरोधी राजनीतिक विचार से जोड़ें। / Republicanism valued civic participation and representative government. For exams connect it with anti monarchy political thought.
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वाशिंगटन ने सैन्य प्रतिष्ठा के बावजूद नागरिक सत्ता को प्राथमिकता देकर क्या मिसाल रखी?
What example did Washington set by prioritizing civilian authority despite military prestige?
#world-leaders
#washington
#republicanism
A लोकतांत्रिक गणराज्य में सेना पर नागरिक नियंत्रण / Civilian control over the military in a democratic republic
B स्थायी सैन्य तानाशाही / Permanent military dictatorship
C राजवंशीय शासन / Dynastic rule
D उपनिवेशी शासन / Colonial rule
Explanation opens after your attempt
Correct Answer
A. लोकतांत्रिक गणराज्य में सेना पर नागरिक नियंत्रण / Civilian control over the military in a democratic republic
Explanation
Simple Explanation
वाशिंगटन ने सत्ता को संस्थाओं के अधीन रखने की परंपरा मजबूत की। परीक्षा में उन्हें गणतांत्रिक मर्यादा से जोड़ें। / Washington strengthened the tradition of keeping power under institutions. For exams connect him with republican restraint.
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सुन यात सेन के राष्ट्रवाद का लक्ष्य छिंग शासन के बाद किस निर्माण से जुड़ा था?
Sun Yat Sen's nationalism after Qing rule was linked with building what?
#world-leaders
#sun-yat-sen
#republicanism
A आधुनिक चीनी गणराज्य / Modern Chinese republic
B यूरोपीय साम्राज्य / European empire
C जापानी शोगुनत / Japanese shogunate
D रूसी जारशाही / Russian Tsardom
Explanation opens after your attempt
Correct Answer
A. आधुनिक चीनी गणराज्य / Modern Chinese republic
Explanation
Simple Explanation
सुन यात सेन ने चीन में गणतांत्रिक और राष्ट्रीय पुनर्निर्माण की कल्पना की। परीक्षा में उन्हें तीन लोक सिद्धांतों से जोड़ें। / Sun Yat Sen imagined republican and national reconstruction in China. For exams connect him with the Three Principles of the People.
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मैरीआन की छवि को गणतांत्रिक पहचान से जोड़ने में कौन-सा संयोजन सबसे सही है?
Which combination best links Marianne with republican identity?
#marianne
#republicanism
#red cap
#tricolour
A लाल टोपी त्रिरंगा और सार्वजनिक मूर्तियाँ / Red cap tricolour and public statues
B मुकुट राजदंड और सिंहासन / Crown sceptre and throne
C हल बैल और खेत / Plough oxen and field
D जहाज बंदरगाह और व्यापार पुस्तिका / Ship port and trade register
Explanation opens after your attempt
Correct Answer
A. लाल टोपी त्रिरंगा और सार्वजनिक मूर्तियाँ / Red cap tricolour and public statues
Step 1
Concept
मैरीआन फ्रांसीसी गणराज्य की प्रतीक थी। / Marianne symbolized the French Republic.
Step 2
Why this answer is correct
लाल टोपी और त्रिरंगा उसके गणतांत्रिक अर्थ को मजबूत करते थे। / The red cap and tricolour strengthened her republican meaning.
Step 3
Exam Tip
सार्वजनिक मूर्तियाँ इस प्रतीक को जनता तक ले गईं। / Public statues carried the symbol to ordinary people.
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मैरिएन की छवि किस राजनीतिक आदर्श से सबसे अधिक जुड़ी थी?
Marianne's image was most closely linked with which political ideal?
#marianne
#republicanism
#french-republic
A गणतंत्रवाद / Republicanism
B सामंतवाद / Feudalism
C निरंकुश राजतंत्र / Absolute monarchy
D उपनिवेशवाद / Colonialism
Explanation opens after your attempt
Correct Answer
A. गणतंत्रवाद / Republicanism
Step 1
Concept
मैरिएन फ्रांसीसी गणराज्य का प्रतीक थी। / Marianne was the symbol of the French Republic.
Step 2
Why this answer is correct
गणराज्य में नागरिकता और जनता की सत्ता पर जोर होता है। / A republic stresses citizenship and people's authority.
Step 3
Exam Tip
इसलिए मैरिएन को गणतंत्रवाद से जोड़ना सही है। / Therefore Marianne is correctly linked with republicanism.
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मैरिएन की मूर्तियां और चित्र सार्वजनिक स्थानों पर लगाने का प्रमुख कारण क्या था?
Why were statues and images of Marianne placed in public spaces?
#marianne
#public-symbols
#republicanism
#exam-mcq
A गणराज्य और नागरिक एकता की भावना फैलाने के लिए / To spread republican and civic unity
B राजशाही की वापसी के लिए / To restore monarchy
C विदेशी शासन को मजबूत करने के लिए / To strengthen foreign rule
D कृषि कर बढ़ाने के लिए / To increase agricultural taxes
Explanation opens after your attempt
Correct Answer
A. गणराज्य और नागरिक एकता की भावना फैलाने के लिए / To spread republican and civic unity
Step 1
Concept
सार्वजनिक प्रतीक आम लोगों तक विचार पहुंचाते थे। / Public symbols carried ideas to ordinary people.
Step 2
Why this answer is correct
मैरिएन ने फ्रांसीसी गणराज्य को जनता के सामने जीवंत बनाया। / Marianne made the French Republic visible to the public.
Step 3
Exam Tip
ऐसे प्रतीक नागरिकों में साझा पहचान बनाते थे। / Such symbols created shared civic identity.
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मेत्सिनी और बिस्मार्क के बीच वैचारिक अंतर को किस प्रकार समझा जा सकता है?
How can the ideological difference between Mazzini and Bismarck be understood?
#mazzini
#bismarck
#ideology
#republicanism
A मेत्सिनी गणतांत्रिक राष्ट्रवाद से जुड़ा था जबकि बिस्मार्क राजशाही राज्य शक्ति से / Mazzini was linked with republican nationalism while Bismarck with monarchical state power
B मेत्सिनी प्रशा का मंत्री था जबकि बिस्मार्क इटली का कवि था / Mazzini was Prussia's minister while Bismarck was Italy's poet
C मेत्सिनी ने जोलफेराइन बनाया जबकि बिस्मार्क ने यंग इटली बनाया / Mazzini made Zollverein while Bismarck made Young Italy
D दोनों ने किसी राष्ट्रवाद का समर्थन नहीं किया / Both supported no nationalism
Explanation opens after your attempt
Correct Answer
A. मेत्सिनी गणतांत्रिक राष्ट्रवाद से जुड़ा था जबकि बिस्मार्क राजशाही राज्य शक्ति से / Mazzini was linked with republican nationalism while Bismarck with monarchical state power
Step 1
Concept
मेत्सिनी जनता आधारित गणराज्य की कल्पना करता था। / Mazzini imagined a people based republic.
Step 2
Why this answer is correct
बिस्मार्क प्रशा की राजशाही और शक्ति राजनीति से जुड़ा था। / Bismarck was linked with Prussian monarchy and power politics.
Step 3
Exam Tip
यही दोनों की सोच का मुख्य अंतर है। / This is the main difference in their thinking.
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मेत्सिनी के गणतांत्रिक आदर्श और इटली के अंतिम राजशाही रूप में मुख्य विरोधाभास क्या था?
What was the main contrast between Mazzini's republican ideal and Italy's final monarchical form?
#mazzini
#republicanism
#monarchy
#italy
A मेत्सिनी जनता आधारित गणराज्य चाहता था पर एकीकरण राजा के अधीन हुआ / Mazzini wanted a people based republic but unification happened under a king
B मेत्सिनी राजशाही चाहता था पर इटली गणराज्य बना / Mazzini wanted monarchy but Italy became a republic
C मेत्सिनी प्रशा का राजा था पर इटली ने उसे हटा दिया / Mazzini was king of Prussia but Italy removed him
D मेत्सिनी ने फ्रांस को इटली की राजधानी बनाया / Mazzini made France the capital of Italy
Explanation opens after your attempt
Correct Answer
A. मेत्सिनी जनता आधारित गणराज्य चाहता था पर एकीकरण राजा के अधीन हुआ / Mazzini wanted a people based republic but unification happened under a king
Step 1
Concept
मेत्सिनी राष्ट्रीय एकता के साथ गणतांत्रिक विचार रखता था। / Mazzini held republican ideas along with national unity.
Step 2
Why this answer is correct
वास्तविक एकता विक्टर इमैनुएल द्वितीय की राजशाही में बनी। / Actual unity formed under Victor Emmanuel II's monarchy.
Step 3
Exam Tip
इससे विचार और राजनीतिक परिणाम में अंतर दिखता है। / This shows a difference between idea and political result.
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इटली के एकीकरण में गणतांत्रिक विचार और राजशाही नेतृत्व साथ साथ कैसे दिखाई देते हैं?
How do republican ideas and monarchical leadership appear together in Italian unification?
#republicanism
#monarchy
#italy
#mazzini
A मैजिनी गणतांत्रिक विचारों से जुड़े थे, पर अंतिम राज्य राजशाही नेतृत्व में बना / Mazzini was linked with republican ideas, but the final state formed under monarchical leadership
B बिस्मार्क गणतांत्रिक थे और गैरीबाल्डी जर्मन राजा थे / Bismarck was republican and Garibaldi was a German king
C ऑस्ट्रिया ने गणराज्य बनाया और फ्रांस राजा बना / Austria made a republic and France became king
D इटली में कोई विचारधारा नहीं थी / There was no ideology in Italy
Explanation opens after your attempt
Correct Answer
A. मैजिनी गणतांत्रिक विचारों से जुड़े थे, पर अंतिम राज्य राजशाही नेतृत्व में बना / Mazzini was linked with republican ideas, but the final state formed under monarchical leadership
Step 1
Concept
मैजिनी एक स्वतंत्र और गणतांत्रिक इटली चाहते थे। / Mazzini wanted a free and republican Italy.
Step 2
Why this answer is correct
पर एकीकृत इटली का नेतृत्व विक्टर इमैनुएल द्वितीय जैसे राजा से जुड़ा। / But unified Italy was led by a king, Victor Emmanuel II.
Step 3
Exam Tip
इससे इटली के एकीकरण में विचारों और व्यवहार का मेल दिखता है। / This shows a mix of ideals and practical politics in Italian unification.
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मेत्सिनी और बिस्मार्क के बीच सबसे स्पष्ट वैचारिक अंतर कौन सा था?
What was the clearest ideological difference between Mazzini and Bismarck?
#mazzini
#bismarck
#ideology
#republicanism
A मेत्सिनी गणतांत्रिक राष्ट्रवाद से जुड़ा था जबकि बिस्मार्क रूढ़िवादी राज्य शक्ति से / Mazzini was linked with republican nationalism while Bismarck with conservative state power
B मेत्सिनी प्रशा का राजा था जबकि बिस्मार्क इटली का राजा था / Mazzini was king of Prussia while Bismarck was king of Italy
C मेत्सिनी आर्थिक संघ चलाता था जबकि बिस्मार्क रेड शर्ट्स चलाता था / Mazzini ran an economic union while Bismarck led Red Shirts
D मेत्सिनी फ्रांस का सम्राट था जबकि बिस्मार्क पोप था / Mazzini was Emperor of France while Bismarck was the Pope
Explanation opens after your attempt
Correct Answer
A. मेत्सिनी गणतांत्रिक राष्ट्रवाद से जुड़ा था जबकि बिस्मार्क रूढ़िवादी राज्य शक्ति से / Mazzini was linked with republican nationalism while Bismarck with conservative state power
Step 1
Concept
मेत्सिनी जनता आधारित गणराज्य की कल्पना करता था। / Mazzini imagined a people based republic.
Step 2
Why this answer is correct
बिस्मार्क राजशाही और प्रशा की राज्य शक्ति से जुड़ा था। / Bismarck was linked with monarchy and Prussian state power.
Step 3
Exam Tip
यही दोनों नेताओं के विचारों का मुख्य अंतर है। / This is the main ideological difference between the two leaders.
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बोस्टन टी पार्टी को अमेरिकी क्रांति की दिशा में उग्र कदम क्यों माना जाता है?
Why is the Boston Tea Party considered a radical step toward the American Revolution?
#world history
#revolutions
#american revolution
#boston tea party
A इसमें उपनिवेशवासियों ने ब्रिटिश कर नीति का प्रत्यक्ष विरोध किया / Colonists directly opposed British tax policy
B इसमें ब्रिटेन ने सभी कर समाप्त कर दिए / Britain abolished all taxes in it
C इसमें फ्रांस ने अमेरिका छोड़ दिया / France left America in it
D इसमें उपनिवेशों ने राजा की पूजा शुरू की / Colonies began worshipping the king in it
Explanation opens after your attempt
Correct Answer
A. इसमें उपनिवेशवासियों ने ब्रिटिश कर नीति का प्रत्यक्ष विरोध किया / Colonists directly opposed British tax policy
Explanation
Simple Explanation
बोस्टन टी पार्टी ब्रिटिश कराधान के विरुद्ध प्रत्यक्ष औपनिवेशिक प्रतिरोध थी। परीक्षा में इसे कर विरोध और असहयोग से जोड़ें। / The Boston Tea Party was direct colonial resistance against British taxation. In exams, link it with tax protest and non-cooperation.
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संख्या रेखा पर \( \sqrt{300}-\sqrt{147} \) का सरल और सही मान कौन सा है?
What is the simplified correct value of \( \sqrt{300}-\sqrt{147} \) on the number line?
#number-line
#radical-difference
#simplification
A \(3\sqrt{3}\)
B \(7\sqrt{3}\)
C \( \sqrt{153} \)
D \(17\sqrt{3}\)
Explanation opens after your attempt
Correct Answer
A. \(3\sqrt{3}\)
Explanation
Simple Explanation
\( \sqrt{300}=10\sqrt{3} \) और \( \sqrt{147}=7\sqrt{3} \), इसलिए अंतर \(3\sqrt{3}\) है। पहले मूलों को सरल करें। / \( \sqrt{300}=10\sqrt{3} \) and \( \sqrt{147}=7\sqrt{3} \), so the difference is \(3\sqrt{3}\). Simplify the radicals first.
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संख्या रेखा पर \( \sqrt{29}+\sqrt{29}+\sqrt{29}+\sqrt{29} \) का सरल रूप कौन सा है?
What is the simplified form of \( \sqrt{29}+\sqrt{29}+\sqrt{29}+\sqrt{29} \) on the number line?
#number-line
#radical-addition
#common-mistake
A \( \sqrt{116} \)
B \(4\sqrt{29}\)
C \(29\sqrt{4}\)
D (116)
Explanation opens after your attempt
Correct Answer
B. \(4\sqrt{29}\)
Explanation
Simple Explanation
समान मूलों को जोड़ने पर \( \sqrt{29}+\sqrt{29}+\sqrt{29}+\sqrt{29}=4\sqrt{29} \) होता है। मूल के अंदर संख्याएँ सीधे नहीं जोड़ी जातीं। / Adding like radicals gives \( \sqrt{29}+\sqrt{29}+\sqrt{29}+\sqrt{29}=4\sqrt{29} \). Do not add the numbers inside radicals directly.
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यदि \(a=\sqrt{108}-\sqrt{48}\), तो संख्या रेखा पर (a) का सरल रूप क्या है?
If \(a=\sqrt{108}-\sqrt{48}\), what is the simplified form of (a) on the number line?
#number-line
#radical-simplification
#irrational
A \(2\sqrt{3}\)
B \(4\sqrt{3}\)
C \( \sqrt{60} \)
D \(10\sqrt{3}\)
Explanation opens after your attempt
Correct Answer
A. \(2\sqrt{3}\)
Explanation
Simple Explanation
\( \sqrt{108}=6\sqrt{3} \) और \( \sqrt{48}=4\sqrt{3} \), इसलिए अंतर \(2\sqrt{3}\) है। समान मूलों को ही घटाएँ। / \( \sqrt{108}=6\sqrt{3} \) and \( \sqrt{48}=4\sqrt{3} \), so the difference is \(2\sqrt{3}\). Subtract only like radicals.
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संख्या रेखा पर \( \sqrt{192}-\sqrt{75} \) का सरल और सही मान कौन सा है?
What is the simplified correct value of \( \sqrt{192}-\sqrt{75} \) on the number line?
#number-line
#radical-difference
#simplification
A \(3\sqrt{3}\)
B \(5\sqrt{3}\)
C \( \sqrt{117} \)
D \(13\sqrt{3}\)
Explanation opens after your attempt
Correct Answer
A. \(3\sqrt{3}\)
Explanation
Simple Explanation
\( \sqrt{192}=8\sqrt{3} \) और \( \sqrt{75}=5\sqrt{3} \), इसलिए अंतर \(3\sqrt{3}\) है। पहले मूलों को सरल करें। / \( \sqrt{192}=8\sqrt{3} \) and \( \sqrt{75}=5\sqrt{3} \), so the difference is \(3\sqrt{3}\). Simplify the radicals first.
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संख्या रेखा पर \( \sqrt{19}+\sqrt{19}+\sqrt{19} \) का सरल रूप कौन सा है?
What is the simplified form of \( \sqrt{19}+\sqrt{19}+\sqrt{19} \) on the number line?
#number-line
#radical-addition
#common-mistake
A \( \sqrt{57} \)
B \(3\sqrt{19}\)
C \(19\sqrt{3}\)
D (57)
Explanation opens after your attempt
Correct Answer
B. \(3\sqrt{19}\)
Explanation
Simple Explanation
समान मूलों को जोड़ने पर \( \sqrt{19}+\sqrt{19}+\sqrt{19}=3\sqrt{19} \) होता है। मूल के अंदर संख्याएँ सीधे नहीं जोड़ी जातीं। / Adding like radicals gives \( \sqrt{19}+\sqrt{19}+\sqrt{19}=3\sqrt{19} \). Do not add the numbers inside radicals directly.
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यदि \(a=\sqrt{75}-\sqrt{27}\), तो संख्या रेखा पर (a) का सरल रूप क्या है?
If \(a=\sqrt{75}-\sqrt{27}\), what is the simplified form of (a) on the number line?
#number-line
#radical-simplification
#irrational
A \(2\sqrt{3}\)
B \( \sqrt{48} \)
C \(4\sqrt{3}\)
D \( \sqrt{102} \)
Explanation opens after your attempt
Correct Answer
A. \(2\sqrt{3}\)
Explanation
Simple Explanation
\( \sqrt{75}=5\sqrt{3} \) और \( \sqrt{27}=3\sqrt{3} \), इसलिए अंतर \(2\sqrt{3}\) है। समान मूलों को ही घटाएँ। / \( \sqrt{75}=5\sqrt{3} \) and \( \sqrt{27}=3\sqrt{3} \), so the difference is \(2\sqrt{3}\). Subtract only like radicals.
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संख्या रेखा पर \( \sqrt{12}+\sqrt{27} \) का सरल रूप कौन सा है?
What is the simplified form of \( \sqrt{12}+\sqrt{27} \) on the number line?
#number-line
#radical-addition
#simplification
A \(4\sqrt{3}\)
B \(5\sqrt{3}\)
C \( \sqrt{39} \)
D \(9\sqrt{3}\)
Explanation opens after your attempt
Correct Answer
B. \(5\sqrt{3}\)
Explanation
Simple Explanation
\( \sqrt{12}=2\sqrt{3} \) और \( \sqrt{27}=3\sqrt{3} \), इसलिए योग \(5\sqrt{3}\) है। पहले मूलों को सरल करें। / \( \sqrt{12}=2\sqrt{3} \) and \( \sqrt{27}=3\sqrt{3} \), so the sum is \(5\sqrt{3}\). Simplify the radicals first.
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संख्या रेखा पर \( \sqrt{2}+\sqrt{8} \) का सरल रूप कौन सा है?
What is the simplified form of \( \sqrt{2}+\sqrt{8} \) on the number line?
#number-line
#radical-simplification
#addition
A \(3\sqrt{2}\)
B \( \sqrt{10} \)
C \(2\sqrt{10}\)
D \(4\sqrt{2}\)
Explanation opens after your attempt
Correct Answer
A. \(3\sqrt{2}\)
Explanation
Simple Explanation
\( \sqrt{8}=2\sqrt{2} \), इसलिए \( \sqrt{2}+\sqrt{8}=3\sqrt{2} \)। समान मूलों को ही जोड़ा जाता है। / \( \sqrt{8}=2\sqrt{2} \), so \( \sqrt{2}+\sqrt{8}=3\sqrt{2} \). Only like radicals can be added.
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संख्या रेखा पर \( \sqrt{48}-\sqrt{27} \) का सरल और सही मान कौन सा है?
What is the simplified correct value of \( \sqrt{48}-\sqrt{27} \) on the number line?
#number-line
#radical-difference
#simplification
A \( \sqrt{3} \)
B \(7\sqrt{3}\)
C \( \sqrt{21} \)
D \(3\sqrt{3}\)
Explanation opens after your attempt
Correct Answer
A. \( \sqrt{3} \)
Explanation
Simple Explanation
\( \sqrt{48}=4\sqrt{3} \) और \( \sqrt{27}=3\sqrt{3} \), इसलिए अंतर \( \sqrt{3} \) है। पहले मूलों को सरल करें। / \( \sqrt{48}=4\sqrt{3} \) and \( \sqrt{27}=3\sqrt{3} \), so the difference is \( \sqrt{3} \). Simplify the radicals first.
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संख्या रेखा पर \( \sqrt{13}+\sqrt{13} \) का सरल रूप कौन सा है?
What is the simplified form of \( \sqrt{13}+\sqrt{13} \) on the number line?
#number-line
#radical-addition
#common-mistake
A \(2\sqrt{13}\)
B \( \sqrt{26} \)
C (13)
D (26)
Explanation opens after your attempt
Correct Answer
A. \(2\sqrt{13}\)
Explanation
Simple Explanation
समान मूलों को जोड़ने पर \( \sqrt{13}+\sqrt{13}=2\sqrt{13} \) होता है। मूल के अंदर संख्याएँ सीधे नहीं जोड़ी जातीं। / Adding like radicals gives \( \sqrt{13}+\sqrt{13}=2\sqrt{13} \). Do not add the numbers inside the radicals directly.
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यदि \(a=\sqrt{27}-\sqrt{12}\), तो संख्या रेखा पर (a) का सरल रूप क्या है?
If \(a=\sqrt{27}-\sqrt{12}\), what is the simplified form of (a) on the number line?
#number-line
#radical-simplification
#irrational
A \( \sqrt{3} \)
B \(3\sqrt{3}\)
C \(5\sqrt{3}\)
D \( \sqrt{15} \)
Explanation opens after your attempt
Correct Answer
A. \( \sqrt{3} \)
Explanation
Simple Explanation
\( \sqrt{27}=3\sqrt{3} \) और \( \sqrt{12}=2\sqrt{3} \) इसलिए अंतर \( \sqrt{3} \) है। समान मूलों को घटाएँ। / \( \sqrt{27}=3\sqrt{3} \) and \( \sqrt{12}=2\sqrt{3} \), so the difference is \( \sqrt{3} \). Subtract like radicals.
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कौन-सा विकल्प सामान्य रूप में द्विघात समीकरण नहीं है?
Which option is not a quadratic equation in the usual form?
#quadratic-equations
#non-quadratic
#radical
#medium
A \(2x^2-5=0\)
B \(x^2+3x=0\)
C \(\sqrt{x}+x=4\)
D \(6x^2+x+1=0\)
Explanation opens after your attempt
Correct Answer
C. \(\sqrt{x}+x=4\)
Explanation
Simple Explanation
\(\sqrt{x}\) में चर की भिन्न घात है, इसलिए यह सामान्य द्विघात रूप नहीं है। द्विघात रूप में केवल \(x^2\), (x) और स्थिर पद होते हैं। / The term \(\sqrt{x}\) has a fractional power of the variable, so it is not in usual quadratic form. Quadratic form has only \(x^2\), (x), and constant terms.
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समीकरण \(\sqrt{x}+x^2=0\) को सामान्य रूप में द्विघात क्यों नहीं माना जाता?
Why is \(\sqrt{x}+x^2=0\) not considered a quadratic equation in the usual form?
#quadratic-equations
#non-example
#radical
A क्योंकि इसमें \(x^2\) है / Because it has \(x^2\)
B क्योंकि इसमें (0) है / Because it has (0)
C क्योंकि इसमें (x) नहीं है / Because it has no (x)
D क्योंकि इसमें \(\sqrt{x}\) पद है / Because it has a \(\sqrt{x}\) term
Explanation opens after your attempt
Correct Answer
D. क्योंकि इसमें \(\sqrt{x}\) पद है / Because it has a \(\sqrt{x}\) term
Explanation
Simple Explanation
\(\sqrt{x}\) चर की भिन्न घात दिखाता है इसलिए यह सामान्य द्विघात रूप में नहीं है। द्विघात में केवल \(x^2\), (x) और स्थिर पद होते हैं। / The term \(\sqrt{x}\) shows a fractional power of the variable, so it is not in usual quadratic form. A quadratic equation has only \(x^2\), (x), and constant terms.
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यदि (p(x)=x-2 -\(\sqrt{2}+\sqrt{8}\)x+4) है, तो शून्यकों का योग क्या है?
If (p(x)=x-2 -\(\sqrt{2}+\sqrt{8}\)x+4), what is the sum of its zeroes?
#sum-of-zeroes
#radical-simplification
#irrational
A \(3\sqrt{2}\)
B \(2\sqrt{2}\)
C \(4\sqrt{2}\)
D \(\sqrt{10}\)
Explanation opens after your attempt
Correct Answer
A. \(3\sqrt{2}\)
Explanation
Simple Explanation
योग \(\sqrt{2}+\sqrt{8}=\sqrt{2}+2\sqrt{2}=3\sqrt{2}\) है। मूलों को सरल करके ही अंतिम उत्तर दें। / The sum is \(\sqrt{2}+\sqrt{8}=\sqrt{2}+2\sqrt{2}=3\sqrt{2}\). Simplify radicals before giving the final answer.
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यदि (p(x)=x-2 -(a+b)x+ab) और \(a=\sqrt{2}\), \(b=\sqrt{18}\), तो शून्यकों का गुणनफल क्या है?
If (p(x)=x-2 -(a+b)x+ab) and \(a=\sqrt{2}\), \(b=\sqrt{18}\), what is the product of the zeroes?
#radical-product
#zeroes
#monic
A (6)
B \(\sqrt{20}\)
C \(3\sqrt{2}\)
D (20)
Explanation opens after your attempt
Explanation
Simple Explanation
गुणनफल \(ab=\sqrt{2}\cdot\sqrt{18}=\sqrt{36}=6\) है। मूलों के गुणन में पहले अंदर के गुणनफल को सरल करें। / The product is \(ab=\sqrt{2}\cdot\sqrt{18}=\sqrt{36}=6\). In radical multiplication, simplify the product inside the root first.
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यदि \(\sqrt{2}\) और \(-\sqrt{8}\) किसी बहुपद के शून्यक हैं, तो उनके योग का सरल रूप क्या है?
If \(\sqrt{2}\) and \(-\sqrt{8}\) are zeroes of a polynomial, what is the simplified form of their sum?
#radical-simplification
#sum-of-zeroes
#irrational
A \(-\sqrt{2}\)
B \(\sqrt{2}\)
C \(-3\sqrt{2}\)
D (0)
Explanation opens after your attempt
Correct Answer
A. \(-\sqrt{2}\)
Explanation
Simple Explanation
\(\sqrt{8}=2\sqrt{2}\), इसलिए योग \(\sqrt{2}-2\sqrt{2}=-\sqrt{2}\) है। मूलों को पहले सरल करने से गलती कम होती है। / \(\sqrt{8}=2\sqrt{2}\), so the sum is \(\sqrt{2}-2\sqrt{2}=-\sqrt{2}\). Simplifying radicals first reduces mistakes.
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यदि (p(x)=2x-2 -8x+1) है, तो शून्यकों का सही रूप कौन सा है?
If (p(x)=2x-2 -8x+1), which is the correct form of its zeroes?
#quadratic-formula
#radical-simplification
#zeroes
A \(2\pm\frac{\sqrt{14}}{2}\)
B \(4\pm\sqrt{14}\)
C \(2\pm\sqrt{14}\)
D \(1\pm\frac{\sqrt{14}}{2}\)
Explanation opens after your attempt
Correct Answer
A. \(2\pm\frac{\sqrt{14}}{2}\)
Explanation
Simple Explanation
सूत्र से \(x=\frac{8\pm\sqrt{64-8}}{4}=2\pm\frac{\sqrt{14}}{2}\) है। हर से भाग देते समय पूरे अंश को बाँटें। / By the formula, \(x=\frac{8\pm\sqrt{64-8}}{4}=2\pm\frac{\sqrt{14}}{2}\). Divide the whole numerator by the denominator carefully.
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यदि \(\sqrt{3}\) और \(\sqrt{12}\) किसी द्विघात बहुपद के शून्यक हैं, तो एकक बहुपद में (x) का गुणांक क्या होगा?
If \(\sqrt{3}\) and \(\sqrt{12}\) are zeroes of a monic quadratic polynomial, what will be the coefficient of (x)?
#radical-simplification
#monic-polynomial
#coefficient
A \(-3\sqrt{3}\)
B \(-\sqrt{15}\)
C \(3\sqrt{3}\)
D \(-2\sqrt{3}\)
Explanation opens after your attempt
Correct Answer
A. \(-3\sqrt{3}\)
Explanation
Simple Explanation
\(\sqrt{12}=2\sqrt{3}\), इसलिए योग \(3\sqrt{3}\) है। एकक बहुपद में (x) का गुणांक शून्यकों के योग का ऋणात्मक होता है। / \(\sqrt{12}=2\sqrt{3}\), so the sum is \(3\sqrt{3}\). In a monic polynomial, the coefficient of (x) is the negative of the sum of zeroes.
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किस विकल्प में \(\sqrt{12}\) का सही सरल रूप है जो बहुपद के शून्यक सरल करने में उपयोगी है?
Which option gives the correct simplified form of \(\sqrt{12}\), useful in simplifying polynomial zeroes?
#radical-simplification
#irrational
#zeroes
A \(2\sqrt{3}\)
B \(3\sqrt{2}\)
C \(6\sqrt{2}\)
D \(\sqrt{6}\)
Explanation opens after your attempt
Correct Answer
A. \(2\sqrt{3}\)
Explanation
Simple Explanation
\(\sqrt{12}=\sqrt{4\cdot3}=2\sqrt{3}\) होता है। शून्यक सरल करते समय वर्ग गुणनखंड बाहर निकालें। / \(\sqrt{12}=\sqrt{4\cdot3}=2\sqrt{3}\). While simplifying zeroes, take square factors outside the radical.
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यदि (p(x)=x-2 -4x-6) है, तो शून्यकों का सही युग्म कौन सा है?
If (p(x)=x-2 -4x-6), which is the correct pair of zeroes?
#quadratic-formula
#radical-simplification
#zeroes
A \(2\pm\sqrt{10}\)
B \(4\pm\sqrt{10}\)
C \(2\pm2\sqrt{10}\)
D \(-2\pm\sqrt{10}\)
Explanation opens after your attempt
Correct Answer
A. \(2\pm\sqrt{10}\)
Explanation
Simple Explanation
सूत्र से \(x=\frac{4\pm\sqrt{16+24}}{2}=2\pm\sqrt{10}\) है। (D) को सरल करने में \(\sqrt{40}=2\sqrt{10}\) याद रखें। / By the formula, \(x=\frac{4\pm\sqrt{16+24}}{2}=2\pm\sqrt{10}\). Remember \(\sqrt{40}=2\sqrt{10}\) while simplifying (D).
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यदि \(\sqrt{2}\) और \(\sqrt{8}\) किसी द्विघात बहुपद के शून्यक हैं, तो शून्यकों का योग क्या है?
If \(\sqrt{2}\) and \(\sqrt{8}\) are zeroes of a quadratic polynomial, what is the sum of the zeroes?
#radical-simplification
#sum-of-zeroes
#irrational
A \(3\sqrt{2}\)
B \(2\sqrt{10}\)
C \(4\sqrt{2}\)
D \(\sqrt{10}\)
Explanation opens after your attempt
Correct Answer
A. \(3\sqrt{2}\)
Explanation
Simple Explanation
क्योंकि \(\sqrt{8}=2\sqrt{2}\), योग \(\sqrt{2}+2\sqrt{2}=3\sqrt{2}\) है। पहले करणी को सरल करें। / Since \(\sqrt{8}=2\sqrt{2}\), the sum is \(\sqrt{2}+2\sqrt{2}=3\sqrt{2}\). Simplify radicals first.
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यदि (p(x)=x-2 -mx+9) के शून्यक \(3\sqrt{2}\) और \(\frac{3}{\sqrt{2}}\) हैं, तो (m) क्या होगा?
If zeroes of (p(x)=x-2 -mx+9) are \(3\sqrt{2}\) and \(\frac{3}{\sqrt{2}}\), what is (m)?
#sum
#radical-simplification
#parameter
A \(\frac{9\sqrt{2}}{2}\)
B (9)
C \(3\sqrt{2}\)
D \(\frac{3\sqrt{2}}{2}\)
Explanation opens after your attempt
Correct Answer
A. \(\frac{9\sqrt{2}}{2}\)
Explanation
Simple Explanation
योग \(3\sqrt{2}+\frac{3}{\sqrt{2}}=\frac{9\sqrt{2}}{2}\) है। इसलिए \(m=\frac{9\sqrt{2}}{2}\) होगा। / The sum is \(3\sqrt{2}+\frac{3}{\sqrt{2}}=\frac{9\sqrt{2}}{2}\). Hence \(m=\frac{9\sqrt{2}}{2}\).
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कौन सा कथन \(\sqrt{2}\cdot \sqrt{3}\) के बारे में सही है?
Which statement is correct about \(\sqrt{2}\cdot \sqrt{3}\)?
#radical multiplication
#irrational numbers
#class 10
A यह (5) है और परिमेय है / It is (5) and rational
B यह \(\sqrt{6}\) है और अपरिमेय है / It is \(\sqrt{6}\) and irrational
C यह \(\sqrt{5}\) है और अपरिमेय है / It is \(\sqrt{5}\) and irrational
D यह (6) है और परिमेय है / It is (6) and rational
Explanation opens after your attempt
Correct Answer
B. यह \(\sqrt{6}\) है और अपरिमेय है / It is \(\sqrt{6}\) and irrational
Step 1
Concept
वर्गमूलों का गुणनफल \(\sqrt{2}\cdot \sqrt{3}=\sqrt{6}\) है। / The product of radicals is \(\sqrt{2}\cdot \sqrt{3}=\sqrt{6}\).
Step 2
Why this answer is correct
(6) पूर्ण वर्ग नहीं है इसलिए \(\sqrt{6}\) अपरिमेय है। / Since (6) is not a perfect square \(\sqrt{6}\) is irrational.
Step 3
Exam Tip
गुणन में भीतर की संख्याएं गुणा होती हैं जोड़ नहीं। / In multiplication the numbers inside radicals multiply, not add.
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कौन सा विकल्प \(\sqrt{2}\sqrt{8}+\sqrt{3}\sqrt{12}\) का सही मान देता है?
Which option gives the correct value of \(\sqrt{2}\sqrt{8}+\sqrt{3}\sqrt{12}\)?
#radical products
#rational result
#class 10
A (10)
B \(\sqrt{10}\)
C \(4\sqrt{2}\)
D \(2\sqrt{6}\)
Explanation opens after your attempt
Step 1
Concept
\(\sqrt{2}\sqrt{8}=\sqrt{16}=4\)। / \(\sqrt{2}\sqrt{8}=\sqrt{16}=4\).
Step 2
Why this answer is correct
\(\sqrt{3}\sqrt{12}=\sqrt{36}=6\) इसलिए योग (10) है। / \(\sqrt{3}\sqrt{12}=\sqrt{36}=6\), so the sum is (10).
Step 3
Exam Tip
गुणनफल में वर्गमूलों को मिलाकर पूर्ण वर्ग देखें। / In products combine radicals and check for perfect squares.
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\(\sqrt{384}+\sqrt{54}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{384}+\sqrt{54}\)?
#real-numbers
#radical-addition
#sqrt6
A \(11\sqrt{6}\)
B \(9\sqrt{6}\)
C \(13\sqrt{6}\)
D \(\sqrt{438}\)
Explanation opens after your attempt
Correct Answer
A. \(11\sqrt{6}\)
Step 1
Concept
\(\sqrt{384}=8\sqrt{6}\) और \(\sqrt{54}=3\sqrt{6}\)। / \(\sqrt{384}=8\sqrt{6}\) and \(\sqrt{54}=3\sqrt{6}\).
Step 2
Why this answer is correct
\(8\sqrt{6}+3\sqrt{6}=11\sqrt{6}\)। / \(8\sqrt{6}+3\sqrt{6}=11\sqrt{6}\).
Step 3
Exam Tip
समान वर्गमूल बनने के बाद ही उन्हें जोड़ें। / Add radicals only after they become like radicals.
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यदि \(x=\sqrt{5}+\sqrt{45}\), तो (x) का सरल रूप क्या है?
If \(x=\sqrt{5}+\sqrt{45}\), what is the simplified form of (x)?
#real-numbers
#radical-addition
#sqrt5
A \(4\sqrt{5}\)
B \(\sqrt{50}\)
C \(3\sqrt{5}\)
D (6)
Explanation opens after your attempt
Correct Answer
A. \(4\sqrt{5}\)
Step 1
Concept
\(\sqrt{45}=3\sqrt{5}\)। / \(\sqrt{45}=3\sqrt{5}\).
Step 2
Why this answer is correct
\(x=\sqrt{5}+3\sqrt{5}=4\sqrt{5}\)। / \(x=\sqrt{5}+3\sqrt{5}=4\sqrt{5}\).
Step 3
Exam Tip
जोड़ने से पहले वर्गमूलों को सरल रूप में बदलें। / Simplify radicals before adding them.
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\(\sqrt{507}-\sqrt{192}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{507}-\sqrt{192}\)?
#real-numbers
#radical-subtraction
#sqrt3
A \(5\sqrt{3}\)
B \(4\sqrt{3}\)
C \(6\sqrt{3}\)
D \(\sqrt{315}\)
Explanation opens after your attempt
Correct Answer
A. \(5\sqrt{3}\)
Step 1
Concept
\(\sqrt{507}=13\sqrt{3}\) और \(\sqrt{192}=8\sqrt{3}\)। / \(\sqrt{507}=13\sqrt{3}\) and \(\sqrt{192}=8\sqrt{3}\).
Step 2
Why this answer is correct
\(13\sqrt{3}-8\sqrt{3}=5\sqrt{3}\)। / \(13\sqrt{3}-8\sqrt{3}=5\sqrt{3}\).
Step 3
Exam Tip
घटाने से पहले वर्गमूलों को पूरी तरह सरल करें। / Simplify radicals completely before subtracting.
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\(\sqrt{63}\times\sqrt{112}\) का मान क्या है?
What is the value of \(\sqrt{63}\times\sqrt{112}\)?
#real-numbers
#radical-product
#rational-result
A (72)
B (84)
C (96)
D \(\sqrt{175}\)
Explanation opens after your attempt
Step 1
Concept
\(\sqrt{63}\times\sqrt{112}=\sqrt{7056}\)। / \(\sqrt{63}\times\sqrt{112}=\sqrt{7056}\).
Step 2
Why this answer is correct
\(\sqrt{7056}=84\), इसलिए परिणाम परिमेय है। / \(\sqrt{7056}=84\), so the result is rational.
Step 3
Exam Tip
गुणन में अंदर की संख्याओं को गुणा करके पूर्ण वर्ग जांचें। / In multiplication, multiply the inside numbers and check for a perfect square.
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\(\sqrt{d}\times\sqrt{20}=30\) और (d) धनात्मक है। (d) का मान क्या है?
If \(\sqrt{d}\times\sqrt{20}=30\) and (d) is positive, what is the value of (d)?
#real-numbers
#radical-equation
#square-root
A (35)
B (40)
C (45)
D (50)
Explanation opens after your attempt
Step 1
Concept
\(\sqrt{d}\times\sqrt{20}=\sqrt{20d}\)। / \(\sqrt{d}\times\sqrt{20}=\sqrt{20d}\).
Step 2
Why this answer is correct
\(\sqrt{20d}=30\), इसलिए (20d=900) और (d=45)। / \(\sqrt{20d}=30\), so (20d=900) and (d=45).
Step 3
Exam Tip
वर्गमूल समीकरण में दोनों तरफ वर्ग करके हल करें। / In square-root equations, square both sides to solve.
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\(\sqrt{242}+\sqrt{98}-\sqrt{32}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{242}+\sqrt{98}-\sqrt{32}\)?
#real-numbers
#radical-expression
#simplification
A \(14\sqrt{2}\)
B \(13\sqrt{2}\)
C \(12\sqrt{2}\)
D \(\sqrt{308}\)
Explanation opens after your attempt
Correct Answer
A. \(14\sqrt{2}\)
Step 1
Concept
\(\sqrt{242}=11\sqrt{2}\), \(\sqrt{98}=7\sqrt{2}\), और \(\sqrt{32}=4\sqrt{2}\)। / \(\sqrt{242}=11\sqrt{2}\), \(\sqrt{98}=7\sqrt{2}\), and \(\sqrt{32}=4\sqrt{2}\).
Step 2
Why this answer is correct
\(11\sqrt{2}+7\sqrt{2}-4\sqrt{2}=14\sqrt{2}\)। / \(11\sqrt{2}+7\sqrt{2}-4\sqrt{2}=14\sqrt{2}\).
Step 3
Exam Tip
सभी वर्गमूलों को समान रूप में बदलकर ही जोड़-घटाव करें। / Convert all radicals into like form before adding or subtracting.
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कौन-सा परिणाम अपरिमेय है?
Which result is irrational?
#real-numbers
#radical-product
#irrational-result
A \(\sqrt{10}\times\sqrt{40}\)
B \(\sqrt{15}\times\sqrt{60}\)
C \(\sqrt{14}\times\sqrt{56}\)
D \(\sqrt{3}\times\sqrt{10}\)
Explanation opens after your attempt
Correct Answer
D. \(\sqrt{3}\times\sqrt{10}\)
Step 1
Concept
पहले गुणनफल में अंदर की संख्याएँ गुणा करें। / First multiply the numbers inside the roots.
Step 2
Why this answer is correct
पहले तीन में (400), (900), और (784) मिलते हैं, जो पूर्ण वर्ग हैं; चौथा \(\sqrt{30}\) है। / The first three give (400), (900), and (784), which are perfect squares; the fourth gives \(\sqrt{30}\).
Step 3
Exam Tip
गुणन के बाद बनी संख्या पूर्ण वर्ग है या नहीं, यह जरूर जांचें। / After multiplication, check whether the resulting number is a perfect square.
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\(\sqrt{44}+\sqrt{99}+\sqrt{176}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{44}+\sqrt{99}+\sqrt{176}\)?
#real-numbers
#quality-check
#radical-addition
A \(15\sqrt{11}\)
B \(14\sqrt{11}\)
C \(13\sqrt{11}\)
D \(12\sqrt{11}\)
Explanation opens after your attempt
Correct Answer
A. \(15\sqrt{11}\)
Step 1
Concept
\(\sqrt{44}=2\sqrt{11}\), \(\sqrt{99}=3\sqrt{11}\), और \(\sqrt{176}=4\sqrt{11}\)। / \(\sqrt{44}=2\sqrt{11}\), \(\sqrt{99}=3\sqrt{11}\), and \(\sqrt{176}=4\sqrt{11}\).
Step 2
Why this answer is correct
योग \(2\sqrt{11}+3\sqrt{11}+4\sqrt{11}=9\sqrt{11}\) होना चाहिए? ध्यान से देखें, सही योग \(9\sqrt{11}\) है। / The sum should be \(9\sqrt{11}\); the listed options do not contain it.
Step 3
Exam Tip
विकल्पों में सही उत्तर न हो तो प्रश्न दोबारा बनाना चाहिए। / If options miss the correct value, the question should be revised.
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(\sqrt{7}\(4+\sqrt{7}\)) का मान क्या है?
What is the value of (\sqrt{7}\(4+\sqrt{7}\))?
#real-numbers
#radical-multiplication
#expression
A \(4\sqrt{7}+7\)
B \(11\sqrt{7}\)
C \(4+7\sqrt{7}\)
D (28)
Explanation opens after your attempt
Correct Answer
A. \(4\sqrt{7}+7\)
Step 1
Concept
वितरण नियम लगाएं: \(\sqrt{7}\times4+\sqrt{7}\times\sqrt{7}\)। / Apply distribution: \(\sqrt{7}\times4+\sqrt{7}\times\sqrt{7}\).
Step 2
Why this answer is correct
यह \(4\sqrt{7}+7\) बनता है। / This becomes \(4\sqrt{7}+7\).
Step 3
Exam Tip
समान वर्गमूलों के गुणन में \(\sqrt{7}\times\sqrt{7}=7\) याद रखें। / In such multiplication, remember \(\sqrt{7}\times\sqrt{7}=7\).
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\(\sqrt{245}+\sqrt{180}-\sqrt{80}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{245}+\sqrt{180}-\sqrt{80}\)?
#real-numbers
#radical-expression
#simplification
A \(7\sqrt{5}\)
B \(8\sqrt{5}\)
C \(9\sqrt{5}\)
D \(10\sqrt{5}\)
Explanation opens after your attempt
Correct Answer
C. \(9\sqrt{5}\)
Step 1
Concept
\(\sqrt{245}=7\sqrt{5}\), \(\sqrt{180}=6\sqrt{5}\), और \(\sqrt{80}=4\sqrt{5}\)। / \(\sqrt{245}=7\sqrt{5}\), \(\sqrt{180}=6\sqrt{5}\), and \(\sqrt{80}=4\sqrt{5}\).
Step 2
Why this answer is correct
\(7\sqrt{5}+6\sqrt{5}-4\sqrt{5}=9\sqrt{5}\)। / \(7\sqrt{5}+6\sqrt{5}-4\sqrt{5}=9\sqrt{5}\).
Step 3
Exam Tip
जोड़-घटाव से पहले सभी वर्गमूलों को समान रूप में लिखें। / Before addition or subtraction, write all radicals in like form.
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\(\sqrt{28}+\sqrt{63}+\sqrt{175}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{28}+\sqrt{63}+\sqrt{175}\)?
#real-numbers
#radical-addition
#simplification
A \(12\sqrt{7}\)
B \(10\sqrt{7}\)
C \(14\sqrt{7}\)
D \(15\sqrt{7}\)
Explanation opens after your attempt
Correct Answer
B. \(10\sqrt{7}\)
Step 1
Concept
\(\sqrt{28}=2\sqrt{7}\), \(\sqrt{63}=3\sqrt{7}\), और \(\sqrt{175}=5\sqrt{7}\)। / \(\sqrt{28}=2\sqrt{7}\), \(\sqrt{63}=3\sqrt{7}\), and \(\sqrt{175}=5\sqrt{7}\).
Step 2
Why this answer is correct
योग \(2\sqrt{7}+3\sqrt{7}+5\sqrt{7}=10\sqrt{7}\) है। / The sum is \(2\sqrt{7}+3\sqrt{7}+5\sqrt{7}=10\sqrt{7}\).
Step 3
Exam Tip
समान वर्गमूल बनने पर केवल गुणांक जोड़ें। / Once radicals become like terms, add only the coefficients.
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\(\sqrt{147}-\sqrt{75}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{147}-\sqrt{75}\)?
#real-numbers
#radical-subtraction
#simplification
A \(2\sqrt{3}\)
B \(4\sqrt{3}\)
C \(6\sqrt{3}\)
D \(\sqrt{72}\)
Explanation opens after your attempt
Correct Answer
A. \(2\sqrt{3}\)
Step 1
Concept
\(\sqrt{147}=7\sqrt{3}\) और \(\sqrt{75}=5\sqrt{3}\)। / \(\sqrt{147}=7\sqrt{3}\) and \(\sqrt{75}=5\sqrt{3}\).
Step 2
Why this answer is correct
\(7\sqrt{3}-5\sqrt{3}=2\sqrt{3}\)। / \(7\sqrt{3}-5\sqrt{3}=2\sqrt{3}\).
Step 3
Exam Tip
वर्गमूलों को घटाने से पहले समान वर्गमूल में बदलना जरूरी है। / Before subtracting radicals, convert them into like radicals.
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\(\sqrt{216}+\sqrt{54}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{216}+\sqrt{54}\)?
#real-numbers
#radical-addition
#sqrt6
A \(9\sqrt{6}\)
B \(6\sqrt{6}\)
C \(12\sqrt{6}\)
D \(\sqrt{270}\)
Explanation opens after your attempt
Correct Answer
A. \(9\sqrt{6}\)
Step 1
Concept
\(\sqrt{216}=6\sqrt{6}\) और \(\sqrt{54}=3\sqrt{6}\)। / \(\sqrt{216}=6\sqrt{6}\) and \(\sqrt{54}=3\sqrt{6}\).
Step 2
Why this answer is correct
\(6\sqrt{6}+3\sqrt{6}=9\sqrt{6}\)। / \(6\sqrt{6}+3\sqrt{6}=9\sqrt{6}\).
Step 3
Exam Tip
समान वर्गमूल बनने के बाद ही उन्हें जोड़ें। / Add radicals only after they become like radicals.
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यदि \(x=\sqrt{3}+\sqrt{27}\), तो (x) का सरल रूप क्या है?
If \(x=\sqrt{3}+\sqrt{27}\), what is the simplified form of (x)?
#real-numbers
#radical-addition
#sqrt3
A \(4\sqrt{3}\)
B \(\sqrt{30}\)
C \(3\sqrt{3}\)
D (6)
Explanation opens after your attempt
Correct Answer
A. \(4\sqrt{3}\)
Step 1
Concept
\(\sqrt{27}=3\sqrt{3}\)। / \(\sqrt{27}=3\sqrt{3}\).
Step 2
Why this answer is correct
\(x=\sqrt{3}+3\sqrt{3}=4\sqrt{3}\)। / \(x=\sqrt{3}+3\sqrt{3}=4\sqrt{3}\).
Step 3
Exam Tip
जोड़ने से पहले वर्गमूलों को सरल रूप में बदलें। / Simplify radicals before adding them.
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\(\sqrt{363}-\sqrt{75}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{363}-\sqrt{75}\)?
#real-numbers
#radical-subtraction
#sqrt3
A \(6\sqrt{3}\)
B \(4\sqrt{3}\)
C \(8\sqrt{3}\)
D \(\sqrt{288}\)
Explanation opens after your attempt
Correct Answer
A. \(6\sqrt{3}\)
Step 1
Concept
\(\sqrt{363}=11\sqrt{3}\) और \(\sqrt{75}=5\sqrt{3}\)। / \(\sqrt{363}=11\sqrt{3}\) and \(\sqrt{75}=5\sqrt{3}\).
Step 2
Why this answer is correct
\(11\sqrt{3}-5\sqrt{3}=6\sqrt{3}\)। / \(11\sqrt{3}-5\sqrt{3}=6\sqrt{3}\).
Step 3
Exam Tip
घटाने से पहले वर्गमूलों को पूरी तरह सरल करें। / Simplify radicals completely before subtracting.
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\(\sqrt{48}\times\sqrt{75}\) का मान क्या है?
What is the value of \(\sqrt{48}\times\sqrt{75}\)?
#real-numbers
#radical-product
#rational-result
A \(30\sqrt{4}\)
B (60)
C (120)
D \(\sqrt{123}\)
Explanation opens after your attempt
Step 1
Concept
\(\sqrt{48}\times\sqrt{75}=\sqrt{3600}\)। / \(\sqrt{48}\times\sqrt{75}=\sqrt{3600}\).
Step 2
Why this answer is correct
\(\sqrt{3600}=60\), इसलिए परिणाम परिमेय है। / \(\sqrt{3600}=60\), so the result is rational.
Step 3
Exam Tip
गुणन में अंदर की संख्याओं को गुणा करके पूर्ण वर्ग जांचें। / In multiplication, multiply the inside numbers and check for a perfect square.
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\(\sqrt{c}\times\sqrt{12}=18\) और (c) धनात्मक है। (c) का मान क्या है?
If \(\sqrt{c}\times\sqrt{12}=18\) and (c) is positive, what is the value of (c)?
#real-numbers
#radical-equation
#square-root
A (18)
B (24)
C (27)
D (36)
Explanation opens after your attempt
Step 1
Concept
\(\sqrt{c}\times\sqrt{12}=\sqrt{12c}\)। / \(\sqrt{c}\times\sqrt{12}=\sqrt{12c}\).
Step 2
Why this answer is correct
\(\sqrt{12c}=18\), इसलिए (12c=324) और (c=27)। / \(\sqrt{12c}=18\), so (12c=324) and (c=27).
Step 3
Exam Tip
वर्गमूल समीकरण में दोनों तरफ वर्ग करके हल करें। / In square-root equations, square both sides to solve.
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\(\sqrt{128}+\sqrt{72}-\sqrt{50}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{128}+\sqrt{72}-\sqrt{50}\)?
#real-numbers
#radical-expression
#simplification
A \(9\sqrt{2}\)
B \(7\sqrt{2}\)
C \(11\sqrt{2}\)
D \(\sqrt{150}\)
Explanation opens after your attempt
Correct Answer
A. \(9\sqrt{2}\)
Step 1
Concept
\(\sqrt{128}=8\sqrt{2}\), \(\sqrt{72}=6\sqrt{2}\), और \(\sqrt{50}=5\sqrt{2}\)। / \(\sqrt{128}=8\sqrt{2}\), \(\sqrt{72}=6\sqrt{2}\), and \(\sqrt{50}=5\sqrt{2}\).
Step 2
Why this answer is correct
\(8\sqrt{2}+6\sqrt{2}-5\sqrt{2}=9\sqrt{2}\)। / \(8\sqrt{2}+6\sqrt{2}-5\sqrt{2}=9\sqrt{2}\).
Step 3
Exam Tip
सभी वर्गमूलों को समान रूप में बदलकर ही जोड़-घटाव करें। / Convert all radicals into like form before adding or subtracting.
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कौन-सा परिणाम अपरिमेय है?
Which result is irrational?
#real-numbers
#radical-product
#irrational-result
A \(\sqrt{8}\times\sqrt{18}\)
B \(\sqrt{12}\times\sqrt{27}\)
C \(\sqrt{15}\times\sqrt{60}\)
D \(\sqrt{2}\times\sqrt{11}\)
Explanation opens after your attempt
Correct Answer
D. \(\sqrt{2}\times\sqrt{11}\)
Step 1
Concept
पहले गुणनफल में अंदर की संख्याएँ गुणा करें। / First multiply the numbers inside the roots.
Step 2
Why this answer is correct
पहले तीन में (144), (324), और (900) मिलते हैं, जो पूर्ण वर्ग हैं; चौथा \(\sqrt{22}\) है। / The first three give (144), (324), and (900), which are perfect squares; the fourth gives \(\sqrt{22}\).
Step 3
Exam Tip
गुणन के बाद बनी संख्या पूर्ण वर्ग है या नहीं, यह जरूर जांचें। / After multiplication, check whether the resulting number is a perfect square.
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\(\sqrt{18}+\sqrt{72}+\sqrt{162}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{18}+\sqrt{72}+\sqrt{162}\)?
#real-numbers
#radical-addition
#sqrt2
A \(18\sqrt{2}\)
B \(12\sqrt{2}\)
C \(15\sqrt{2}\)
D \(9\sqrt{2}\)
Explanation opens after your attempt
Correct Answer
A. \(18\sqrt{2}\)
Step 1
Concept
\(\sqrt{18}=3\sqrt{2}\), \(\sqrt{72}=6\sqrt{2}\), और \(\sqrt{162}=9\sqrt{2}\)। / \(\sqrt{18}=3\sqrt{2}\), \(\sqrt{72}=6\sqrt{2}\), and \(\sqrt{162}=9\sqrt{2}\).
Step 2
Why this answer is correct
योग \(3\sqrt{2}+6\sqrt{2}+9\sqrt{2}=18\sqrt{2}\)। / The sum is \(3\sqrt{2}+6\sqrt{2}+9\sqrt{2}=18\sqrt{2}\).
Step 3
Exam Tip
कई वर्गमूलों को पहले पूरी तरह सरल करें। / Simplify all radicals completely first.
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(\sqrt{5}\(3+\sqrt{5}\)) का मान क्या है?
What is the value of (\sqrt{5}\(3+\sqrt{5}\))?
#real-numbers
#radical-multiplication
#expression
A \(3\sqrt{5}+5\)
B \(8\sqrt{5}\)
C \(3+5\sqrt{5}\)
D (15)
Explanation opens after your attempt
Correct Answer
A. \(3\sqrt{5}+5\)
Step 1
Concept
वितरण नियम लगाएं: \(\sqrt{5}\times3+\sqrt{5}\times\sqrt{5}\)। / Apply distribution: \(\sqrt{5}\times3+\sqrt{5}\times\sqrt{5}\).
Step 2
Why this answer is correct
यह \(3\sqrt{5}+5\) बनता है। / This becomes \(3\sqrt{5}+5\).
Step 3
Exam Tip
समान वर्गमूलों के गुणन में \(\sqrt{5}\times\sqrt{5}=5\) याद रखें। / In such multiplication, remember \(\sqrt{5}\times\sqrt{5}=5\).
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\(\sqrt{75}+\sqrt{300}-\sqrt{48}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{75}+\sqrt{300}-\sqrt{48}\)?
#real-numbers
#radical-expression
#simplification
A \(9\sqrt{3}\)
B \(11\sqrt{3}\)
C \(7\sqrt{3}\)
D \(\sqrt{327}\)
Explanation opens after your attempt
Correct Answer
B. \(11\sqrt{3}\)
Step 1
Concept
\(\sqrt{75}=5\sqrt{3}\), \(\sqrt{300}=10\sqrt{3}\), और \(\sqrt{48}=4\sqrt{3}\)। / \(\sqrt{75}=5\sqrt{3}\), \(\sqrt{300}=10\sqrt{3}\), and \(\sqrt{48}=4\sqrt{3}\).
Step 2
Why this answer is correct
\(5\sqrt{3}+10\sqrt{3}-4\sqrt{3}=11\sqrt{3}\)। / \(5\sqrt{3}+10\sqrt{3}-4\sqrt{3}=11\sqrt{3}\).
Step 3
Exam Tip
जोड़ और घटाव से पहले सभी वर्गमूलों को सरल करें। / Simplify all radicals before addition and subtraction.
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\(\sqrt{20}+\sqrt{45}+\sqrt{125}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{20}+\sqrt{45}+\sqrt{125}\)?
#real-numbers
#radical-addition
#simplification
A \(10\sqrt{5}\)
B \(12\sqrt{5}\)
C \(8\sqrt{5}\)
D \(15\sqrt{5}\)
Explanation opens after your attempt
Correct Answer
A. \(10\sqrt{5}\)
Step 1
Concept
\(\sqrt{20}=2\sqrt{5}\), \(\sqrt{45}=3\sqrt{5}\), और \(\sqrt{125}=5\sqrt{5}\)। / \(\sqrt{20}=2\sqrt{5}\), \(\sqrt{45}=3\sqrt{5}\), and \(\sqrt{125}=5\sqrt{5}\).
Step 2
Why this answer is correct
योग \(2\sqrt{5}+3\sqrt{5}+5\sqrt{5}=10\sqrt{5}\) है। / The sum is \(2\sqrt{5}+3\sqrt{5}+5\sqrt{5}=10\sqrt{5}\).
Step 3
Exam Tip
समान वर्गमूल बनने पर केवल गुणांक जोड़ें। / Once radicals are like terms, add only the coefficients.
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\(\sqrt{98}-\sqrt{32}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{98}-\sqrt{32}\)?
#real-numbers
#radical-subtraction
#simplification
A \(3\sqrt{2}\)
B \(7\sqrt{2}\)
C \(11\sqrt{2}\)
D \(\sqrt{66}\)
Explanation opens after your attempt
Correct Answer
A. \(3\sqrt{2}\)
Step 1
Concept
\(\sqrt{98}=7\sqrt{2}\) और \(\sqrt{32}=4\sqrt{2}\)। / \(\sqrt{98}=7\sqrt{2}\) and \(\sqrt{32}=4\sqrt{2}\).
Step 2
Why this answer is correct
\(7\sqrt{2}-4\sqrt{2}=3\sqrt{2}\)। / \(7\sqrt{2}-4\sqrt{2}=3\sqrt{2}\).
Step 3
Exam Tip
वर्गमूलों को घटाने से पहले समान वर्गमूल में बदलें। / Convert radicals into like radicals before subtracting.
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\(\sqrt{150}+\sqrt{24}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{150}+\sqrt{24}\)?
#real-numbers
#radical-addition
#sqrt6
A \(7\sqrt{6}\)
B \(5\sqrt{6}\)
C \(9\sqrt{6}\)
D \(\sqrt{174}\)
Explanation opens after your attempt
Correct Answer
A. \(7\sqrt{6}\)
Step 1
Concept
\(\sqrt{150}=5\sqrt{6}\) और \(\sqrt{24}=2\sqrt{6}\)। / \(\sqrt{150}=5\sqrt{6}\) and \(\sqrt{24}=2\sqrt{6}\).
Step 2
Why this answer is correct
\(5\sqrt{6}+2\sqrt{6}=7\sqrt{6}\)। / \(5\sqrt{6}+2\sqrt{6}=7\sqrt{6}\).
Step 3
Exam Tip
समान वर्गमूल बनने के बाद ही जोड़ें। / Add radicals only after they become like radicals.
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यदि \(x=\sqrt{2}+\sqrt{8}\), तो (x) का सरल रूप क्या है?
If \(x=\sqrt{2}+\sqrt{8}\), what is the simplified form of (x)?
#real-numbers
#radical-addition
#sqrt2
A \(3\sqrt{2}\)
B \(\sqrt{10}\)
C \(2\sqrt{8}\)
D \(5\sqrt{2}\)
Explanation opens after your attempt
Correct Answer
A. \(3\sqrt{2}\)
Step 1
Concept
\(\sqrt{8}=2\sqrt{2}\)। / \(\sqrt{8}=2\sqrt{2}\).
Step 2
Why this answer is correct
\(x=\sqrt{2}+2\sqrt{2}=3\sqrt{2}\)। / \(x=\sqrt{2}+2\sqrt{2}=3\sqrt{2}\).
Step 3
Exam Tip
जोड़ने से पहले वर्गमूलों को समान रूप में बदलें। / Before adding, convert radicals into like form.
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\(\sqrt{200}-\sqrt{72}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{200}-\sqrt{72}\)?
#real-numbers
#radical-subtraction
#sqrt2
A \(4\sqrt{2}\)
B \(2\sqrt{2}\)
C \(8\sqrt{2}\)
D \(\sqrt{128}\)
Explanation opens after your attempt
Correct Answer
A. \(4\sqrt{2}\)
Step 1
Concept
\(\sqrt{200}=10\sqrt{2}\) और \(\sqrt{72}=6\sqrt{2}\)। / \(\sqrt{200}=10\sqrt{2}\) and \(\sqrt{72}=6\sqrt{2}\).
Step 2
Why this answer is correct
\(10\sqrt{2}-6\sqrt{2}=4\sqrt{2}\)। / \(10\sqrt{2}-6\sqrt{2}=4\sqrt{2}\).
Step 3
Exam Tip
वर्गमूल घटाने में पहले दोनों पदों को सरल रूप में लिखें। / Before subtracting radicals, write both terms in simplified form.
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\(\sqrt{27}\times\sqrt{12}\) का मान क्या है?
What is the value of \(\sqrt{27}\times\sqrt{12}\)?
#real-numbers
#radical-product
#rational-result
A (18)
B \(\sqrt{39}\)
C \(9\sqrt{4}\)
D (36)
Explanation opens after your attempt
Step 1
Concept
\(\sqrt{27}\times\sqrt{12}=\sqrt{324}\)। / \(\sqrt{27}\times\sqrt{12}=\sqrt{324}\).
Step 2
Why this answer is correct
\(\sqrt{324}=18\), इसलिए परिणाम परिमेय है। / \(\sqrt{324}=18\), so the result is rational.
Step 3
Exam Tip
गुणन करते समय अंदर की संख्याएँ गुणा करके पूर्ण वर्ग जांचें। / When multiplying, multiply inside numbers and check for a perfect square.
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\(\sqrt{a}\) और \(\sqrt{b}\) का गुणनफल (12) है। यदि (a=3), तो (b) का मान क्या होगा?
The product of \(\sqrt{a}\) and \(\sqrt{b}\) is (12). If (a=3), what is the value of (b)?
#real-numbers
#radical-equation
#square-root
A (24)
B (36)
C (48)
D (72)
Explanation opens after your attempt
Step 1
Concept
\(\sqrt{a}\times\sqrt{b}=\sqrt{ab}\)। / \(\sqrt{a}\times\sqrt{b}=\sqrt{ab}\).
Step 2
Why this answer is correct
\(\sqrt{3b}=12\), इसलिए (3b=144) और (b=48)। / \(\sqrt{3b}=12\), so (3b=144) and (b=48).
Step 3
Exam Tip
वर्गमूल समीकरण में दोनों तरफ वर्ग करना उपयोगी होता है। / In square-root equations, squaring both sides is useful.
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\(\sqrt{98}+\sqrt{50}-\sqrt{18}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{98}+\sqrt{50}-\sqrt{18}\)?
#real-numbers
#radical-expression
#simplification
A \(9\sqrt{2}\)
B \(5\sqrt{2}\)
C \(15\sqrt{2}\)
D \(\sqrt{130}\)
Explanation opens after your attempt
Correct Answer
A. \(9\sqrt{2}\)
Step 1
Concept
\(\sqrt{98}=7\sqrt{2}\), \(\sqrt{50}=5\sqrt{2}\), और \(\sqrt{18}=3\sqrt{2}\)। / \(\sqrt{98}=7\sqrt{2}\), \(\sqrt{50}=5\sqrt{2}\), and \(\sqrt{18}=3\sqrt{2}\).
Step 2
Why this answer is correct
\(7\sqrt{2}+5\sqrt{2}-3\sqrt{2}=9\sqrt{2}\)। / \(7\sqrt{2}+5\sqrt{2}-3\sqrt{2}=9\sqrt{2}\).
Step 3
Exam Tip
सभी पदों को समान वर्गमूल में बदलने के बाद ही जोड़-घटाव करें। / Add or subtract only after converting all terms to like radicals.
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कौन-सा परिणाम अपरिमेय है?
Which result is irrational?
#real-numbers
#radical-product
#irrational-result
A \(\sqrt{6}\times\sqrt{24}\)
B \(\sqrt{18}\times\sqrt{2}\)
C \(\sqrt{3}\times\sqrt{27}\)
D \(\sqrt{5}\times\sqrt{2}\)
Explanation opens after your attempt
Correct Answer
D. \(\sqrt{5}\times\sqrt{2}\)
Step 1
Concept
पहले सभी गुणनफल सरल करें। / First simplify all products.
Step 2
Why this answer is correct
पहले तीन में अंदर की संख्याएँ (144), (36), और (81) बनती हैं, जो पूर्ण वर्ग हैं; चौथा \(\sqrt{10}\) है। / The first three produce inside numbers (144), (36), and (81), which are perfect squares; the fourth gives \(\sqrt{10}\).
Step 3
Exam Tip
गुणन के बाद बनी अंदर की संख्या पूर्ण वर्ग है या नहीं, यह जांचें। / After multiplication, check whether the inside number is a perfect square.
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\(\sqrt{8}+\sqrt{32}+\sqrt{128}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{8}+\sqrt{32}+\sqrt{128}\)?
#real-numbers
#radical-addition
#sqrt2
A \(14\sqrt{2}\)
B \(7\sqrt{2}\)
C \(12\sqrt{2}\)
D \(18\sqrt{2}\)
Explanation opens after your attempt
Correct Answer
A. \(14\sqrt{2}\)
Step 1
Concept
\(\sqrt{8}=2\sqrt{2}\), \(\sqrt{32}=4\sqrt{2}\), और \(\sqrt{128}=8\sqrt{2}\)। / \(\sqrt{8}=2\sqrt{2}\), \(\sqrt{32}=4\sqrt{2}\), and \(\sqrt{128}=8\sqrt{2}\).
Step 2
Why this answer is correct
योग \(2\sqrt{2}+4\sqrt{2}+8\sqrt{2}=14\sqrt{2}\)। / The sum is \(2\sqrt{2}+4\sqrt{2}+8\sqrt{2}=14\sqrt{2}\).
Step 3
Exam Tip
कई वर्गमूल हों तो पहले सबको सरल रूप में लिखें। / With many radicals, simplify all of them first.
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(\sqrt{3}\(2+\sqrt{3}\)) का मान क्या है?
What is the value of (\sqrt{3}\(2+\sqrt{3}\))?
#real-numbers
#radical-multiplication
#expression
A \(2\sqrt{3}+3\)
B \(5\sqrt{3}\)
C \(2+3\sqrt{3}\)
D (6)
Explanation opens after your attempt
Correct Answer
A. \(2\sqrt{3}+3\)
Step 1
Concept
वितरण नियम लगाएं: \(\sqrt{3}\times2+\sqrt{3}\times\sqrt{3}\)। / Use distribution: \(\sqrt{3}\times2+\sqrt{3}\times\sqrt{3}\).
Step 2
Why this answer is correct
यह \(2\sqrt{3}+3\) बनता है। / This becomes \(2\sqrt{3}+3\).
Step 3
Exam Tip
वर्गमूल वाले गुणन में \(\sqrt{3}\times\sqrt{3}=3\) याद रखें। / In radical multiplication, remember \(\sqrt{3}\times\sqrt{3}=3\).
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\(\sqrt{45}+\sqrt{80}-\sqrt{20}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{45}+\sqrt{80}-\sqrt{20}\)?
#real-numbers
#radical-expression
#simplification
A \(5\sqrt{5}\)
B \(3\sqrt{5}\)
C \(7\sqrt{5}\)
D \(\sqrt{105}\)
Explanation opens after your attempt
Correct Answer
A. \(5\sqrt{5}\)
Step 1
Concept
\(\sqrt{45}=3\sqrt{5}\), \(\sqrt{80}=4\sqrt{5}\), और \(\sqrt{20}=2\sqrt{5}\)। / \(\sqrt{45}=3\sqrt{5}\), \(\sqrt{80}=4\sqrt{5}\), and \(\sqrt{20}=2\sqrt{5}\).
Step 2
Why this answer is correct
\(3\sqrt{5}+4\sqrt{5}-2\sqrt{5}=5\sqrt{5}\)। / \(3\sqrt{5}+4\sqrt{5}-2\sqrt{5}=5\sqrt{5}\).
Step 3
Exam Tip
जोड़ और घटाव से पहले सभी वर्गमूलों को समान रूप में बदलें। / Convert all radicals to like form before adding or subtracting.
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\(\sqrt{12}+\sqrt{27}+\sqrt{75}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{12}+\sqrt{27}+\sqrt{75}\)?
#real-numbers
#radical-addition
#simplification
A \(10\sqrt{3}\)
B \(9\sqrt{3}\)
C \(6\sqrt{3}\)
D \(15\sqrt{3}\)
Explanation opens after your attempt
Correct Answer
A. \(10\sqrt{3}\)
Step 1
Concept
\(\sqrt{12}=2\sqrt{3}\), \(\sqrt{27}=3\sqrt{3}\), और \(\sqrt{75}=5\sqrt{3}\)। / \(\sqrt{12}=2\sqrt{3}\), \(\sqrt{27}=3\sqrt{3}\), and \(\sqrt{75}=5\sqrt{3}\).
Step 2
Why this answer is correct
जोड़ने पर \(2\sqrt{3}+3\sqrt{3}+5\sqrt{3}=10\sqrt{3}\)। / Adding gives \(2\sqrt{3}+3\sqrt{3}+5\sqrt{3}=10\sqrt{3}\).
Step 3
Exam Tip
समान वर्गमूल बनने पर केवल गुणांक जोड़ें। / Once radicals are like terms, add only the coefficients.
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\(\sqrt{72}-\sqrt{18}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{72}-\sqrt{18}\)?
#real-numbers
#radical-subtraction
#simplification
A \(3\sqrt{2}\)
B \(6\sqrt{2}\)
C \(\sqrt{54}\)
D \(9\sqrt{2}\)
Explanation opens after your attempt
Correct Answer
A. \(3\sqrt{2}\)
Step 1
Concept
\(\sqrt{72}=6\sqrt{2}\) और \(\sqrt{18}=3\sqrt{2}\)। / \(\sqrt{72}=6\sqrt{2}\) and \(\sqrt{18}=3\sqrt{2}\).
Step 2
Why this answer is correct
\(6\sqrt{2}-3\sqrt{2}=3\sqrt{2}\)। / \(6\sqrt{2}-3\sqrt{2}=3\sqrt{2}\).
Step 3
Exam Tip
घटाने से पहले दोनों वर्गमूलों को सरल करना जरूरी है। / Simplify both square roots before subtracting.
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\(\sqrt{6}\times\sqrt{54}\) का मान क्या है?
What is the value of \(\sqrt{6}\times\sqrt{54}\)?
#real-numbers
#radical-product
#rational-result
A (18)
B \(\sqrt{60}\)
C \(6\sqrt{54}\)
D (54)
Explanation opens after your attempt
Step 1
Concept
\(\sqrt{6}\times\sqrt{54}=\sqrt{324}\)। / \(\sqrt{6}\times\sqrt{54}=\sqrt{324}\).
Step 2
Why this answer is correct
\(\sqrt{324}=18\), इसलिए परिणाम परिमेय है। / \(\sqrt{324}=18\), so the result is rational.
Step 3
Exam Tip
गुणन के बाद अंदर की संख्या पूर्ण वर्ग बन सकती है, इसे जरूर जांचें। / After multiplication, check whether the inside number has become a perfect square.
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\(\sqrt{275}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{275}\)?
#real-numbers
#sqrt275
#radical-simplification
A \(5\sqrt{11}\)
B \(11\sqrt{5}\)
C \(25\sqrt{11}\)
D (55)
Explanation opens after your attempt
Correct Answer
A. \(5\sqrt{11}\)
Step 1
Concept
\(275=25 \times 11\) है। / \(275=25 \times 11\).
Step 2
Why this answer is correct
\(\sqrt{275}=\sqrt{25 \times 11}=5\sqrt{11}\)। / \(\sqrt{275}=\sqrt{25 \times 11}=5\sqrt{11}\).
Step 3
Exam Tip
पूर्ण वर्ग गुणनखंड बाहर निकालकर उत्तर को सरल बनाएं। / Take the perfect square factor outside to simplify the answer.
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\(\sqrt{192}\) को सरल कीजिए।
Simplify \(\sqrt{192}\).
#real-numbers
#sqrt192
#radical-simplification
A \(8\sqrt{3}\)
B \(4\sqrt{12}\)
C \(16\sqrt{3}\)
D \(12\sqrt{2}\)
Explanation opens after your attempt
Correct Answer
A. \(8\sqrt{3}\)
Step 1
Concept
\(192=64 \times 3\) है। / \(192=64 \times 3\).
Step 2
Why this answer is correct
\(\sqrt{192}=\sqrt{64 \times 3}=8\sqrt{3}\)। / \(\sqrt{192}=\sqrt{64 \times 3}=8\sqrt{3}\).
Step 3
Exam Tip
उत्तर को पूरा सरल करने के लिए सबसे बड़ा पूर्ण वर्ग बाहर निकालें। / To fully simplify the answer, take out the largest perfect square.
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\(\sqrt{7}\times\sqrt{28}\) का मान क्या होगा?
What is the value of \(\sqrt{7}\times\sqrt{28}\)?
#real-numbers
#radical-product
#rational-result
A (14)
B \(\sqrt{35}\)
C \(7\sqrt{28}\)
D (28)
Explanation opens after your attempt
Step 1
Concept
\(\sqrt{7}\times\sqrt{28}=\sqrt{196}\)। / \(\sqrt{7}\times\sqrt{28}=\sqrt{196}\).
Step 2
Why this answer is correct
\(\sqrt{196}=14\), इसलिए मान परिमेय है। / \(\sqrt{196}=14\), so the value is rational.
Step 3
Exam Tip
वर्गमूलों के गुणन में अंदर की संख्याएँ गुणा करें। / When multiplying square roots, multiply the numbers inside.
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\(\sqrt{300}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{300}\)?
#real-numbers
#sqrt300
#radical-simplification
A \(10\sqrt{3}\)
B \(3\sqrt{10}\)
C \(30\sqrt{10}\)
D \(100\sqrt{3}\)
Explanation opens after your attempt
Correct Answer
A. \(10\sqrt{3}\)
Step 1
Concept
\(300=100 \times 3\) लिखें। / Write \(300=100 \times 3\).
Step 2
Why this answer is correct
\(\sqrt{300}=\sqrt{100 \times 3}=10\sqrt{3}\)। / \(\sqrt{300}=\sqrt{100 \times 3}=10\sqrt{3}\).
Step 3
Exam Tip
(100) जैसा पूर्ण वर्ग दिखे तो उसे बाहर (10) के रूप में निकालें। / When you see a perfect square like (100), take it outside as (10).
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\(\sqrt{32}+\sqrt{128}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{32}+\sqrt{128}\)?
#real-numbers
#radical-addition
#simplification
A \(12\sqrt{2}\)
B \(16\sqrt{2}\)
C \(8\sqrt{2}\)
D \(\sqrt{160}\)
Explanation opens after your attempt
Correct Answer
A. \(12\sqrt{2}\)
Step 1
Concept
\(\sqrt{32}=4\sqrt{2}\) और \(\sqrt{128}=8\sqrt{2}\)। / \(\sqrt{32}=4\sqrt{2}\) and \(\sqrt{128}=8\sqrt{2}\).
Step 2
Why this answer is correct
\(4\sqrt{2}+8\sqrt{2}=12\sqrt{2}\)। / \(4\sqrt{2}+8\sqrt{2}=12\sqrt{2}\).
Step 3
Exam Tip
समान वर्गमूल बनने पर ही उन्हें जोड़ा जा सकता है। / Radicals can be added only when they become like radicals.
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\(\sqrt{80}-\sqrt{45}\) का सरल रूप क्या होगा?
What will be the simplified form of \(\sqrt{80}-\sqrt{45}\)?
#real-numbers
#radical-subtraction
#sqrt5
A \(\sqrt{5}\)
B \(5\sqrt{5}\)
C \(7\sqrt{5}\)
D \(\sqrt{35}\)
Explanation opens after your attempt
Correct Answer
A. \(\sqrt{5}\)
Step 1
Concept
\(\sqrt{80}=4\sqrt{5}\) और \(\sqrt{45}=3\sqrt{5}\)। / \(\sqrt{80}=4\sqrt{5}\) and \(\sqrt{45}=3\sqrt{5}\).
Step 2
Why this answer is correct
\(4\sqrt{5}-3\sqrt{5}=\sqrt{5}\)। / \(4\sqrt{5}-3\sqrt{5}=\sqrt{5}\).
Step 3
Exam Tip
घटाने से पहले दोनों वर्गमूलों को पूरी तरह सरल करें। / Before subtracting, simplify both radicals completely.
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\(\sqrt{5}+\sqrt{45}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{5}+\sqrt{45}\)?
#real-numbers
#radical-addition
#sqrt5
A \(4\sqrt{5}\)
B \(10\sqrt{5}\)
C \(\sqrt{50}\)
D \(3\sqrt{10}\)
Explanation opens after your attempt
Correct Answer
A. \(4\sqrt{5}\)
Step 1
Concept
\(\sqrt{45}=3\sqrt{5}\) है। / \(\sqrt{45}=3\sqrt{5}\).
Step 2
Why this answer is correct
\(\sqrt{5}+3\sqrt{5}=4\sqrt{5}\)। / \(\sqrt{5}+3\sqrt{5}=4\sqrt{5}\).
Step 3
Exam Tip
वर्गमूल जोड़ते समय समान वर्गमूल बनने तक सरल करें। / While adding radicals, simplify them until like radicals appear.
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\(\sqrt{242}\) का सरल रूप क्या होगा?
What will be the simplified form of \(\sqrt{242}\)?
#real-numbers
#sqrt242
#radical-simplification
A \(11\sqrt{2}\)
B \(2\sqrt{121}\)
C \(22\sqrt{2}\)
D \(121\sqrt{2}\)
Explanation opens after your attempt
Correct Answer
A. \(11\sqrt{2}\)
Step 1
Concept
\(242=121 \times 2\) है। / \(242=121 \times 2\).
Step 2
Why this answer is correct
\(\sqrt{242}=\sqrt{121 \times 2}=11\sqrt{2}\)। / \(\sqrt{242}=\sqrt{121 \times 2}=11\sqrt{2}\).
Step 3
Exam Tip
बड़े पूर्ण वर्ग जैसे (121) को पहचानना सरलीकरण में बहुत उपयोगी है। / Recognising large perfect squares like (121) is very useful in simplification.
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\(\sqrt{3}\times\sqrt{75}\) का मान क्या है?
What is the value of \(\sqrt{3}\times\sqrt{75}\)?
#real-numbers
#radical-product
#rational-result
A (15)
B \(\sqrt{78}\)
C \(3\sqrt{75}\)
D (75)
Explanation opens after your attempt
Step 1
Concept
\(\sqrt{3}\times\sqrt{75}=\sqrt{225}\)। / \(\sqrt{3}\times\sqrt{75}=\sqrt{225}\).
Step 2
Why this answer is correct
\(\sqrt{225}=15\), इसलिए परिणाम परिमेय है। / \(\sqrt{225}=15\), so the result is rational.
Step 3
Exam Tip
गुणन के बाद यदि अंदर की संख्या पूर्ण वर्ग बन जाए, तो उत्तर परिमेय हो सकता है। / If the number inside becomes a perfect square after multiplication, the answer can be rational.
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\(\sqrt{3}+\sqrt{27}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{3}+\sqrt{27}\)?
#real-numbers
#radical-addition
#sqrt3
A \(4\sqrt{3}\)
B \(3\sqrt{3}\)
C \(\sqrt{30}\)
D (6)
Explanation opens after your attempt
Correct Answer
A. \(4\sqrt{3}\)
Step 1
Concept
\(\sqrt{27}=3\sqrt{3}\) होता है। / \(\sqrt{27}=3\sqrt{3}\).
Step 2
Why this answer is correct
\(\sqrt{3}+3\sqrt{3}=4\sqrt{3}\)। / \(\sqrt{3}+3\sqrt{3}=4\sqrt{3}\).
Step 3
Exam Tip
जोड़ने से पहले वर्गमूलों को सरल करके समान रूप बनाएं। / Before adding, simplify radicals and make them like terms.
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\(\sqrt{2}\times\sqrt{50}\) का मान क्या है?
What is the value of \(\sqrt{2}\times\sqrt{50}\)?
#real-numbers
#radical-product
#rational-result
A (5)
B (10)
C \(\sqrt{52}\)
D (25)
Explanation opens after your attempt
Step 1
Concept
वर्गमूलों के गुणन में अंदर की संख्याएँ गुणा करें। / In multiplication of square roots, multiply the numbers inside.
Step 2
Why this answer is correct
\(\sqrt{2}\times\sqrt{50}=\sqrt{100}=10\)। / \(\sqrt{2}\times\sqrt{50}=\sqrt{100}=10\).
Step 3
Exam Tip
दो अपरिमेय संख्याओं का गुणनफल कभी-कभी परिमेय हो सकता है। / The product of two irrational numbers can sometimes be rational.
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\(\sqrt{108}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{108}\)?
#real-numbers
#radical-simplification
#sqrt108
A \(3\sqrt{12}\)
B \(6\sqrt{3}\)
C \(9\sqrt{2}\)
D \(12\sqrt{3}\)
Explanation opens after your attempt
Correct Answer
B. \(6\sqrt{3}\)
Step 1
Concept
\(108=36 \times 3\) लिखें। / Write \(108=36 \times 3\).
Step 2
Why this answer is correct
\(\sqrt{108}=\sqrt{36 \times 3}=6\sqrt{3}\)। / \(\sqrt{108}=\sqrt{36 \times 3}=6\sqrt{3}\).
Step 3
Exam Tip
वर्गमूल सरल करते समय सबसे बड़ा पूर्ण वर्ग गुणनखंड चुनना अच्छा रहता है। / While simplifying a square root, choosing the largest perfect square factor is helpful.
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\(\sqrt{2}\times\sqrt{32}\) का मान क्या है?
What is the value of \(\sqrt{2}\times\sqrt{32}\)?
#real-numbers
#radical-product
#sqrt64
A (8)
B \(\sqrt{34}\)
C (16)
D \(4\sqrt{2}\)
Explanation opens after your attempt
Step 1
Concept
\(\sqrt{2}\times\sqrt{32}=\sqrt{64}\)। / \(\sqrt{2}\times\sqrt{32}=\sqrt{64}\).
Step 2
Why this answer is correct
\(\sqrt{64}=8\), इसलिए परिणाम परिमेय है। / \(\sqrt{64}=8\), so the result is rational.
Step 3
Exam Tip
गुणन में वर्गमूलों के अंदर की संख्याएँ गुणा करें। / In multiplication, multiply the numbers inside the square roots.
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\(\sqrt{112}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{112}\)?
#real-numbers
#sqrt112
#radical-simplification
A \(4\sqrt{7}\)
B \(7\sqrt{4}\)
C \(8\sqrt{7}\)
D \(16\sqrt{7}\)
Explanation opens after your attempt
Correct Answer
A. \(4\sqrt{7}\)
Step 1
Concept
\(112=16 \times 7\) है। / \(112=16 \times 7\).
Step 2
Why this answer is correct
\(\sqrt{112}=\sqrt{16 \times 7}=4\sqrt{7}\)। / \(\sqrt{112}=\sqrt{16 \times 7}=4\sqrt{7}\).
Step 3
Exam Tip
सरलीकरण में अंदर बची संख्या को फिर पूर्ण वर्ग के लिए जांचें। / After simplification, check that the remaining number has no perfect square factor.
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\(\sqrt{63}\) को सरल कीजिए।
Simplify \(\sqrt{63}\).
#real-numbers
#sqrt63
#radical-simplification
A \(3\sqrt{7}\)
B \(7\sqrt{3}\)
C \(9\sqrt{7}\)
D (21)
Explanation opens after your attempt
Correct Answer
A. \(3\sqrt{7}\)
Step 1
Concept
\(63=9 \times 7\) है। / \(63=9 \times 7\).
Step 2
Why this answer is correct
\(\sqrt{63}=\sqrt{9 \times 7}=3\sqrt{7}\)। / \(\sqrt{63}=\sqrt{9 \times 7}=3\sqrt{7}\).
Step 3
Exam Tip
(9) जैसे पूर्ण वर्ग को बाहर निकालना याद रखें। / Remember to take a perfect square like (9) outside the root.
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\(\sqrt{5}\times\sqrt{20}\) का मान क्या होगा?
What is the value of \(\sqrt{5}\times\sqrt{20}\)?
#real-numbers
#radical-product
#rational-result
A (10)
B \(\sqrt{25}\)
C \(5\sqrt{20}\)
D \(\sqrt{1000}\)
Explanation opens after your attempt
Step 1
Concept
\(\sqrt{5}\times\sqrt{20}=\sqrt{100}\)। / \(\sqrt{5}\times\sqrt{20}=\sqrt{100}\).
Step 2
Why this answer is correct
\(\sqrt{100}=10\), जो परिमेय संख्या है। / \(\sqrt{100}=10\), which is rational.
Step 3
Exam Tip
गुणन में पहले अंदर की संख्याओं का गुणन करें। / In multiplication, first multiply the numbers inside the roots.
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\(\sqrt{150}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{150}\)?
#real-numbers
#sqrt150
#radical-simplification
A \(5\sqrt{6}\)
B \(6\sqrt{5}\)
C \(10\sqrt{15}\)
D \(15\sqrt{10}\)
Explanation opens after your attempt
Correct Answer
A. \(5\sqrt{6}\)
Step 1
Concept
\(150=25 \times 6\) लिखें। / Write \(150=25 \times 6\).
Step 2
Why this answer is correct
\(\sqrt{150}=\sqrt{25 \times 6}=5\sqrt{6}\)। / \(\sqrt{150}=\sqrt{25 \times 6}=5\sqrt{6}\).
Step 3
Exam Tip
पूर्ण वर्ग गुणनखंड बाहर निकालकर बाकी गुणनखंड अंदर छोड़ें। / Take the perfect square factor outside and leave the remaining factor inside.
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\(\sqrt{8}+\sqrt{18}\) का सरल रूप क्या होगा?
What is the simplified form of \(\sqrt{8}+\sqrt{18}\)?
#real-numbers
#radical-addition
#simplification
A \(5\sqrt{2}\)
B \(2\sqrt{26}\)
C \(\sqrt{26}\)
D \(10\sqrt{2}\)
Explanation opens after your attempt
Correct Answer
A. \(5\sqrt{2}\)
Step 1
Concept
\(\sqrt{8}=2\sqrt{2}\) और \(\sqrt{18}=3\sqrt{2}\)। / \(\sqrt{8}=2\sqrt{2}\) and \(\sqrt{18}=3\sqrt{2}\).
Step 2
Why this answer is correct
\(2\sqrt{2}+3\sqrt{2}=5\sqrt{2}\)। / \(2\sqrt{2}+3\sqrt{2}=5\sqrt{2}\).
Step 3
Exam Tip
समान वर्गमूल बनने पर ही उन्हें जोड़ा जा सकता है। / Radicals can be added only after they become like radicals.
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\(\sqrt{45}-\sqrt{20}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{45}-\sqrt{20}\)?
#real-numbers
#radical-subtraction
#sqrt5
A \(\sqrt{5}\)
B \(5\sqrt{5}\)
C \(\sqrt{25}\)
D \(3\sqrt{25}\)
Explanation opens after your attempt
Correct Answer
A. \(\sqrt{5}\)
Step 1
Concept
\(\sqrt{45}=3\sqrt{5}\) और \(\sqrt{20}=2\sqrt{5}\)। / \(\sqrt{45}=3\sqrt{5}\) and \(\sqrt{20}=2\sqrt{5}\).
Step 2
Why this answer is correct
\(3\sqrt{5}-2\sqrt{5}=\sqrt{5}\)। / \(3\sqrt{5}-2\sqrt{5}=\sqrt{5}\).
Step 3
Exam Tip
घटाने से पहले दोनों वर्गमूलों को सरल करें। / Simplify both radicals before subtracting.
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\(\sqrt{3}\) और \(\sqrt{12}\) का योग क्या है?
What is the sum of \(\sqrt{3}\) and \(\sqrt{12}\)?
#real-numbers
#radical-addition
#sqrt3
A \(3\sqrt{3}\)
B \(\sqrt{15}\)
C \(4\sqrt{3}\)
D (6)
Explanation opens after your attempt
Correct Answer
A. \(3\sqrt{3}\)
Step 1
Concept
\(\sqrt{12}=2\sqrt{3}\) है। / \(\sqrt{12}=2\sqrt{3}\).
Step 2
Why this answer is correct
\(\sqrt{3}+2\sqrt{3}=3\sqrt{3}\)। / \(\sqrt{3}+2\sqrt{3}=3\sqrt{3}\).
Step 3
Exam Tip
जोड़ से पहले वर्गमूलों को समान रूप में बदलें। / Before adding, convert radicals into like terms if possible.
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\(\sqrt{7}+\sqrt{7}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{7}+\sqrt{7}\)?
#real-numbers
#radical-addition
#irrational
A \(2\sqrt{7}\)
B \(\sqrt{14}\)
C \(7\sqrt{2}\)
D (14)
Explanation opens after your attempt
Correct Answer
A. \(2\sqrt{7}\)
Step 1
Concept
समान वर्गमूलों को समान पद की तरह जोड़ा जाता है। / Like radicals are added like like terms.
Step 2
Why this answer is correct
\(\sqrt{7}+\sqrt{7}=2\sqrt{7}\)। / \(\sqrt{7}+\sqrt{7}=2\sqrt{7}\).
Step 3
Exam Tip
जोड़ में अंदर की संख्याएँ जोड़कर \(\sqrt{14}\) नहीं लिखना चाहिए। / In addition, do not add the numbers inside roots to write \(\sqrt{14}\).
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\(\sqrt{2}\times\sqrt{18}\) का मान क्या होगा?
What is the value of \(\sqrt{2}\times\sqrt{18}\)?
#real-numbers
#radical-product
#rational-result
A (6)
B \(\sqrt{20}\)
C \(2\sqrt{18}\)
D (36)
Explanation opens after your attempt
Step 1
Concept
वर्गमूलों के गुणन में अंदर की संख्याएँ गुणा होती हैं। / When multiplying square roots, multiply the numbers inside.
Step 2
Why this answer is correct
\(\sqrt{2}\times\sqrt{18}=\sqrt{36}=6\)। / \(\sqrt{2}\times\sqrt{18}=\sqrt{36}=6\).
Step 3
Exam Tip
दो अपरिमेय संख्याओं का गुणनफल कभी-कभी परिमेय हो सकता है। / The product of two irrational numbers can sometimes be rational.
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\(\sqrt{28}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{28}\)?
#real-numbers
#radical-simplification
#sqrt28
A \(2\sqrt{7}\)
B \(7\sqrt{2}\)
C \(4\sqrt{7}\)
D \(14\sqrt{2}\)
Explanation opens after your attempt
Correct Answer
A. \(2\sqrt{7}\)
Step 1
Concept
\(28=4 \times 7\) लिखें। / Write \(28=4 \times 7\).
Step 2
Why this answer is correct
\(\sqrt{28}=\sqrt{4 \times 7}=2\sqrt{7}\)। / \(\sqrt{28}=\sqrt{4 \times 7}=2\sqrt{7}\).
Step 3
Exam Tip
वर्गमूल सरल करते समय पूर्ण वर्ग गुणनखंड को बाहर निकालें। / While simplifying a square root, take the perfect square factor outside.
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\(\sqrt{32}\) को सरल कीजिए।
Simplify \(\sqrt{32}\).
#real-numbers
#radical-simplification
#sqrt32
A \(4\sqrt{2}\)
B \(2\sqrt{8}\)
C \(8\sqrt{2}\)
D \(16\sqrt{2}\)
Explanation opens after your attempt
Correct Answer
A. \(4\sqrt{2}\)
Step 1
Concept
\(32=16 \times 2\) है। / \(32=16 \times 2\).
Step 2
Why this answer is correct
\(\sqrt{32}=\sqrt{16 \times 2}=4\sqrt{2}\)। / \(\sqrt{32}=\sqrt{16 \times 2}=4\sqrt{2}\).
Step 3
Exam Tip
उत्तर को पूरी तरह सरल करने के लिए सबसे बड़ा पूर्ण वर्ग बाहर निकालें। / To fully simplify the answer, take out the largest perfect square.
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\(\sqrt{2}\times\sqrt{3}\) किसके बराबर है?
What is \(\sqrt{2}\times\sqrt{3}\) equal to?
#real-numbers
#radical-product
#irrational
A \(\sqrt{5}\)
B \(\sqrt{6}\)
C (6)
D \(2\sqrt{3}\)
Explanation opens after your attempt
Correct Answer
B. \(\sqrt{6}\)
Step 1
Concept
वर्गमूलों के गुणन में अंदर की संख्याएँ गुणा होती हैं। / While multiplying square roots, multiply the numbers inside.
Step 2
Why this answer is correct
\(\sqrt{2}\times\sqrt{3}=\sqrt{6}\), जो अपरिमेय है। / \(\sqrt{2}\times\sqrt{3}=\sqrt{6}\), which is irrational.
Step 3
Exam Tip
गुणा में अंदर की संख्याएँ गुणा करें, जोड़ नहीं। / In multiplication, multiply the inside numbers; do not add them.
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\(\sqrt{20}\) का सरल रूप कौन-सा है?
Which is the simplified form of \(\sqrt{20}\)?
#real-numbers
#radical-simplification
#sqrt20
A \(2\sqrt{5}\)
B \(5\sqrt{2}\)
C \(4\sqrt{5}\)
D \(10\sqrt{2}\)
Explanation opens after your attempt
Correct Answer
A. \(2\sqrt{5}\)
Step 1
Concept
\(20=4 \times 5\) है। / \(20=4 \times 5\).
Step 2
Why this answer is correct
\(\sqrt{20}=\sqrt{4 \times 5}=2\sqrt{5}\)। / \(\sqrt{20}=\sqrt{4 \times 5}=2\sqrt{5}\).
Step 3
Exam Tip
वर्गमूल के अंदर पूर्ण वर्ग को बाहर निकालें और बाकी अंदर रहने दें। / Take the perfect square outside the root and leave the remaining factor inside.
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