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Mathematics Quiz - Class 10 Mathematics Real Numbers...

Question 1/50 Easy Mathematics Real Numbers Irrational numbers Class 10 Level 15

निम्नलिखित में से कौन-सी संख्या अपरिमेय है?

Which of the following numbers is irrational?

Explanation opens after your attempt

Correct Answer

A. \(\sqrt{14}\)

Step 1

Concept

अपरिमेय संख्या को \(\frac{p}{q}\) के रूप में ठीक-ठीक नहीं लिखा जा सकता। / An irrational number cannot be written exactly in the form \(\frac{p}{q}\).

Step 2

Why this answer is correct

(14) पूर्ण वर्ग नहीं है, इसलिए \(\sqrt{14}\) अपरिमेय है। / (14) is not a perfect square, so \(\sqrt{14}\) is irrational.

Step 3

Exam Tip

वर्गमूल में अंदर की संख्या पूर्ण वर्ग है या नहीं, पहले यही जांचें। / In square-root questions, first check whether the number inside is a perfect square.

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Question 2/50 Easy Mathematics Real Numbers Irrational numbers Class 10 Level 15

\(\sqrt{121}\) किस प्रकार की संख्या है?

What type of number is \(\sqrt{121}\)?

Explanation opens after your attempt

Correct Answer

B. परिमेय संख्याRational number

Step 1

Concept

(121) एक पूर्ण वर्ग है। / (121) is a perfect square.

Step 2

Why this answer is correct

\(\sqrt{121}=11\), और (11) को \(\frac{11}{1}\) के रूप में लिखा जा सकता है। / \(\sqrt{121}=11\), and (11) can be written as \(\frac{11}{1}\).

Step 3

Exam Tip

पूर्ण वर्गों के वर्गमूल परिमेय होते हैं। / Square roots of perfect squares are rational.

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Question 3/50 Easy Mathematics Real Numbers Irrational numbers Class 10 Level 15

कौन-सा दशमलव अपरिमेय संख्या का रूप हो सकता है?

Which decimal can represent an irrational number?

Explanation opens after your attempt

Correct Answer

C. \(0.01001000100001\ldots\)

Step 1

Concept

समाप्त और आवर्ती दशमलव परिमेय होते हैं। / Terminating and recurring decimals are rational.

Step 2

Why this answer is correct

\(0.01001000100001\ldots\) में निश्चित दोहराव नहीं है, इसलिए यह अनवसानी और अनावर्ती है। / \(0.01001000100001\ldots\) has no fixed repeating pattern, so it is non-terminating and non-recurring.

Step 3

Exam Tip

दशमलव में केवल लंबाई नहीं, दोहराव का नियम देखना जरूरी है। / For decimals, check the repetition pattern, not just the length.

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Question 4/50 Easy Mathematics Real Numbers Irrational numbers Class 10 Level 15

\(\sqrt{108}\) का सरल रूप क्या है?

What is the simplified form of \(\sqrt{108}\)?

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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Question 5/50 Easy Mathematics Real Numbers Irrational numbers Class 10 Level 15

\(\sqrt{7}+4\) के बारे में सही कथन कौन-सा है?

Which statement is correct about \(\sqrt{7}+4\)?

Explanation opens after your attempt

Correct Answer

C. यह अपरिमेय हैIt is irrational

Step 1

Concept

\(\sqrt{7}\) अपरिमेय है और (4) परिमेय है। / \(\sqrt{7}\) is irrational and (4) is rational.

Step 2

Why this answer is correct

परिमेय संख्या जोड़ने से अपरिमेय भाग समाप्त नहीं होता। / Adding a rational number does not remove the irrational part.

Step 3

Exam Tip

परिमेय और अपरिमेय संख्या का योग सामान्यतः अपरिमेय होता है। / The sum of a rational and an irrational number is generally irrational.

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Question 6/50 Easy Mathematics Real Numbers Irrational numbers Class 10 Level 15

\(\sqrt{2}\times\sqrt{50}\) का मान क्या है?

What is the value of \(\sqrt{2}\times\sqrt{50}\)?

Explanation opens after your attempt

Correct Answer

B. (10)

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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Question 7/50 Easy Mathematics Real Numbers Irrational numbers Class 10 Level 15

निम्नलिखित में से कौन-सा विकल्प परिमेय संख्या है?

Which of the following options is a rational number?

Explanation opens after your attempt

Correct Answer

C. \(\sqrt{144}\)

Step 1

Concept

परिमेय विकल्प के लिए पूर्ण वर्ग का वर्गमूल खोजें। / To find the rational option, look for the square root of a perfect square.

Step 2

Why this answer is correct

(144) पूर्ण वर्ग है और \(\sqrt{144}=12\)। / (144) is a perfect square and \(\sqrt{144}=12\).

Step 3

Exam Tip

पूर्ण वर्ग पहचानने से ऐसे प्रश्न बहुत जल्दी हल होते हैं। / Recognising perfect squares makes such questions very quick.

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Question 8/50 Easy Mathematics Real Numbers Irrational numbers Class 10 Level 15

\(\sqrt{3}+\sqrt{27}\) का सरल रूप क्या है?

What is the simplified form of \(\sqrt{3}+\sqrt{27}\)?

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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Question 9/50 Easy Mathematics Real Numbers Irrational numbers Class 10 Level 15

किस संख्या का दशमलव विस्तार आवर्ती है?

Which number has a recurring decimal expansion?

Explanation opens after your attempt

Correct Answer

B. \(\frac{5}{6}\)

Step 1

Concept

\(\frac{5}{6}\) परिमेय संख्या है। / \(\frac{5}{6}\) is a rational number.

Step 2

Why this answer is correct

इसका दशमलव \(0.8333\ldots\) के रूप में आवर्ती होता है। / Its decimal form is \(0.8333\ldots\), which is recurring.

Step 3

Exam Tip

परिमेय संख्याओं का दशमलव समाप्त या आवर्ती होता है। / Rational numbers have decimal expansions that are either terminating or recurring.

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Question 10/50 Easy Mathematics Real Numbers Irrational numbers Class 10 Level 15

\(\sqrt{11}+\sqrt{11}\) का सरल रूप क्या होगा?

What will be the simplified form of \(\sqrt{11}+\sqrt{11}\)?

Explanation opens after your attempt

Correct Answer

C. \(2\sqrt{11}\)

Step 1

Concept

दोनों पद समान वर्गमूल वाले हैं। / Both terms have the same square root.

Step 2

Why this answer is correct

\(\sqrt{11}+\sqrt{11}=2\sqrt{11}\)। / \(\sqrt{11}+\sqrt{11}=2\sqrt{11}\).

Step 3

Exam Tip

समान वर्गमूलों में अंदर की संख्याएँ नहीं, केवल गुणांक जोड़े जाते हैं। / For like radicals, add only the coefficients, not the numbers inside the roots.

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Question 11/50 Easy Mathematics Real Numbers Irrational numbers Class 10 Level 15

\(\sqrt{19}-\sqrt{19}\) का मान क्या है?

What is the value of \(\sqrt{19}-\sqrt{19}\)?

Explanation opens after your attempt

Correct Answer

B. (0)

Step 1

Concept

किसी संख्या में से वही संख्या घटाने पर (0) मिलता है। / Subtracting a number from itself gives (0).

Step 2

Why this answer is correct

इसलिए \(\sqrt{19}-\sqrt{19}=0\), जो परिमेय है। / So \(\sqrt{19}-\sqrt{19}=0\), which is rational.

Step 3

Exam Tip

अपरिमेय पदों पर भी सामान्य घटाव नियम लागू होता है। / Ordinary subtraction rules also apply to irrational terms.

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Question 12/50 Easy Mathematics Real Numbers Irrational numbers Class 10 Level 15

\(\sqrt{3}\times\sqrt{75}\) का मान क्या है?

What is the value of \(\sqrt{3}\times\sqrt{75}\)?

Explanation opens after your attempt

Correct Answer

A. (15)

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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Question 13/50 Easy Mathematics Real Numbers Irrational numbers Class 10 Level 15

कौन-सा कथन सत्य है?

Which statement is true?

Explanation opens after your attempt

Correct Answer

C. पूर्ण वर्ग का वर्गमूल परिमेय होता हैThe square root of a perfect square is rational

Step 1

Concept

पूर्ण वर्गों के वर्गमूल पूर्णांक होते हैं। / Square roots of perfect squares are integers.

Step 2

Why this answer is correct

जैसे \(\sqrt{49}=7\), इसलिए यह परिमेय है। / For example, \(\sqrt{49}=7\), so it is rational.

Step 3

Exam Tip

कथन वाले प्रश्नों में उदाहरण लगाकर सत्यता जांचना आसान होता है। / In statement-based questions, using an example helps check the truth.

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Question 14/50 Easy Mathematics Real Numbers Irrational numbers Class 10 Level 15

\(\sqrt{242}\) का सरल रूप क्या होगा?

What will be the simplified form of \(\sqrt{242}\)?

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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Question 15/50 Easy Mathematics Real Numbers Irrational numbers Class 10 Level 15

\(\sqrt{5}+\sqrt{45}\) का सरल रूप क्या है?

What is the simplified form of \(\sqrt{5}+\sqrt{45}\)?

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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Question 16/50 Easy Mathematics Real Numbers Irrational numbers Class 10 Level 15

कौन-सी संख्या (6) और (7) के बीच स्थित अपरिमेय संख्या है?

Which number is an irrational number between (6) and (7)?

Explanation opens after your attempt

Correct Answer

C. \(\sqrt{45}\)

Step 1

Concept

(36<45<49), इसलिए \(6<\sqrt{45}<7\)। / Since (36<45<49), \(6<\sqrt{45}<7\).

Step 2

Why this answer is correct

(45) पूर्ण वर्ग नहीं है, इसलिए \(\sqrt{45}\) अपरिमेय है। / (45) is not a perfect square, so \(\sqrt{45}\) is irrational.

Step 3

Exam Tip

अंतराल वाले प्रश्नों में पास के पूर्ण वर्गों का उपयोग करें। / In interval questions, use nearby perfect squares.

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Question 17/50 Easy Mathematics Real Numbers Irrational numbers Class 10 Level 15

\(\frac{\sqrt{7}}{3}\) कैसी संख्या है?

What type of number is \(\frac{\sqrt{7}}{3}\)?

Explanation opens after your attempt

Correct Answer

B. अपरिमेयIrrational

Step 1

Concept

\(\sqrt{7}\) अपरिमेय है। / \(\sqrt{7}\) is irrational.

Step 2

Why this answer is correct

इसे अशून्य परिमेय संख्या (3) से भाग देने पर परिणाम अपरिमेय रहता है। / Dividing it by the non-zero rational number (3) keeps the result irrational.

Step 3

Exam Tip

अशून्य परिमेय से भाग करने पर अपरिमेयता समाप्त नहीं होती। / Division by a non-zero rational number does not remove irrationality.

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Question 18/50 Easy Mathematics Real Numbers Irrational numbers Class 10 Level 15

कौन-सा युग्म एक परिमेय और एक अपरिमेय संख्या से बना है?

Which pair is made of one rational and one irrational number?

Explanation opens after your attempt

Correct Answer

B. \(8,\sqrt{15}\)

Step 1

Concept

(8) परिमेय संख्या है। / (8) is rational.

Step 2

Why this answer is correct

\(\sqrt{15}\) अपरिमेय है क्योंकि (15) पूर्ण वर्ग नहीं है। / \(\sqrt{15}\) is irrational because (15) is not a perfect square.

Step 3

Exam Tip

युग्म वाले प्रश्न में दोनों संख्याओं की प्रकृति अलग-अलग जांचें। / In pair questions, check the nature of both numbers separately.

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Question 19/50 Easy Mathematics Real Numbers Irrational numbers Class 10 Level 15

\(\sqrt{175}\) का सरल रूप क्या है?

What is the simplified form of \(\sqrt{175}\)?

Explanation opens after your attempt

Correct Answer

C. \(5\sqrt{7}\)

Step 1

Concept

\(175=25 \times 7\) लिखें। / Write \(175=25 \times 7\).

Step 2

Why this answer is correct

\(\sqrt{175}=\sqrt{25 \times 7}=5\sqrt{7}\)। / \(\sqrt{175}=\sqrt{25 \times 7}=5\sqrt{7}\).

Step 3

Exam Tip

पूर्ण वर्ग गुणनखंड को बाहर और बाकी संख्या को अंदर रखें। / Take the perfect square factor outside and keep the remaining number inside.

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Question 20/50 Easy Mathematics Real Numbers Irrational numbers Class 10 Level 15

\(\sqrt{10}+\sqrt{10}+\sqrt{10}+\sqrt{10}\) का सरल रूप क्या है?

What is the simplified form of \(\sqrt{10}+\sqrt{10}+\sqrt{10}+\sqrt{10}\)?

Explanation opens after your attempt

Correct Answer

A. \(4\sqrt{10}\)

Step 1

Concept

चार समान वर्गमूल पद जोड़े जा रहे हैं। / Four like radical terms are being added.

Step 2

Why this answer is correct

\(\sqrt{10}+\sqrt{10}+\sqrt{10}+\sqrt{10}=4\sqrt{10}\)। / \(\sqrt{10}+\sqrt{10}+\sqrt{10}+\sqrt{10}=4\sqrt{10}\).

Step 3

Exam Tip

समान वर्गमूलों को जोड़ते समय केवल गुणांक जोड़ें। / When adding like radicals, add only the coefficients.

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Question 21/50 Easy Mathematics Real Numbers Irrational numbers Class 10 Level 15

\(\sqrt{80}-\sqrt{45}\) का सरल रूप क्या होगा?

What will be the simplified form of \(\sqrt{80}-\sqrt{45}\)?

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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Question 22/50 Easy Mathematics Real Numbers Irrational numbers Class 10 Level 15

\(\sqrt{13}\) का वर्ग किसके बराबर है?

The square of \(\sqrt{13}\) is equal to what?

Explanation opens after your attempt

Correct Answer

C. (13)

Step 1

Concept

वर्गमूल का वर्ग करने पर अंदर की संख्या मिलती है। / Squaring a square root gives the number inside it.

Step 2

Why this answer is correct

(\(\sqrt{13}\)²=13)। / (\(\sqrt{13}\)²=13).

Step 3

Exam Tip

(\(\sqrt{a}\)²=a) को सीधे लागू करें। / Apply (\(\sqrt{a}\)²=a) directly.

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Question 23/50 Easy Mathematics Real Numbers Irrational numbers Class 10 Level 15

यदि \(x=\sqrt{6}\), तो (2x) किस प्रकार की संख्या होगी?

If \(x=\sqrt{6}\), what type of number is (2x)?

Explanation opens after your attempt

Correct Answer

C. अपरिमेयIrrational

Step 1

Concept

\(x=\sqrt{6}\) अपरिमेय है। / \(x=\sqrt{6}\) is irrational.

Step 2

Why this answer is correct

\(2x=2\sqrt{6}\), और (2) अशून्य परिमेय संख्या है। / \(2x=2\sqrt{6}\), and (2) is a non-zero rational number.

Step 3

Exam Tip

अपरिमेय संख्या को अशून्य परिमेय से गुणा करने पर परिणाम अपरिमेय रहता है। / Multiplying an irrational number by a non-zero rational number keeps it irrational.

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Question 24/50 Easy Mathematics Real Numbers Irrational numbers Class 10 Level 15

कौन-सा विकल्प अपरिमेय संख्या नहीं है?

Which option is not an irrational number?

Explanation opens after your attempt

Correct Answer

B. \(\sqrt{64}\)

Step 1

Concept

प्रश्न अपरिमेय नहीं पूछ रहा है, इसलिए परिमेय संख्या खोजें। / The question asks for the number that is not irrational, so look for a rational number.

Step 2

Why this answer is correct

\(\sqrt{64}=8\), जो परिमेय है। / \(\sqrt{64}=8\), which is rational.

Step 3

Exam Tip

ऐसे प्रश्नों में नकारात्मक शब्दों को ध्यान से पढ़ें। / Read negative wording carefully in such questions.

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Question 25/50 Easy Mathematics Real Numbers Irrational numbers Class 10 Level 15

\(\sqrt{32}+\sqrt{128}\) का सरल रूप क्या है?

What is the simplified form of \(\sqrt{32}+\sqrt{128}\)?

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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Question 26/50 Easy Mathematics Real Numbers Irrational numbers Class 10 Level 15

निम्नलिखित में से कौन-सा कथन गलत है?

Which of the following statements is false?

Explanation opens after your attempt

Correct Answer

C. \(\sqrt{169}\) अपरिमेय है\(\sqrt{169}\) is irrational

Step 1

Concept

(169) पूर्ण वर्ग है। / (169) is a perfect square.

Step 2

Why this answer is correct

\(\sqrt{169}=13\), जो परिमेय है, इसलिए इसे अपरिमेय कहना गलत है। / \(\sqrt{169}=13\), which is rational, so calling it irrational is false.

Step 3

Exam Tip

गलत कथन चुनते समय पूर्ण वर्गों को जरूर पहचानें। / While choosing a false statement, identify perfect squares carefully.

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Question 27/50 Easy Mathematics Real Numbers Irrational numbers Class 10 Level 15

\(\sqrt{300}\) का सरल रूप क्या है?

What is the simplified form of \(\sqrt{300}\)?

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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Question 28/50 Easy Mathematics Real Numbers Irrational numbers Class 10 Level 15

\(\sqrt{7}\times\sqrt{28}\) का मान क्या होगा?

What is the value of \(\sqrt{7}\times\sqrt{28}\)?

Explanation opens after your attempt

Correct Answer

A. (14)

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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Question 29/50 Easy Mathematics Real Numbers Irrational numbers Class 10 Level 15

कौन-सी संख्या (7) और (8) के बीच स्थित है?

Which number lies between (7) and (8)?

Explanation opens after your attempt

Correct Answer

B. \(\sqrt{55}\)

Step 1

Concept

(49<55<64), इसलिए \(7<\sqrt{55}<8\)। / Since (49<55<64), \(7<\sqrt{55}<8\).

Step 2

Why this answer is correct

(55) पूर्ण वर्ग नहीं है, इसलिए \(\sqrt{55}\) अपरिमेय है। / (55) is not a perfect square, so \(\sqrt{55}\) is irrational.

Step 3

Exam Tip

वर्गमूल की स्थिति पास के पूर्ण वर्गों से आसानी से मिलती है। / Nearby perfect squares help locate a square root easily.

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Question 30/50 Easy Mathematics Real Numbers Irrational numbers Class 10 Level 15

\(\sqrt{288}\) का सरल रूप कौन-सा है?

Which is the simplified form of \(\sqrt{288}\)?

Explanation opens after your attempt

Correct Answer

A. \(12\sqrt{2}\)

Step 1

Concept

\(288=144 \times 2\) है। / \(288=144 \times 2\).

Step 2

Why this answer is correct

\(\sqrt{288}=\sqrt{144 \times 2}=12\sqrt{2}\)। / \(\sqrt{288}=\sqrt{144 \times 2}=12\sqrt{2}\).

Step 3

Exam Tip

बड़े पूर्ण वर्ग का उपयोग करने से उत्तर सीधे सरल रूप में मिलता है। / Using a large perfect square gives the simplified form directly.

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Question 31/50 Easy Mathematics Real Numbers Irrational numbers Class 10 Level 15

\(\sqrt{7}+2\sqrt{7}\) किसके बराबर है?

What is \(\sqrt{7}+2\sqrt{7}\) equal to?

Explanation opens after your attempt

Correct Answer

B. \(3\sqrt{7}\)

Step 1

Concept

दोनों पदों में \(\sqrt{7}\) समान है। / Both terms contain the same radical \(\sqrt{7}\).

Step 2

Why this answer is correct

\(1\sqrt{7}+2\sqrt{7}=3\sqrt{7}\)। / \(1\sqrt{7}+2\sqrt{7}=3\sqrt{7}\).

Step 3

Exam Tip

समान वर्गमूलों में केवल बाहर के गुणांक जोड़ें। / For like radicals, add only the outside coefficients.

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Question 32/50 Easy Mathematics Real Numbers Irrational numbers Class 10 Level 15

\(\sqrt{7}\) का लगभग मान किसके सबसे निकट है?

The approximate value of \(\sqrt{7}\) is closest to which number?

Explanation opens after your attempt

Correct Answer

B. (2.65)

Step 1

Concept

\(\sqrt{7}\) का मान लगभग (2.646) है। / The value of \(\sqrt{7}\) is about (2.646).

Step 2

Why this answer is correct

दिए गए विकल्पों में (2.65) सबसे निकट है। / Among the options, (2.65) is closest.

Step 3

Exam Tip

अनुमान में पास के पूर्ण वर्ग (4) और (9) से सीमा समझें। / For estimation, use nearby perfect squares (4) and (9) to understand the range.

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Question 33/50 Easy Mathematics Real Numbers Irrational numbers Class 10 Level 15

\(\sqrt{26}\) का मान किन दो पूर्णांकों के बीच होगा?

Between which two integers does \(\sqrt{26}\) lie?

Explanation opens after your attempt

Correct Answer

B. (5) और (6)(5) and (6)

Step 1

Concept

(25<26<36) है।

Step 2

Why this answer is correct

इसलिए \(\sqrt{25}<\sqrt{26}<\sqrt{36}\), यानी \(5<\sqrt{26}<6\)। / So \(\sqrt{25}<\sqrt{26}<\sqrt{36}\), meaning \(5<\sqrt{26}<6\).

Step 3

Exam Tip

वर्गमूल की सीमा के लिए पास के पूर्ण वर्ग देखें। / To find the range of a square root, look at nearby perfect squares.

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Question 34/50 Easy Mathematics Real Numbers Irrational numbers Class 10 Level 15

\(\sqrt{192}\) को सरल कीजिए।

Simplify \(\sqrt{192}\).

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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Question 35/50 Easy Mathematics Real Numbers Irrational numbers Class 10 Level 15

यदि \(y=\sqrt{17}\), तो \(y^2\) का मान क्या होगा?

If \(y=\sqrt{17}\), what is the value of \(y^2\)?

Explanation opens after your attempt

Correct Answer

C. (17)

Step 1

Concept

\(y=\sqrt{17}\) दिया है। / We are given \(y=\sqrt{17}\).

Step 2

Why this answer is correct

(y^-2=\(\sqrt{17}\)²=17)। / (y^-2=\(\sqrt{17}\)²=17).

Step 3

Exam Tip

वर्गमूल का वर्ग करने पर अंदर की संख्या ही मिलती है। / Squaring a square root gives the number inside it.

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Question 36/50 Easy Mathematics Real Numbers Irrational numbers Class 10 Level 15

कौन-सा विकल्प दो अपरिमेय संख्याओं का ऐसा गुणनफल है जो परिमेय बनता है?

Which option is a product of two irrational numbers that becomes rational?

Explanation opens after your attempt

Correct Answer

A. \(\sqrt{5}\times\sqrt{5}\)

Step 1

Concept

\(\sqrt{5}\) अपरिमेय है। / \(\sqrt{5}\) is irrational.

Step 2

Why this answer is correct

\(\sqrt{5}\times\sqrt{5}=5\), जो परिमेय है। / \(\sqrt{5}\times\sqrt{5}=5\), which is rational.

Step 3

Exam Tip

दो अपरिमेय संख्याओं का गुणनफल हमेशा अपरिमेय नहीं होता। / The product of two irrational numbers is not always irrational.

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Question 37/50 Easy Mathematics Real Numbers Irrational numbers Class 10 Level 15

\(\sqrt{11}+0\) किसके बराबर है?

What is \(\sqrt{11}+0\) equal to?

Explanation opens after your attempt

Correct Answer

C. \(\sqrt{11}\)

Step 1

Concept

शून्य जोड़ने से संख्या का मान नहीं बदलता। / Adding zero does not change the value of a number.

Step 2

Why this answer is correct

\(\sqrt{11}+0=\sqrt{11}\), जो अपरिमेय है। / \(\sqrt{11}+0=\sqrt{11}\), which is irrational.

Step 3

Exam Tip

शून्य के साथ भी मूल संख्या की प्रकृति पहचानें। / Even with zero, identify the nature of the original number.

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Question 38/50 Easy Mathematics Real Numbers Irrational numbers Class 10 Level 15

\(\sqrt{21}\) का दशमलव विस्तार कैसा होगा?

What kind of decimal expansion does \(\sqrt{21}\) have?

Explanation opens after your attempt

Correct Answer

C. अनवसानी और अनावर्तीNon-terminating and non-recurring

Step 1

Concept

(21) पूर्ण वर्ग नहीं है। / (21) is not a perfect square.

Step 2

Why this answer is correct

इसलिए \(\sqrt{21}\) अपरिमेय है और इसका दशमलव अनवसानी अनावर्ती होगा। / So \(\sqrt{21}\) is irrational and its decimal expansion is non-terminating and non-recurring.

Step 3

Exam Tip

अपरिमेय संख्या में कोई निश्चित आवर्ती समूह नहीं होता। / An irrational number has no fixed recurring block.

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Question 39/50 Easy Mathematics Real Numbers Irrational numbers Class 10 Level 15

\(\sqrt{135}\) का सरल रूप क्या है?

What is the simplified form of \(\sqrt{135}\)?

Explanation opens after your attempt

Correct Answer

B. \(3\sqrt{15}\)

Step 1

Concept

\(135=9 \times 15\) लिखें। / Write \(135=9 \times 15\).

Step 2

Why this answer is correct

\(\sqrt{135}=\sqrt{9 \times 15}=3\sqrt{15}\)। / \(\sqrt{135}=\sqrt{9 \times 15}=3\sqrt{15}\).

Step 3

Exam Tip

अंदर बची संख्या में पूर्ण वर्ग गुणनखंड न हो, तब रूप सरल माना जाता है। / The form is simplified when the remaining number inside has no perfect square factor.

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Question 40/50 Easy Mathematics Real Numbers Irrational numbers Class 10 Level 15

कौन-सी संख्या \(\sqrt{75}\) के बराबर है?

Which number is equal to \(\sqrt{75}\)?

Explanation opens after your attempt

Correct Answer

B. \(5\sqrt{3}\)

Step 1

Concept

\(75=25 \times 3\) है। / \(75=25 \times 3\).

Step 2

Why this answer is correct

\(\sqrt{75}=5\sqrt{3}\)। / \(\sqrt{75}=5\sqrt{3}\).

Step 3

Exam Tip

बराबर रूप पहचानने के लिए पहले वर्गमूल को सरल करें। / To identify an equivalent form, simplify the square root first.

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Question 41/50 Easy Mathematics Real Numbers Irrational numbers Class 10 Level 15

\(\sqrt{13}\) और \(-\sqrt{13}\) का योग क्या है?

What is the sum of \(\sqrt{13}\) and \(-\sqrt{13}\)?

Explanation opens after your attempt

Correct Answer

A. (0)

Step 1

Concept

ये दोनों पद एक-दूसरे के विपरीत हैं। / The two terms are opposites of each other.

Step 2

Why this answer is correct

(\sqrt{13}+\(-\sqrt{13}\)=0)। / (\sqrt{13}+\(-\sqrt{13}\)=0).

Step 3

Exam Tip

विपरीत पदों का योग हमेशा शून्य होता है। / The sum of opposite terms is always zero.

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Question 42/50 Easy Mathematics Real Numbers Irrational numbers Class 10 Level 15

यदि (a) अपरिमेय है और (r) अशून्य परिमेय है, तो \(\frac{a}{r}\) कैसी संख्या होगी?

If (a) is irrational and (r) is a non-zero rational number, what type of number is \(\frac{a}{r}\)?

Explanation opens after your attempt

Correct Answer

B. अपरिमेयIrrational

Step 1

Concept

अशून्य परिमेय संख्या से भाग करने पर अपरिमेयता समाप्त नहीं होती। / Dividing by a non-zero rational number does not remove irrationality.

Step 2

Why this answer is correct

जैसे \(\frac{\sqrt{2}}{5}\) अपरिमेय है। / For example, \(\frac{\sqrt{2}}{5}\) is irrational.

Step 3

Exam Tip

यहां \(r\neq0\) शर्त जरूरी है क्योंकि शून्य से भाग संभव नहीं होता। / The condition \(r\neq0\) is necessary because division by zero is not possible.

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Question 43/50 Easy Mathematics Real Numbers Irrational numbers Class 10 Level 15

\(\sqrt{275}\) का सरल रूप क्या है?

What is the simplified form of \(\sqrt{275}\)?

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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Question 44/50 Easy Mathematics Real Numbers Irrational numbers Class 10 Level 15

निम्नलिखित में से कौन-सा अपरिमेय संख्या का दशमलव रूप हो सकता है?

Which of the following can be the decimal form of an irrational number?

Explanation opens after your attempt

Correct Answer

C. \(1.01011011101111\ldots\) बिना निश्चित दोहराव\(1.01011011101111\ldots\) with no fixed repetition

Step 1

Concept

आवर्ती या समाप्त दशमलव परिमेय होते हैं। / Recurring or terminating decimals are rational.

Step 2

Why this answer is correct

बिना निश्चित दोहराव वाला अनवसानी दशमलव अपरिमेय हो सकता है। / A non-terminating decimal with no fixed repetition can be irrational.

Step 3

Exam Tip

दोहराव का नियम न दिखे तो संख्या की प्रकृति ध्यान से जांचें। / If no repeating rule is visible, examine the number carefully.

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Question 45/50 Easy Mathematics Real Numbers Irrational numbers Class 10 Level 15

\(\sqrt{243}\) को सरल कीजिए।

Simplify \(\sqrt{243}\).

Explanation opens after your attempt

Correct Answer

B. \(9\sqrt{3}\)

Step 1

Concept

\(243=81 \times 3\) लिखें। / Write \(243=81 \times 3\).

Step 2

Why this answer is correct

\(\sqrt{243}=\sqrt{81 \times 3}=9\sqrt{3}\)। / \(\sqrt{243}=\sqrt{81 \times 3}=9\sqrt{3}\).

Step 3

Exam Tip

बड़ा पूर्ण वर्ग चुनने से उत्तर एक ही चरण में सरल हो जाता है। / Choosing a larger perfect square simplifies the answer in one step.

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Question 46/50 Easy Mathematics Real Numbers Irrational numbers Class 10 Level 15

\(\sqrt{6}\times\sqrt{54}\) का मान क्या है?

What is the value of \(\sqrt{6}\times\sqrt{54}\)?

Explanation opens after your attempt

Correct Answer

A. (18)

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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Question 47/50 Easy Mathematics Real Numbers Irrational numbers Class 10 Level 15

\(\sqrt{11}\) का लगभग मान कौन-सा है?

What is the approximate value of \(\sqrt{11}\)?

Explanation opens after your attempt

Correct Answer

B. (3.32)

Step 1

Concept

(9<11<16), इसलिए \(\sqrt{11}\) (3) और (4) के बीच होगा। / Since (9<11<16), \(\sqrt{11}\) lies between (3) and (4).

Step 2

Why this answer is correct

इसका लगभग मान (3.316) है, इसलिए (3.32) निकट है। / Its approximate value is (3.316), so (3.32) is close.

Step 3

Exam Tip

अनुमान में पहले पूर्ण वर्गों से सीमा तय करें। / In estimation, first set the range using perfect squares.

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Question 48/50 Easy Mathematics Real Numbers Irrational numbers Class 10 Level 15

कौन-सा विकल्प \(\sqrt{216}\) का सरल रूप है?

Which option is the simplified form of \(\sqrt{216}\)?

Explanation opens after your attempt

Correct Answer

A. \(6\sqrt{6}\)

Step 1

Concept

\(216=36 \times 6\) है। / \(216=36 \times 6\).

Step 2

Why this answer is correct

\(\sqrt{216}=\sqrt{36 \times 6}=6\sqrt{6}\)। / \(\sqrt{216}=\sqrt{36 \times 6}=6\sqrt{6}\).

Step 3

Exam Tip

अंदर बचे (6) में कोई पूर्ण वर्ग गुणनखंड नहीं है, इसलिए रूप सरल है। / The remaining (6) has no perfect square factor, so the form is simplified.

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Question 49/50 Easy Mathematics Real Numbers Irrational numbers Class 10 Level 15

\(\sqrt{39}\) का मान किन दो पूर्णांकों के बीच है?

Between which two integers does \(\sqrt{39}\) lie?

Explanation opens after your attempt

Correct Answer

C. (6) और (7)(6) and (7)

Step 1

Concept

(36<39<49) है।

Step 2

Why this answer is correct

इसलिए \(6<\sqrt{39}<7\)। / Therefore, \(6<\sqrt{39}<7\).

Step 3

Exam Tip

वर्गमूल की तुलना के लिए पास के पूर्ण वर्ग सबसे अच्छे संकेत देते हैं। / Nearby perfect squares give the best clues for comparing square roots.

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Question 50/50 Easy Mathematics Real Numbers Irrational numbers Class 10 Level 15

निम्नलिखित में से कौन-सा परिणाम अपरिमेय है?

Which of the following results is irrational?

Explanation opens after your attempt

Correct Answer

B. \(\sqrt{7}+\sqrt{28}\)

Step 1

Concept

\(\sqrt{28}=2\sqrt{7}\), इसलिए \(\sqrt{7}+\sqrt{28}=3\sqrt{7}\)। / \(\sqrt{28}=2\sqrt{7}\), so \(\sqrt{7}+\sqrt{28}=3\sqrt{7}\).

Step 2

Why this answer is correct

\(3\sqrt{7}\) अपरिमेय है क्योंकि \(\sqrt{7}\) अपरिमेय है। / \(3\sqrt{7}\) is irrational because \(\sqrt{7}\) is irrational.

Step 3

Exam Tip

विकल्पों में परिणाम की प्रकृति तय करने से पहले सरलीकरण करें। / In options, simplify first before deciding the nature of the result.

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Class 10 Mathematics - Real Numbers - Proof of irrationality of √2, √3, √5 Easy Quiz

निम्नलिखित में से कौन-सी संख्या अपरिमेय है?

Concept

Why this answer is correct

Exam Tip

\(\sqrt{121}\) किस प्रकार की संख्या है?

Concept

Why this answer is correct

Exam Tip

कौन-सा दशमलव अपरिमेय संख्या का रूप हो सकता है?

Concept

Why this answer is correct

Exam Tip

\(\sqrt{108}\) का सरल रूप क्या है?

Concept

Why this answer is correct

Exam Tip

\(\sqrt{7}+4\) के बारे में सही कथन कौन-सा है?

Concept

Why this answer is correct

Exam Tip

\(\sqrt{2}\times\sqrt{50}\) का मान क्या है?

Concept

Why this answer is correct

Exam Tip

निम्नलिखित में से कौन-सा विकल्प परिमेय संख्या है?

Concept

Why this answer is correct

Exam Tip

\(\sqrt{3}+\sqrt{27}\) का सरल रूप क्या है?

Concept

Why this answer is correct

Exam Tip

किस संख्या का दशमलव विस्तार आवर्ती है?

Concept

Why this answer is correct

Exam Tip

\(\sqrt{11}+\sqrt{11}\) का सरल रूप क्या होगा?

Concept

Why this answer is correct

Exam Tip

\(\sqrt{19}-\sqrt{19}\) का मान क्या है?

Concept

Why this answer is correct

Exam Tip

\(\sqrt{3}\times\sqrt{75}\) का मान क्या है?

Concept

Why this answer is correct

Exam Tip

कौन-सा कथन सत्य है?

Concept

Why this answer is correct

Exam Tip

\(\sqrt{242}\) का सरल रूप क्या होगा?

Concept

Why this answer is correct

Exam Tip

\(\sqrt{5}+\sqrt{45}\) का सरल रूप क्या है?

Concept

Why this answer is correct

Exam Tip

कौन-सी संख्या (6) और (7) के बीच स्थित अपरिमेय संख्या है?

Concept

Why this answer is correct

Exam Tip

\(\frac{\sqrt{7}}{3}\) कैसी संख्या है?

Concept

Why this answer is correct

Exam Tip

कौन-सा युग्म एक परिमेय और एक अपरिमेय संख्या से बना है?

Concept

Why this answer is correct

Exam Tip

\(\sqrt{175}\) का सरल रूप क्या है?

Concept

Why this answer is correct

Exam Tip

\(\sqrt{10}+\sqrt{10}+\sqrt{10}+\sqrt{10}\) का सरल रूप क्या है?

Concept

Why this answer is correct