कौन सा विकल्प \(\sqrt{75}-\sqrt{27}\) का सही मान है?
Which option is the correct value of \(\sqrt{75}-\sqrt{27}\)?
#surds
#subtraction
#simplification
A \(2\sqrt{3}\)
B \(8\sqrt{3}\)
C \(\sqrt{48}\)
D \(3\sqrt{2}\)
Explanation opens after your attempt
Correct Answer
A. \(2\sqrt{3}\)
Step 1
Concept
\(\sqrt{75}=5\sqrt{3}\) and \(\sqrt{27}=3\sqrt{3}\). The difference is \(2\sqrt{3}\).
Step 2
Why this answer is correct
The correct answer is A. \(2\sqrt{3}\). \(\sqrt{75}=5\sqrt{3}\) and \(\sqrt{27}=3\sqrt{3}\). The difference is \(2\sqrt{3}\).
Step 3
Exam Tip
\(\sqrt{75}=5\sqrt{3}\) और \(\sqrt{27}=3\sqrt{3}\) है। अंतर \(2\sqrt{3}\) मिलेगा।
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यदि \(a=\sqrt{20}\) है तो (a) का सरल रूप क्या है?
If \(a=\sqrt{20}\), what is the simplified form of (a)?
#surds
#simplification
#irrational-numbers
A \(2\sqrt{5}\)
B \(4\sqrt{5}\)
C \(\sqrt{10}\)
D \(5\sqrt{2}\)
Explanation opens after your attempt
Correct Answer
A. \(2\sqrt{5}\)
Step 1
Concept
\(\sqrt{20}=\sqrt{4\times5}=2\sqrt{5}\). Look for a perfect square factor inside the root.
Step 2
Why this answer is correct
The correct answer is A. \(2\sqrt{5}\). \(\sqrt{20}=\sqrt{4\times5}=2\sqrt{5}\). Look for a perfect square factor inside the root.
Step 3
Exam Tip
\(\sqrt{20}=\sqrt{4\times5}=2\sqrt{5}\) होता है। जड़ में पूर्ण वर्ग गुणनखंड खोजें।
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कौन सा विकल्प \(\sqrt{242}\) का सरल रूप है?
Which option is the simplified form of \(\sqrt{242}\)?
#surds
#simplification
#square-root
A \(11\sqrt{2}\)
B \(22\sqrt{2}\)
C \(2\sqrt{11}\)
D \(\sqrt{121}\)
Explanation opens after your attempt
Correct Answer
A. \(11\sqrt{2}\)
Step 1
Concept
\(\sqrt{242}=\sqrt{121\times2}=11\sqrt{2}\). Identify the perfect square factor inside the root.
Step 2
Why this answer is correct
The correct answer is A. \(11\sqrt{2}\). \(\sqrt{242}=\sqrt{121\times2}=11\sqrt{2}\). Identify the perfect square factor inside the root.
Step 3
Exam Tip
\(\sqrt{242}=\sqrt{121\times2}=11\sqrt{2}\) है। जड़ में पूर्ण वर्ग गुणनखंड पहचानें।
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\(\sqrt{2}+\sqrt{18}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{2}+\sqrt{18}\)?
#surds
#addition
#simplification
A \(4\sqrt{2}\)
B \(2\sqrt{20}\)
C \(\sqrt{20}\)
D \(10\sqrt{2}\)
Explanation opens after your attempt
Correct Answer
A. \(4\sqrt{2}\)
Step 1
Concept
\(\sqrt{18}=3\sqrt{2}\) so the sum is \(4\sqrt{2}\). First simplify the root and then add.
Step 2
Why this answer is correct
The correct answer is A. \(4\sqrt{2}\). \(\sqrt{18}=3\sqrt{2}\) so the sum is \(4\sqrt{2}\). First simplify the root and then add.
Step 3
Exam Tip
\(\sqrt{18}=3\sqrt{2}\) इसलिए योग \(4\sqrt{2}\) है। पहले जड़ को सरल करें फिर जोड़ें।
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कौन सा विकल्प \(\sqrt{200}\) का सरल रूप है?
Which option is the simplified form of \(\sqrt{200}\)?
#surds
#square-root
#simplification
A \(10\sqrt{2}\)
B \(20\sqrt{2}\)
C \(5\sqrt{8}\)
D \(2\sqrt{100}\)
Explanation opens after your attempt
Correct Answer
A. \(10\sqrt{2}\)
Step 1
Concept
\(\sqrt{200}=\sqrt{100\times2}=10\sqrt{2}\). Taking out the greatest perfect square is a good method.
Step 2
Why this answer is correct
The correct answer is A. \(10\sqrt{2}\). \(\sqrt{200}=\sqrt{100\times2}=10\sqrt{2}\). Taking out the greatest perfect square is a good method.
Step 3
Exam Tip
\(\sqrt{200}=\sqrt{100\times2}=10\sqrt{2}\) है। सबसे बड़े पूर्ण वर्ग को बाहर निकालना अच्छा तरीका है।
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कौन सा विकल्प \(\sqrt{150}\) का सरल रूप है?
Which option is the simplified form of \(\sqrt{150}\)?
#surds
#simplification
#square-root
A \(5\sqrt{6}\)
B \(15\sqrt{10}\)
C \(10\sqrt{15}\)
D \(3\sqrt{50}\)
Explanation opens after your attempt
Correct Answer
A. \(5\sqrt{6}\)
Step 1
Concept
\(\sqrt{150}=\sqrt{25\times6}=5\sqrt{6}\). The perfect square factor inside the root is (25).
Step 2
Why this answer is correct
The correct answer is A. \(5\sqrt{6}\). \(\sqrt{150}=\sqrt{25\times6}=5\sqrt{6}\). The perfect square factor inside the root is (25).
Step 3
Exam Tip
\(\sqrt{150}=\sqrt{25\times6}=5\sqrt{6}\) है। जड़ में पूर्ण वर्ग गुणनखंड (25) है।
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\(\frac{5}{\sqrt{5}}\) का सरल मान क्या है?
What is the simplified value of \(\frac{5}{\sqrt{5}}\)?
#division
#simplification
#irrational-numbers
A \(\sqrt{5}\)
B \(5\sqrt{5}\)
C (1)
D \(\frac{1}{5}\)
Explanation opens after your attempt
Correct Answer
A. \(\sqrt{5}\)
Step 1
Concept
\(\frac{5}{\sqrt{5}}=\sqrt{5}\) because \(5=\sqrt{5}\times\sqrt{5}\). Learn to simplify denominators with roots.
Step 2
Why this answer is correct
The correct answer is A. \(\sqrt{5}\). \(\frac{5}{\sqrt{5}}=\sqrt{5}\) because \(5=\sqrt{5}\times\sqrt{5}\). Learn to simplify denominators with roots.
Step 3
Exam Tip
\(\frac{5}{\sqrt{5}}=\sqrt{5}\) है क्योंकि \(5=\sqrt{5}\times\sqrt{5}\)। जड़ वाले हर को सरल करना सीखें।
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\(\sqrt{98}-\sqrt{50}\) का मान क्या है?
What is the value of \(\sqrt{98}-\sqrt{50}\)?
#surds
#subtraction
#simplification
A \(2\sqrt{2}\)
B \(\sqrt{48}\)
C \(12\sqrt{2}\)
D \(7\sqrt{5}\)
Explanation opens after your attempt
Correct Answer
A. \(2\sqrt{2}\)
Step 1
Concept
\(\sqrt{98}=7\sqrt{2}\) and \(\sqrt{50}=5\sqrt{2}\). Their difference is \(2\sqrt{2}\).
Step 2
Why this answer is correct
The correct answer is A. \(2\sqrt{2}\). \(\sqrt{98}=7\sqrt{2}\) and \(\sqrt{50}=5\sqrt{2}\). Their difference is \(2\sqrt{2}\).
Step 3
Exam Tip
\(\sqrt{98}=7\sqrt{2}\) और \(\sqrt{50}=5\sqrt{2}\) है। अंतर \(2\sqrt{2}\) होगा।
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कौन सा विकल्प \(\sqrt{108}\) का सही सरल रूप है?
Which option is the correct simplified form of \(\sqrt{108}\)?
#surds
#square-root
#simplification
A \(6\sqrt{3}\)
B \(3\sqrt{6}\)
C \(9\sqrt{3}\)
D \(12\sqrt{3}\)
Explanation opens after your attempt
Correct Answer
A. \(6\sqrt{3}\)
Step 1
Concept
\(\sqrt{108}=\sqrt{36\times3}=6\sqrt{3}\). Taking out the perfect square simplifies the root.
Step 2
Why this answer is correct
The correct answer is A. \(6\sqrt{3}\). \(\sqrt{108}=\sqrt{36\times3}=6\sqrt{3}\). Taking out the perfect square simplifies the root.
Step 3
Exam Tip
\(\sqrt{108}=\sqrt{36\times3}=6\sqrt{3}\) है। पूर्ण वर्ग बाहर निकालने से जड़ सरल होती है।
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कौन सा विकल्प \(\sqrt{72}\) का सरल रूप है?
Which option is the simplified form of \(\sqrt{72}\)?
#surds
#simplification
#square-root
A \(6\sqrt{2}\)
B \(8\sqrt{2}\)
C \(3\sqrt{8}\)
D \(12\sqrt{2}\)
Explanation opens after your attempt
Correct Answer
A. \(6\sqrt{2}\)
Step 1
Concept
\(\sqrt{72}=\sqrt{36\times2}=6\sqrt{2}\). Find the large perfect square inside the root.
Step 2
Why this answer is correct
The correct answer is A. \(6\sqrt{2}\). \(\sqrt{72}=\sqrt{36\times2}=6\sqrt{2}\). Find the large perfect square inside the root.
Step 3
Exam Tip
\(\sqrt{72}=\sqrt{36\times2}=6\sqrt{2}\) है। जड़ के अंदर बड़ा पूर्ण वर्ग खोजें।
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कौन सा विकल्प \(\sqrt{80}\) का सही सरल रूप है?
Which option is the correct simplified form of \(\sqrt{80}\)?
#surds
#simplification
#square-root
A \(4\sqrt{5}\)
B \(8\sqrt{5}\)
C \(5\sqrt{4}\)
D \(2\sqrt{20}\)
Explanation opens after your attempt
Correct Answer
A. \(4\sqrt{5}\)
Step 1
Concept
\(\sqrt{80}=\sqrt{16\times5}=4\sqrt{5}\). Look for a perfect square factor inside the root.
Step 2
Why this answer is correct
The correct answer is A. \(4\sqrt{5}\). \(\sqrt{80}=\sqrt{16\times5}=4\sqrt{5}\). Look for a perfect square factor inside the root.
Step 3
Exam Tip
\(\sqrt{80}=\sqrt{16\times5}=4\sqrt{5}\) है। जड़ के अंदर पूर्ण वर्ग गुणनखंड खोजें।
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कौन सा विकल्प \(\sqrt{147}\) का सरल रूप है?
Which option is the simplified form of \(\sqrt{147}\)?
#surds
#simplification
#square-root
A \(7\sqrt{3}\)
B \(3\sqrt{7}\)
C \(21\sqrt{3}\)
D \(\sqrt{49}\)
Explanation opens after your attempt
Correct Answer
A. \(7\sqrt{3}\)
Step 1
Concept
\(\sqrt{147}=\sqrt{49\times3}=7\sqrt{3}\). Take the large perfect square outside the root.
Step 2
Why this answer is correct
The correct answer is A. \(7\sqrt{3}\). \(\sqrt{147}=\sqrt{49\times3}=7\sqrt{3}\). Take the large perfect square outside the root.
Step 3
Exam Tip
\(\sqrt{147}=\sqrt{49\times3}=7\sqrt{3}\) है। बड़े पूर्ण वर्ग को जड़ से बाहर निकालें।
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कौन सा विकल्प \(\sqrt{28}\) का सरल रूप है?
Which option is the simplified form of \(\sqrt{28}\)?
#surds
#square-root
#simplification
A \(2\sqrt{7}\)
B \(7\sqrt{2}\)
C \(4\sqrt{7}\)
D \(\sqrt{14}\)
Explanation opens after your attempt
Correct Answer
A. \(2\sqrt{7}\)
Step 1
Concept
\(\sqrt{28}=\sqrt{4\times7}=2\sqrt{7}\). The perfect square (4) comes outside.
Step 2
Why this answer is correct
The correct answer is A. \(2\sqrt{7}\). \(\sqrt{28}=\sqrt{4\times7}=2\sqrt{7}\). The perfect square (4) comes outside.
Step 3
Exam Tip
\(\sqrt{28}=\sqrt{4\times7}=2\sqrt{7}\) है। पूर्ण वर्ग (4) बाहर आता है।
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\(\frac{3}{\sqrt{3}}\) का सरल मान क्या है?
What is the simplified value of \(\frac{3}{\sqrt{3}}\)?
#simplification
#irrational-numbers
#division
A \(\sqrt{3}\)
B \(3\sqrt{3}\)
C (1)
D \(\frac{1}{3}\)
Explanation opens after your attempt
Correct Answer
A. \(\sqrt{3}\)
Step 1
Concept
\(\frac{3}{\sqrt{3}}=\sqrt{3}\) because \(3=\sqrt{3}\times\sqrt{3}\). Practice simplifying denominators with roots.
Step 2
Why this answer is correct
The correct answer is A. \(\sqrt{3}\). \(\frac{3}{\sqrt{3}}=\sqrt{3}\) because \(3=\sqrt{3}\times\sqrt{3}\). Practice simplifying denominators with roots.
Step 3
Exam Tip
\(\frac{3}{\sqrt{3}}=\sqrt{3}\) क्योंकि \(3=\sqrt{3}\times\sqrt{3}\)। जड़ वाले हर को सरल करने का अभ्यास करें।
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\(\sqrt{45}-\sqrt{20}\) का मान क्या है?
What is the value of \(\sqrt{45}-\sqrt{20}\)?
#surds
#subtraction
#simplification
A \(\sqrt{5}\)
B \(5\sqrt{5}\)
C \(\sqrt{25}\)
D \(13\sqrt{5}\)
Explanation opens after your attempt
Correct Answer
A. \(\sqrt{5}\)
Step 1
Concept
\(\sqrt{45}=3\sqrt{5}\) and \(\sqrt{20}=2\sqrt{5}\). The difference is \(\sqrt{5}\).
Step 2
Why this answer is correct
The correct answer is A. \(\sqrt{5}\). \(\sqrt{45}=3\sqrt{5}\) and \(\sqrt{20}=2\sqrt{5}\). The difference is \(\sqrt{5}\).
Step 3
Exam Tip
\(\sqrt{45}=3\sqrt{5}\) और \(\sqrt{20}=2\sqrt{5}\) है। अंतर \(\sqrt{5}\) है।
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\(\sqrt{75}\) का सही सरल रूप कौन सा है?
Which is the correct simplified form of \(\sqrt{75}\)?
#surds
#square-root
#simplification
A \(5\sqrt{3}\)
B \(3\sqrt{5}\)
C \(25\sqrt{3}\)
D \(\sqrt{15}\)
Explanation opens after your attempt
Correct Answer
A. \(5\sqrt{3}\)
Step 1
Concept
\(\sqrt{75}=\sqrt{25\times3}=5\sqrt{3}\). Take the perfect square factor (25) outside.
Step 2
Why this answer is correct
The correct answer is A. \(5\sqrt{3}\). \(\sqrt{75}=\sqrt{25\times3}=5\sqrt{3}\). Take the perfect square factor (25) outside.
Step 3
Exam Tip
\(\sqrt{75}=\sqrt{25\times3}=5\sqrt{3}\) है। पूर्ण वर्ग गुणनखंड (25) को बाहर निकालें।
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\(\sqrt{32}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{32}\)?
#surds
#simplification
#square-root
A \(4\sqrt{2}\)
B \(8\sqrt{2}\)
C \(2\sqrt{8}\)
D \(\sqrt{16}\)
Explanation opens after your attempt
Correct Answer
A. \(4\sqrt{2}\)
Step 1
Concept
\(\sqrt{32}=\sqrt{16\times2}=4\sqrt{2}\). Take out the greatest perfect square.
Step 2
Why this answer is correct
The correct answer is A. \(4\sqrt{2}\). \(\sqrt{32}=\sqrt{16\times2}=4\sqrt{2}\). Take out the greatest perfect square.
Step 3
Exam Tip
\(\sqrt{32}=\sqrt{16\times2}=4\sqrt{2}\) है। सबसे बड़ा पूर्ण वर्ग बाहर निकालें।
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\(\sqrt{98}\) को सरल करने पर क्या मिलेगा?
What do we get after simplifying \(\sqrt{98}\)?
#square-root
#surds
#simplification
A \(7\sqrt{2}\)
B \(14\sqrt{2}\)
C \(2\sqrt{7}\)
D \(\sqrt{49}\)
Explanation opens after your attempt
Correct Answer
A. \(7\sqrt{2}\)
Step 1
Concept
\(\sqrt{98}=\sqrt{49\times2}=7\sqrt{2}\). Take the perfect square (49) outside the root.
Step 2
Why this answer is correct
The correct answer is A. \(7\sqrt{2}\). \(\sqrt{98}=\sqrt{49\times2}=7\sqrt{2}\). Take the perfect square (49) outside the root.
Step 3
Exam Tip
\(\sqrt{98}=\sqrt{49\times2}=7\sqrt{2}\) है। पूर्ण वर्ग (49) को जड़ से बाहर निकालें।
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यदि \(x=2+\sqrt{5}\) है तो (x-2) किस प्रकार की संख्या है?
If \(x=2+\sqrt{5}\), what type of number is (x-2)?
#irrational-numbers
#expression
#simplification
A अपरिमेय संख्या / Irrational number
B परिमेय संख्या / Rational number
C पूर्णांक / Integer
D शून्य / Zero
Explanation opens after your attempt
Correct Answer
A. अपरिमेय संख्या / Irrational number
Step 1
Concept
\(x-2=\sqrt{5}\), which is irrational. In such questions simplify the expression first.
Step 2
Why this answer is correct
The correct answer is A. अपरिमेय संख्या / Irrational number. \(x-2=\sqrt{5}\), which is irrational. In such questions simplify the expression first.
Step 3
Exam Tip
\(x-2=\sqrt{5}\) है जो अपरिमेय है। ऐसे प्रश्नों में पहले अभिव्यक्ति को सरल करें।
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कौन सी संख्या \(\sqrt{50}\) का सही सरल रूप है?
Which number is the correct simplified form of \(\sqrt{50}\)?
#surds
#simplification
#irrational-numbers
A \(5\sqrt{2}\)
B \(10\sqrt{5}\)
C \(2\sqrt{5}\)
D \(\sqrt{25}\)
Explanation opens after your attempt
Correct Answer
A. \(5\sqrt{2}\)
Step 1
Concept
\(\sqrt{50}=\sqrt{25\times2}=5\sqrt{2}\). Find the greatest perfect square inside the root.
Step 2
Why this answer is correct
The correct answer is A. \(5\sqrt{2}\). \(\sqrt{50}=\sqrt{25\times2}=5\sqrt{2}\). Find the greatest perfect square inside the root.
Step 3
Exam Tip
\(\sqrt{50}=\sqrt{25\times2}=5\sqrt{2}\) है। जड़ के अंदर सबसे बड़ा पूर्ण वर्ग खोजें।
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\(\sqrt{27}\) का सरल रूप कौन सा है?
Which is the simplified form of \(\sqrt{27}\)?
#square-root
#surds
#simplification
A \(3\sqrt{3}\)
B \(9\sqrt{3}\)
C \(\sqrt{9}\)
D \(2\sqrt{3}\)
Explanation opens after your attempt
Correct Answer
A. \(3\sqrt{3}\)
Step 1
Concept
\(\sqrt{27}=\sqrt{9\times3}=3\sqrt{3}\). Take out the greatest perfect square factor.
Step 2
Why this answer is correct
The correct answer is A. \(3\sqrt{3}\). \(\sqrt{27}=\sqrt{9\times3}=3\sqrt{3}\). Take out the greatest perfect square factor.
Step 3
Exam Tip
\(\sqrt{27}=\sqrt{9\times3}=3\sqrt{3}\) है। सबसे बड़े पूर्ण वर्ग गुणनखंड को निकालें।
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\(\sqrt{20}+\sqrt{45}\) का सरल रूप क्या है?
What is the simplest form of \(\sqrt{20}+\sqrt{45}\)?
#surds
#addition
#simplification
A \(5\sqrt{5}\)
B \(\sqrt{65}\)
C \(13\sqrt{5}\)
D \(25\sqrt{5}\)
Explanation opens after your attempt
Correct Answer
A. \(5\sqrt{5}\)
Step 1
Concept
\(\sqrt{20}=2\sqrt{5}\) and \(\sqrt{45}=3\sqrt{5}\). Adding gives \(5\sqrt{5}\).
Step 2
Why this answer is correct
The correct answer is A. \(5\sqrt{5}\). \(\sqrt{20}=2\sqrt{5}\) and \(\sqrt{45}=3\sqrt{5}\). Adding gives \(5\sqrt{5}\).
Step 3
Exam Tip
\(\sqrt{20}=2\sqrt{5}\) और \(\sqrt{45}=3\sqrt{5}\) है। जोड़ने पर \(5\sqrt{5}\) मिलता है।
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\(\sqrt{2}\) और \(\sqrt{8}\) के बारे में सही संबंध क्या है?
What is the correct relation between \(\sqrt{2}\) and \(\sqrt{8}\)?
#surds
#simplification
#irrational-numbers
A \(\sqrt{8}=2\sqrt{2}\)
B \(\sqrt{8}=4\sqrt{2}\)
C \(\sqrt{8}=\sqrt{2}\)
D \(\sqrt{8}=8\sqrt{2}\)
Explanation opens after your attempt
Correct Answer
A. \(\sqrt{8}=2\sqrt{2}\)
Step 1
Concept
\(\sqrt{8}=\sqrt{4\times2}=2\sqrt{2}\). Take the square factor outside.
Step 2
Why this answer is correct
The correct answer is A. \(\sqrt{8}=2\sqrt{2}\). \(\sqrt{8}=\sqrt{4\times2}=2\sqrt{2}\). Take the square factor outside.
Step 3
Exam Tip
\(\sqrt{8}=\sqrt{4\times2}=2\sqrt{2}\) है। वर्ग गुणनखंड को बाहर निकालें।
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\(\sqrt{12}\) को सरल करने पर क्या मिलेगा?
What do we get after simplifying \(\sqrt{12}\)?
#surds
#simplification
#square-root
A \(2\sqrt{3}\)
B \(3\sqrt{2}\)
C \(6\sqrt{2}\)
D \(\sqrt{6}\)
Explanation opens after your attempt
Correct Answer
A. \(2\sqrt{3}\)
Step 1
Concept
\(\sqrt{12}=\sqrt{4\times3}=2\sqrt{3}\). Look for a perfect square inside the root.
Step 2
Why this answer is correct
The correct answer is A. \(2\sqrt{3}\). \(\sqrt{12}=\sqrt{4\times3}=2\sqrt{3}\). Look for a perfect square inside the root.
Step 3
Exam Tip
\(\sqrt{12}=\sqrt{4\times3}=2\sqrt{3}\) है। जड़ के अंदर पूर्ण वर्ग खोजें।
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\(\sqrt{18}\) का सही सरल रूप कौन सा है?
Which is the correct simplified form of \(\sqrt{18}\)?
#simplification
#square-root
#surds
A \(3\sqrt{2}\)
B \(9\sqrt{2}\)
C \(2\sqrt{3}\)
D \(\sqrt{9}\)
Explanation opens after your attempt
Correct Answer
A. \(3\sqrt{2}\)
Step 1
Concept
\(\sqrt{18}=\sqrt{9\times2}=3\sqrt{2}\). Take the perfect square outside the root.
Step 2
Why this answer is correct
The correct answer is A. \(3\sqrt{2}\). \(\sqrt{18}=\sqrt{9\times2}=3\sqrt{2}\). Take the perfect square outside the root.
Step 3
Exam Tip
\(\sqrt{18}=\sqrt{9\times2}=3\sqrt{2}\) है। पूर्ण वर्ग को जड़ से बाहर निकालें।
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\(\sqrt{2}+\sqrt{2}\) का सरल रूप क्या है?
What is the simplest form of \(\sqrt{2}+\sqrt{2}\)?
#surds
#simplification
#irrational-numbers
A \(2\sqrt{2}\)
B \(\sqrt{4}\)
C (4)
D \(\sqrt{2}\)
Explanation opens after your attempt
Correct Answer
A. \(2\sqrt{2}\)
Step 1
Concept
Adding like terms gives \(2\sqrt{2}\). Writing it as \(\sqrt{4}\) is wrong.
Step 2
Why this answer is correct
The correct answer is A. \(2\sqrt{2}\). Adding like terms gives \(2\sqrt{2}\). Writing it as \(\sqrt{4}\) is wrong.
Step 3
Exam Tip
समान पदों को जोड़ने पर \(2\sqrt{2}\) मिलता है। इसे \(\sqrt{4}\) लिखना गलत है।
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\(\frac{18}{999}\) का दशमलव प्रसार कैसा होगा?
What type of decimal expansion will \(\frac{18}{999}\) have?
#recurring-decimal
#denominator-test
#simplification
#real-numbers
A सांत / Terminating
B असांत आवर्ती / Non-terminating recurring
C असांत अनावर्ती / Non-terminating non-recurring
D शून्य / Zero
Explanation opens after your attempt
Correct Answer
B. असांत आवर्ती / Non-terminating recurring
Step 1
Concept
\(\frac{18}{999}=\frac{2}{111}\).
Step 2
Why this answer is correct
\(111=3\cdot 37\), which has factors other than (2) and (5). Therefore the decimal is non-terminating recurring.
Step 3
Exam Tip
Fractions from recurring decimals often have denominators made from (9)'s. चरण 1: \(\frac{18}{999}=\frac{2}{111}\) है। चरण 2: \(111=3\cdot 37\), जिसमें (2) और (5) के अलावा गुणनखंड हैं। इसलिए दशमलव असांत आवर्ती होगा। चरण 3: आवर्ती दशमलव से आई भिन्नों में हर में अक्सर (9) वाले गुणनखंड होते हैं।
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\(\frac{27}{2^3\cdot 3^3\cdot 5^2}\) को सरल करने के बाद हर क्या बचेगा?
What denominator remains after reducing \(\frac{27}{2^3\cdot 3^3\cdot 5^2}\)?
#simplification
#prime-powers
#denominator
#terminating-decimal
A \(2^3\cdot 5^2\)
B \(3^3\cdot 5^2\)
C \(2^3\cdot 3\cdot 5^2\)
D \(5^2\)
Explanation opens after your attempt
Correct Answer
A. \(2^3\cdot 5^2\)
Step 1
Concept
\(27=3^3\).
Step 2
Why this answer is correct
The full factor \(3^3\) cancels from the denominator, leaving \(2^3\cdot 5^2\).
Step 3
Exam Tip
Decide the decimal type from the denominator left after cancellation. चरण 1: \(27=3^3\) है। चरण 2: हर का \(3^3\) पूरा कट जाएगा, इसलिए हर \(2^3\cdot 5^2\) बचेगा। चरण 3: कटौती के बाद बचे हर से ही दशमलव का प्रकार तय करें।
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\(\frac{6}{375}\) को सरलतम रूप में लिखने पर दशमलव प्रसार कैसा होगा?
What type of decimal expansion will \(\frac{6}{375}\) have after reducing it to lowest form?
#simplification
#terminating-decimal
#decimal-places
#class-10
A सांत और (3) स्थानों पर समाप्त / Terminating after (3) places
B सांत और (4) स्थानों पर समाप्त / Terminating after (4) places
C असांत आवर्ती / Non-terminating recurring
D असांत अनावर्ती / Non-terminating non-recurring
Explanation opens after your attempt
Correct Answer
A. सांत और (3) स्थानों पर समाप्त / Terminating after (3) places
Step 1
Concept
\(\frac{6}{375}=\frac{2}{125}\).
Step 2
Why this answer is correct
Since \(125=5^3\), the decimal terminates after (3) places.
Step 3
Exam Tip
Even for small fractions, reduce to lowest form first. चरण 1: \(\frac{6}{375}=\frac{2}{125}\) है। चरण 2: \(125=5^3\), इसलिए दशमलव (3) स्थानों पर समाप्त होगा। चरण 3: छोटी भिन्नों में भी सरलतम रूप निकालना जरूरी है।
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कथन: \(\frac{35}{280}\) का दशमलव सांत है। कारण: \(\frac{35}{280}=\frac{1}{8}\) है। सही विकल्प चुनिए।
Assertion: The decimal expansion of \(\frac{35}{280}\) is terminating. Reason: \(\frac{35}{280}=\frac{1}{8}\). Choose the correct option.
#assertion-reason
#simplification
#terminating-decimal
#pyq-pattern
A कथन और कारण दोनों सही हैं तथा कारण कथन को समझाता है / Both assertion and reason are true, and the reason explains the assertion
B कथन और कारण दोनों सही हैं पर कारण कथन को नहीं समझाता / Both are true, but the reason does not explain the assertion
C कथन सही है पर कारण गलत है / Assertion is true, but reason is false
D कथन गलत है पर कारण सही है / Assertion is false, but reason is true
Explanation opens after your attempt
Correct Answer
A. कथन और कारण दोनों सही हैं तथा कारण कथन को समझाता है / Both assertion and reason are true, and the reason explains the assertion
Step 1
Concept
Dividing \(\frac{35}{280}\) by (35) gives \(\frac{1}{8}\).
Step 2
Why this answer is correct
Since \(8=2^3\), the decimal terminates. The reason correctly explains the assertion.
Step 3
Exam Tip
In assertion-reason questions, also check whether the reason explains the assertion. चरण 1: \(\frac{35}{280}\) को (35) से भाग देने पर \(\frac{1}{8}\) मिलता है। चरण 2: \(8=2^3\), इसलिए दशमलव सांत होगा। कारण कथन को सही ढंग से समझाता है। चरण 3: कथन-कारण प्रश्न में कारण की व्याख्या भी जाँचें।
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