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( \(4\sqrt{3}+3\sqrt{2}\)2 ) का विस्तार क्या है?
What is the expansion of ( \(4\sqrt{3}+3\sqrt{2}\)2 )?
#real numbers
#surd square
#identity
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A \(66+24\sqrt{6}\)
B \(30+24\sqrt{6}\)
C \(66+12\sqrt{6}\)
D \(48+18\sqrt{6}\)
Explanation opens after your attempt
Correct Answer
A. \(66+24\sqrt{6}\)
Step 1
Concept
The first square is (48) and the second square is (18). The middle term is \(2\times4\sqrt{3}\times3\sqrt{2}=24\sqrt{6}\).
Step 2
Why this answer is correct
The correct answer is A. \(66+24\sqrt{6}\). The first square is (48) and the second square is (18). The middle term is \(2\times4\sqrt{3}\times3\sqrt{2}=24\sqrt{6}\).
Step 3
Exam Tip
पहला वर्ग (48) और दूसरा वर्ग (18) है। मध्य पद \(2\times4\sqrt{3}\times3\sqrt{2}=24\sqrt{6}\) है।
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( \(6\sqrt{5}-\sqrt{7}\)2 ) का सरल रूप क्या है?
What is the simplified form of ( \(6\sqrt{5}-\sqrt{7}\)2 )?
#real numbers
#surd square
#minus
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A \(187-12\sqrt{35}\)
B \(173-6\sqrt{35}\)
C \(187-6\sqrt{35}\)
D \(180-12\sqrt{35}\)
Explanation opens after your attempt
Correct Answer
A. \(187-12\sqrt{35}\)
Step 1
Concept
( \(6\sqrt{5}\)2 =180 ) and ( \(\sqrt{7}\)2 =7 ). The middle term \(12\sqrt{35}\) is subtracted.
Step 2
Why this answer is correct
The correct answer is A. \(187-12\sqrt{35}\). ( \(6\sqrt{5}\)2 =180 ) and ( \(\sqrt{7}\)2 =7 ). The middle term \(12\sqrt{35}\) is subtracted.
Step 3
Exam Tip
( \(6\sqrt{5}\)2 =180 ) और ( \(\sqrt{7}\)2 =7 ) हैं। मध्य पद \(12\sqrt{35}\) घटेगा।
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( \(3\sqrt{11}+2\sqrt{6}\)\(3\sqrt{11}-2\sqrt{6}\) ) का मान क्या है?
What is the value of ( \(3\sqrt{11}+2\sqrt{6}\)\(3\sqrt{11}-2\sqrt{6}\) )?
#real numbers
#conjugate
#difference of squares
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A (75)
B (123)
C (51)
D \(99-4\sqrt{66}\)
Explanation opens after your attempt
Step 1
Concept
This is a difference of squares. ( \(3\sqrt{11}\)2 -\(2\sqrt{6}\)2 =99-24=75 ).
Step 2
Why this answer is correct
The correct answer is A. (75). This is a difference of squares. ( \(3\sqrt{11}\)2 -\(2\sqrt{6}\)2 =99-24=75 ).
Step 3
Exam Tip
यह अंतर के वर्ग का रूप है। ( \(3\sqrt{11}\)2 -\(2\sqrt{6}\)2 =99-24=75 )।
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\( \sqrt{14-4\sqrt{10}} \) का धनात्मक सरल रूप क्या है?
What is the positive simplified form of \( \sqrt{14-4\sqrt{10}} \)?
#real numbers
#nested radical
#principal root
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A \( \sqrt{10}-2 \)
B \( \sqrt{10}+2 \)
C \(2-\sqrt{10}\)
D \( \sqrt{14}-\sqrt{10} \)
Explanation opens after your attempt
Correct Answer
A. \( \sqrt{10}-2 \)
Step 1
Concept
( \(\sqrt{10}-2\)2 =10-4\sqrt{10}+4=14-4\sqrt{10} ). The positive principal square root is \( \sqrt{10}-2 \).
Step 2
Why this answer is correct
The correct answer is A. \( \sqrt{10}-2 \). ( \(\sqrt{10}-2\)2 =10-4\sqrt{10}+4=14-4\sqrt{10} ). The positive principal square root is \( \sqrt{10}-2 \).
Step 3
Exam Tip
( \(\sqrt{10}-2\)2 =10-4\sqrt{10}+4=14-4\sqrt{10} )। धनात्मक मुख्य वर्गमूल \( \sqrt{10}-2 \) है।
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\( \sqrt{130} \) और (11.4) में कौन बड़ा है?
Which is greater between \( \sqrt{130} \) and (11.4)?
#real numbers
#comparison
#square root
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A \( \sqrt{130} \)
B (11.4)
C दोनों बराबर / Both are equal
D निर्धारित नहीं / Cannot be determined
Explanation opens after your attempt
Correct Answer
A. \( \sqrt{130} \)
Step 1
Concept
\(11.4^2=129.96\), which is slightly less than (130). Therefore \( \sqrt{130}>11.4 \).
Step 2
Why this answer is correct
The correct answer is A. \( \sqrt{130} \). \(11.4^2=129.96\), which is slightly less than (130). Therefore \( \sqrt{130}>11.4 \).
Step 3
Exam Tip
\(11.4^2=129.96\) जो (130) से थोड़ा कम है। इसलिए \( \sqrt{130}>11.4 \) है।
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यदि \( \sqrt{n} \) (18) और (19) के बीच है तो (n) के लिए सही सीमा कौन सी है?
If \( \sqrt{n} \) lies between (18) and (19), which range is correct for (n)?
#real numbers
#inequality
#square root
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A (324<n<361)
B (18<n<19)
C (289<n<324)
D (361<n<400)
Explanation opens after your attempt
Correct Answer
A. (324<n<361)
Step 1
Concept
Squaring both sides gives \(18^2<n<19^2\). Therefore (324<n<361) is correct.
Step 2
Why this answer is correct
The correct answer is A. (324<n<361). Squaring both sides gives \(18^2<n<19^2\). Therefore (324<n<361) is correct.
Step 3
Exam Tip
दोनों ओर वर्ग करने पर \(18^2<n<19^2\) मिलेगा। इसलिए (324<n<361) सही है।
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\( \sqrt{a+b}=\sqrt{a}+\sqrt{b} \) को जाँचने के लिए कौन सा उदाहरण इसे गलत दिखाता है?
Which example shows that \( \sqrt{a+b}=\sqrt{a}+\sqrt{b} \) is false?
#real numbers
#common error
#square roots
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A \( \sqrt{4+9}\neq\sqrt{4}+\sqrt{9} \)
B \( \sqrt{0+9}=\sqrt{0}+\sqrt{9} \)
C \( \sqrt{4+0}=\sqrt{4}+\sqrt{0} \)
D \( \sqrt{1+0}=\sqrt{1}+\sqrt{0} \)
Explanation opens after your attempt
Correct Answer
A. \( \sqrt{4+9}\neq\sqrt{4}+\sqrt{9} \)
Step 1
Concept
\( \sqrt{13} \) and (2+3=5) are not equal. Therefore square root cannot be distributed directly over addition.
Step 2
Why this answer is correct
The correct answer is A. \( \sqrt{4+9}\neq\sqrt{4}+\sqrt{9} \). \( \sqrt{13} \) and (2+3=5) are not equal. Therefore square root cannot be distributed directly over addition.
Step 3
Exam Tip
\( \sqrt{13} \) और (2+3=5) बराबर नहीं हैं। इसलिए वर्गमूल को जोड़ के अंदर सीधे नहीं बाँटते।
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\( \sqrt{ab}\times\sqrt{ab} \) का मान क्या है जहाँ \(ab\geq0\)?
What is the value of \( \sqrt{ab}\times\sqrt{ab} \) where \(ab\geq0\)?
#real numbers
#square root property
#concept
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A (ab)
B (2ab)
C \( \sqrt{2ab} \)
D \(a^2b^2\)
Explanation opens after your attempt
Step 1
Concept
Multiplying the square root of a non-negative number by itself gives the same number. Therefore the value is (ab).
Step 2
Why this answer is correct
The correct answer is A. (ab). Multiplying the square root of a non-negative number by itself gives the same number. Therefore the value is (ab).
Step 3
Exam Tip
किसी गैर-ऋणात्मक संख्या के वर्गमूल को स्वयं से गुणा करने पर वही संख्या मिलती है। इसलिए मान (ab) है।
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