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( \(3\sqrt{2}+2\sqrt{3}\)2 ) का विस्तार क्या है?
What is the expansion of ( \(3\sqrt{2}+2\sqrt{3}\)2 )?
#real numbers
#surd square
#identity
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A \(30+12\sqrt{6}\)
B \(18+12\sqrt{6}\)
C \(30+6\sqrt{6}\)
D \(24+12\sqrt{5}\)
Explanation opens after your attempt
Correct Answer
A. \(30+12\sqrt{6}\)
Step 1
Concept
Using \(a^2+2ab+b^2\), we get \(18+12\sqrt{6}+12=30+12\sqrt{6}\). Do not forget the middle term.
Step 2
Why this answer is correct
The correct answer is A. \(30+12\sqrt{6}\). Using \(a^2+2ab+b^2\), we get \(18+12\sqrt{6}+12=30+12\sqrt{6}\). Do not forget the middle term.
Step 3
Exam Tip
\(a^2+2ab+b^2\) लगाने पर \(18+12\sqrt{6}+12=30+12\sqrt{6}\) मिलता है। मध्य पद को न भूलें।
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( \(5\sqrt{3}-2\sqrt{5}\)2 ) का सरल रूप क्या है?
What is the simplified form of ( \(5\sqrt{3}-2\sqrt{5}\)2 )?
#real numbers
#surd square
#minus
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A \(95-20\sqrt{15}\)
B \(75-20\sqrt{15}\)
C \(55-10\sqrt{15}\)
D \(95-10\sqrt{15}\)
Explanation opens after your attempt
Correct Answer
A. \(95-20\sqrt{15}\)
Step 1
Concept
( \(5\sqrt{3}\)2 =75 ) and ( \(2\sqrt{5}\)2 =20 ). The middle term \(2\times5\sqrt{3}\times2\sqrt{5}=20\sqrt{15}\) is subtracted.
Step 2
Why this answer is correct
The correct answer is A. \(95-20\sqrt{15}\). ( \(5\sqrt{3}\)2 =75 ) and ( \(2\sqrt{5}\)2 =20 ). The middle term \(2\times5\sqrt{3}\times2\sqrt{5}=20\sqrt{15}\) is subtracted.
Step 3
Exam Tip
( \(5\sqrt{3}\)2 =75 ) और ( \(2\sqrt{5}\)2 =20 ) हैं। मध्य पद \(2\times5\sqrt{3}\times2\sqrt{5}=20\sqrt{15}\) घटेगा।
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( \(2\sqrt{7}+\sqrt{5}\)\(2\sqrt{7}-\sqrt{5}\) ) का मान क्या है?
What is the value of ( \(2\sqrt{7}+\sqrt{5}\)\(2\sqrt{7}-\sqrt{5}\) )?
#real numbers
#conjugate
#difference of squares
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A (23)
B (33)
C \(28-2\sqrt{35}\)
D \(28+\sqrt{5}\)
Explanation opens after your attempt
Step 1
Concept
This is a difference of squares. ( \(2\sqrt{7}\)2 -\(\sqrt{5}\)2 =28-5=23 ).
Step 2
Why this answer is correct
The correct answer is A. (23). This is a difference of squares. ( \(2\sqrt{7}\)2 -\(\sqrt{5}\)2 =28-5=23 ).
Step 3
Exam Tip
यह अंतर के वर्ग का रूप है। ( \(2\sqrt{7}\)2 -\(\sqrt{5}\)2 =28-5=23 )।
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\( \sqrt{11-6\sqrt{2}} \) का धनात्मक सरल रूप क्या है?
What is the positive simplified form of \( \sqrt{11-6\sqrt{2}} \)?
#real numbers
#nested radical
#principal root
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A \(3-\sqrt{2}\)
B \(3+\sqrt{2}\)
C \( \sqrt{11}-\sqrt{2} \)
D \( \sqrt{9}-\sqrt{2} \)
Explanation opens after your attempt
Correct Answer
A. \(3-\sqrt{2}\)
Step 1
Concept
( \(3-\sqrt{2}\)2 =9-6\sqrt{2}+2=11-6\sqrt{2} ). Choose the positive principal square root.
Step 2
Why this answer is correct
The correct answer is A. \(3-\sqrt{2}\). ( \(3-\sqrt{2}\)2 =9-6\sqrt{2}+2=11-6\sqrt{2} ). Choose the positive principal square root.
Step 3
Exam Tip
( \(3-\sqrt{2}\)2 =9-6\sqrt{2}+2=11-6\sqrt{2} )। धनात्मक मुख्य वर्गमूल चुनें।
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\( \sqrt{50} \) और (7.08) में कौन बड़ा है?
Which is greater between \( \sqrt{50} \) and (7.08)?
#real numbers
#comparison
#square root
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A \( \sqrt{50} \)
B (7.08)
C दोनों बराबर / Both are equal
D निर्धारित नहीं / Cannot be determined
Explanation opens after your attempt
Step 1
Concept
\(7.08^2=50.1264\), which is greater than (50). Therefore \(7.08>\sqrt{50}\).
Step 2
Why this answer is correct
The correct answer is B. (7.08). \(7.08^2=50.1264\), which is greater than (50). Therefore \(7.08>\sqrt{50}\).
Step 3
Exam Tip
\(7.08^2=50.1264\) जो (50) से बड़ा है। इसलिए \(7.08>\sqrt{50}\) है।
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यदि \( \sqrt{n} \) (12) और (13) के बीच है तो (n) के लिए सही सीमा कौन सी है?
If \( \sqrt{n} \) lies between (12) and (13), which range is correct for (n)?
#real numbers
#inequality
#square root
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A (144<n<169)
B (12<n<13)
C (121<n<144)
D (169<n<196)
Explanation opens after your attempt
Correct Answer
A. (144<n<169)
Step 1
Concept
Squaring both sides gives \(12^2<n<13^2\). Therefore (144<n<169) is correct.
Step 2
Why this answer is correct
The correct answer is A. (144<n<169). Squaring both sides gives \(12^2<n<13^2\). Therefore (144<n<169) is correct.
Step 3
Exam Tip
दोनों ओर वर्ग करने पर \(12^2<n<13^2\) मिलेगा। इसलिए (144<n<169) सही है।
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\( \sqrt{a}+\sqrt{b}=\sqrt{a+b} \) सामान्यतः कब सही नहीं होता?
When is \( \sqrt{a}+\sqrt{b}=\sqrt{a+b} \) generally not correct?
#real numbers
#common error
#square roots
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A जब (a) और (b) दोनों धनात्मक हों / When (a) and (b) are both positive
B जब (a=0) हो / When (a=0)
C जब (b=0) हो / When (b=0)
D जब एक पद शून्य हो / When one term is zero
Explanation opens after your attempt
Correct Answer
A. जब (a) और (b) दोनों धनात्मक हों / When (a) and (b) are both positive
Step 1
Concept
Generally \( \sqrt{a}+\sqrt{b} \neq \sqrt{a+b} \). For example, \( \sqrt{4}+\sqrt{9}=5 \), not \( \sqrt{13} \).
Step 2
Why this answer is correct
The correct answer is A. जब (a) और (b) दोनों धनात्मक हों / When (a) and (b) are both positive. Generally \( \sqrt{a}+\sqrt{b} \neq \sqrt{a+b} \). For example, \( \sqrt{4}+\sqrt{9}=5 \), not \( \sqrt{13} \).
Step 3
Exam Tip
सामान्यतः \( \sqrt{a}+\sqrt{b} \neq \sqrt{a+b} \) होता है। उदाहरण के लिए \( \sqrt{4}+\sqrt{9}=5 \) लेकिन \( \sqrt{13} \) नहीं।
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\( \sqrt{a}\times\sqrt{a} \) का मान क्या है जहाँ \(a\geq0\)?
What is the value of \( \sqrt{a}\times\sqrt{a} \) where \(a\geq0\)?
#real numbers
#square root property
#concept
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A (a)
B (2a)
C \( \sqrt{2a} \)
D \(a^2\)
Explanation opens after your attempt
Step 1
Concept
Multiplying the square root of the same non-negative number by itself gives the number. Therefore the value is (a).
Step 2
Why this answer is correct
The correct answer is A. (a). Multiplying the square root of the same non-negative number by itself gives the number. Therefore the value is (a).
Step 3
Exam Tip
एक ही गैर-ऋणात्मक संख्या के वर्गमूल को स्वयं से गुणा करने पर वही संख्या मिलती है। इसलिए मान (a) है।
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