\( \sqrt{1125} \) का सरल करणी रूप क्या है?
What is the simplified surd form of \( \sqrt{1125} \)?
#real numbers
#surds
#simplification
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A \(25\sqrt{5}\)
B \(15\sqrt{3}\)
C \(15\sqrt{5}\)
D \(75\sqrt{5}\)
Explanation opens after your attempt
Correct Answer
C. \(15\sqrt{5}\)
Step 1
Concept
Since \(1125=225\times5\), \( \sqrt{1125}=15\sqrt{5} \). First take out the largest perfect-square factor.
Step 2
Why this answer is correct
The correct answer is C. \(15\sqrt{5}\). Since \(1125=225\times5\), \( \sqrt{1125}=15\sqrt{5} \). First take out the largest perfect-square factor.
Step 3
Exam Tip
\(1125=225\times5\) इसलिए \( \sqrt{1125}=15\sqrt{5} \)। सबसे बड़ा पूर्ण वर्ग गुणनखंड पहले निकालें।
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\( \sqrt{1452} \) को सरल करने पर क्या मिलेगा?
What is obtained by simplifying \( \sqrt{1452} \)?
#real numbers
#radicals
#simplification
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A \(11\sqrt{12}\)
B \(22\sqrt{3}\)
C \(44\sqrt{3}\)
D \(121\sqrt{3}\)
Explanation opens after your attempt
Correct Answer
B. \(22\sqrt{3}\)
Step 1
Concept
\(1452=484\times3\) and \( \sqrt{484}=22 \). So the simplified form is \(22\sqrt{3}\).
Step 2
Why this answer is correct
The correct answer is B. \(22\sqrt{3}\). \(1452=484\times3\) and \( \sqrt{484}=22 \). So the simplified form is \(22\sqrt{3}\).
Step 3
Exam Tip
\(1452=484\times3\) और \( \sqrt{484}=22 \) है। इसलिए सरल रूप \(22\sqrt{3}\) है।
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\(5\sqrt{20}-2\sqrt{125}+\sqrt{45}\) का सरल रूप क्या है?
What is the simplified form of \(5\sqrt{20}-2\sqrt{125}+\sqrt{45}\)?
#real numbers
#surd combination
#calculation
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A \(13\sqrt{5}\)
B \(5\sqrt{5}\)
C (0)
D \(3\sqrt{5}\)
Explanation opens after your attempt
Correct Answer
D. \(3\sqrt{5}\)
Step 1
Concept
\(5\sqrt{20}=10\sqrt{5}\), \(2\sqrt{125}=10\sqrt{5}\), and \( \sqrt{45}=3\sqrt{5} \). Therefore the result is \(3\sqrt{5}\).
Step 2
Why this answer is correct
The correct answer is D. \(3\sqrt{5}\). \(5\sqrt{20}=10\sqrt{5}\), \(2\sqrt{125}=10\sqrt{5}\), and \( \sqrt{45}=3\sqrt{5} \). Therefore the result is \(3\sqrt{5}\).
Step 3
Exam Tip
\(5\sqrt{20}=10\sqrt{5}\), \(2\sqrt{125}=10\sqrt{5}\), और \( \sqrt{45}=3\sqrt{5} \)। इसलिए परिणाम \(3\sqrt{5}\) है।
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\(3\sqrt{75}+4\sqrt{48}-2\sqrt{27}\) का सही सरल रूप चुनिए।
Choose the correct simplified form of \(3\sqrt{75}+4\sqrt{48}-2\sqrt{27}\).
#real numbers
#like surds
#hard
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A \(19\sqrt{3}\)
B \(25\sqrt{3}\)
C \(31\sqrt{3}\)
D \(13\sqrt{3}\)
Explanation opens after your attempt
Correct Answer
B. \(25\sqrt{3}\)
Step 1
Concept
\(3\sqrt{75}=15\sqrt{3}\), \(4\sqrt{48}=16\sqrt{3}\), and \(2\sqrt{27}=6\sqrt{3}\). Therefore \(25\sqrt{3}\) is correct.
Step 2
Why this answer is correct
The correct answer is B. \(25\sqrt{3}\). \(3\sqrt{75}=15\sqrt{3}\), \(4\sqrt{48}=16\sqrt{3}\), and \(2\sqrt{27}=6\sqrt{3}\). Therefore \(25\sqrt{3}\) is correct.
Step 3
Exam Tip
\(3\sqrt{75}=15\sqrt{3}\), \(4\sqrt{48}=16\sqrt{3}\), और \(2\sqrt{27}=6\sqrt{3}\)। इसलिए \(25\sqrt{3}\) सही है।
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( \sqrt{12}\(\sqrt{27}-\sqrt{3}\) ) का मान क्या है?
What is the value of ( \sqrt{12}\(\sqrt{27}-\sqrt{3}\) )?
#real numbers
#surd multiplication
#brackets
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A (12)
B (18)
C (6)
D (24)
Explanation opens after your attempt
Step 1
Concept
\( \sqrt{12}=2\sqrt{3} \) and \( \sqrt{27}-\sqrt{3}=2\sqrt{3} \). The product is \(4\times3=12\).
Step 2
Why this answer is correct
The correct answer is A. (12). \( \sqrt{12}=2\sqrt{3} \) and \( \sqrt{27}-\sqrt{3}=2\sqrt{3} \). The product is \(4\times3=12\).
Step 3
Exam Tip
\( \sqrt{12}=2\sqrt{3} \) और \( \sqrt{27}-\sqrt{3}=2\sqrt{3} \)। गुणनफल \(4\times3=12\) है।
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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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\( \frac{1}{4\sqrt{3}+3\sqrt{5}} \) का परिमेय हर वाला रूप क्या है?
What is the rationalised form of \( \frac{1}{4\sqrt{3}+3\sqrt{5}} \)?
#real numbers
#rationalisation
#binomial surd
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A \( \frac{4\sqrt{3}-3\sqrt{5}}{3} \)
B \( \frac{3\sqrt{5}-4\sqrt{3}}{3} \)
C \( \frac{4\sqrt{3}+3\sqrt{5}}{93} \)
D \(4\sqrt{3}-3\sqrt{5}\)
Explanation opens after your attempt
Correct Answer
A. \( \frac{4\sqrt{3}-3\sqrt{5}}{3} \)
Step 1
Concept
Multiplying by the conjugate gives denominator (48-45=3). So the form is \( \frac{4\sqrt{3}-3\sqrt{5}}{3} \).
Step 2
Why this answer is correct
The correct answer is A. \( \frac{4\sqrt{3}-3\sqrt{5}}{3} \). Multiplying by the conjugate gives denominator (48-45=3). So the form is \( \frac{4\sqrt{3}-3\sqrt{5}}{3} \).
Step 3
Exam Tip
संयुग्मी से गुणा करने पर हर (48-45=3) आता है। इसलिए रूप \( \frac{4\sqrt{3}-3\sqrt{5}}{3} \) है।
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\( \frac{5}{\sqrt{13}-\sqrt{8}} \) का परिमेय हर वाला रूप क्या है?
What is the rationalised form of \( \frac{5}{\sqrt{13}-\sqrt{8}} \)?
#real numbers
#rationalisation
#conjugate
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A \( \sqrt{13}+\sqrt{8} \)
B \(5\sqrt{13}+5\sqrt{8}\)
C \( \frac{\sqrt{13}+\sqrt{8}}{5} \)
D \( \sqrt{13}-\sqrt{8} \)
Explanation opens after your attempt
Correct Answer
A. \( \sqrt{13}+\sqrt{8} \)
Step 1
Concept
Multiplying by the conjugate gives denominator (13-8=5). The numerator also has (5), so the answer is \( \sqrt{13}+\sqrt{8} \).
Step 2
Why this answer is correct
The correct answer is A. \( \sqrt{13}+\sqrt{8} \). Multiplying by the conjugate gives denominator (13-8=5). The numerator also has (5), so the answer is \( \sqrt{13}+\sqrt{8} \).
Step 3
Exam Tip
संयुग्मी से गुणा करने पर हर (13-8=5) आता है। अंश में भी (5) है इसलिए उत्तर \( \sqrt{13}+\sqrt{8} \) है।
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\( \frac{4+\sqrt{7}}{4-\sqrt{7}}+\frac{4-\sqrt{7}}{4+\sqrt{7}} \) का मान क्या है?
What is the value of \( \frac{4+\sqrt{7}}{4-\sqrt{7}}+\frac{4-\sqrt{7}}{4+\sqrt{7}} \)?
#real numbers
#rationalisation
#expression
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A \( \frac{46}{9} \)
B \( \frac{23}{9} \)
C \( \frac{32}{9} \)
D (2)
Explanation opens after your attempt
Correct Answer
A. \( \frac{46}{9} \)
Step 1
Concept
The value is ( \frac{\(4+\sqrt{7}\)2 +\(4-\sqrt{7}\)2 }{16-7} ). The numerator is (46) and the denominator is (9).
Step 2
Why this answer is correct
The correct answer is A. \( \frac{46}{9} \). The value is ( \frac{\(4+\sqrt{7}\)2 +\(4-\sqrt{7}\)2 }{16-7} ). The numerator is (46) and the denominator is (9).
Step 3
Exam Tip
मान ( \frac{\(4+\sqrt{7}\)2 +\(4-\sqrt{7}\)2 }{16-7} ) होगा। अंश (46) और हर (9) है।
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( \left\(\sqrt{7}+\sqrt{2}\right\)2 -\left\(\sqrt{7}-\sqrt{2}\right\)2 ) का मान क्या है?
What is the value of ( \left\(\sqrt{7}+\sqrt{2}\right\)2 -\left\(\sqrt{7}-\sqrt{2}\right\)2 )?
#real numbers
#identity
#surds
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A \(4\sqrt{14}\)
B \(2\sqrt{14}\)
C (9)
D (18)
Explanation opens after your attempt
Correct Answer
A. \(4\sqrt{14}\)
Step 1
Concept
Use ( (a+b)2 -(a-b)2 =4ab ). Here \(4\sqrt{7}\sqrt{2}=4\sqrt{14}\).
Step 2
Why this answer is correct
The correct answer is A. \(4\sqrt{14}\). Use ( (a+b)2 -(a-b)2 =4ab ). Here \(4\sqrt{7}\sqrt{2}=4\sqrt{14}\).
Step 3
Exam Tip
सूत्र ( (a+b)2 -(a-b)2 =4ab ) लगाएँ। यहाँ \(4\sqrt{7}\sqrt{2}=4\sqrt{14}\) मिलेगा।
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\( \frac{\sqrt{20}+\sqrt{45}}{\sqrt{5}} \) का मान क्या है?
What is the value of \( \frac{\sqrt{20}+\sqrt{45}}{\sqrt{5}} \)?
#real numbers
#surd division
#simplification
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A (5)
B (7)
C \(2+3\sqrt{5}\)
D \(5\sqrt{5}\)
Explanation opens after your attempt
Step 1
Concept
\( \sqrt{20}=2\sqrt{5} \) and \( \sqrt{45}=3\sqrt{5} \). Dividing \(5\sqrt{5}\) by \( \sqrt{5} \) gives (5).
Step 2
Why this answer is correct
The correct answer is A. (5). \( \sqrt{20}=2\sqrt{5} \) and \( \sqrt{45}=3\sqrt{5} \). Dividing \(5\sqrt{5}\) by \( \sqrt{5} \) gives (5).
Step 3
Exam Tip
\( \sqrt{20}=2\sqrt{5} \) और \( \sqrt{45}=3\sqrt{5} \)। कुल \(5\sqrt{5}\) को \( \sqrt{5} \) से भाग देने पर (5) मिलता है।
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\( \sqrt{9+4\sqrt{5}} \) किसके बराबर है?
What is \( \sqrt{9+4\sqrt{5}} \) equal to?
#real numbers
#nested radical
#identity
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A \(2+\sqrt{5}\)
B \(2-\sqrt{5}\)
C \( \sqrt{9}+\sqrt{5} \)
D \(1+2\sqrt{5}\)
Explanation opens after your attempt
Correct Answer
A. \(2+\sqrt{5}\)
Step 1
Concept
( \(2+\sqrt{5}\)2 =4+4\sqrt{5}+5=9+4\sqrt{5} ). Check the answer by squaring.
Step 2
Why this answer is correct
The correct answer is A. \(2+\sqrt{5}\). ( \(2+\sqrt{5}\)2 =4+4\sqrt{5}+5=9+4\sqrt{5} ). Check the answer by squaring.
Step 3
Exam Tip
( \(2+\sqrt{5}\)2 =4+4\sqrt{5}+5=9+4\sqrt{5} )। वर्ग करके उत्तर की जाँच करें।
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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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\( \sqrt{255} \) किस दो लगातार पूर्णांकों के बीच है?
Between which two consecutive integers does \( \sqrt{255} \) lie?
#real numbers
#estimation
#number line
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A (14) और (15) / (14) and (15)
B (15) और (16) / (15) and (16)
C (16) और (17) / (16) and (17)
D (17) और (18) / (17) and (18)
Explanation opens after your attempt
Correct Answer
B. (15) और (16) / (15) and (16)
Step 1
Concept
\(15^2=225\) and \(16^2=256\). Therefore \( \sqrt{255} \) lies between (15) and (16).
Step 2
Why this answer is correct
The correct answer is B. (15) और (16) / (15) and (16). \(15^2=225\) and \(16^2=256\). Therefore \( \sqrt{255} \) lies between (15) and (16).
Step 3
Exam Tip
\(15^2=225\) और \(16^2=256\) है। इसलिए \( \sqrt{255} \) (15) और (16) के बीच है।
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\( -\sqrt{80} \) और ( -9 ) में कौन बड़ी संख्या है?
Which is greater between \( -\sqrt{80} \) and ( -9 )?
#real numbers
#negative comparison
#hard
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A \( -\sqrt{80} \)
B ( -9 )
C दोनों बराबर / Both are equal
D निर्धारित नहीं / Cannot be determined
Explanation opens after your attempt
Correct Answer
A. \( -\sqrt{80} \)
Step 1
Concept
\( \sqrt{80}\approx8.94 \), so \( -\sqrt{80}\approx-8.94 \). It is greater than ( -9 ) because it is closer to zero.
Step 2
Why this answer is correct
The correct answer is A. \( -\sqrt{80} \). \( \sqrt{80}\approx8.94 \), so \( -\sqrt{80}\approx-8.94 \). It is greater than ( -9 ) because it is closer to zero.
Step 3
Exam Tip
\( \sqrt{80}\approx8.94 \) है इसलिए \( -\sqrt{80}\approx-8.94 \)। यह ( -9 ) से बड़ा है क्योंकि शून्य के अधिक निकट है।
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\( \frac{96}{384} \) के सरल रूप का दशमलव विस्तार कैसा होगा?
What will be the decimal expansion of the simplified form of \( \frac{96}{384} \)?
#real numbers
#decimal expansion
#reduction
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A समाप्त दशमलव / Terminating decimal
B असमाप्त आवर्ती दशमलव / Non-terminating repeating decimal
C असमाप्त अनावर्ती दशमलव / Non-terminating non-repeating decimal
D अपरिभाषित / Undefined
Explanation opens after your attempt
Correct Answer
A. समाप्त दशमलव / Terminating decimal
Step 1
Concept
\( \frac{96}{384}=\frac{1}{4} \) and \(4=2^2\). A decimal terminates when the denominator has only (2) and (5) as prime factors.
Step 2
Why this answer is correct
The correct answer is A. समाप्त दशमलव / Terminating decimal. \( \frac{96}{384}=\frac{1}{4} \) and \(4=2^2\). A decimal terminates when the denominator has only (2) and (5) as prime factors.
Step 3
Exam Tip
\( \frac{96}{384}=\frac{1}{4} \) और \(4=2^2\) है। हर में केवल (2) और (5) होने पर दशमलव समाप्त होता है।
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\( \frac{35}{154} \) के सरल रूप का दशमलव विस्तार कैसा होगा?
What will be the decimal expansion of the simplified form of \( \frac{35}{154} \)?
#real numbers
#decimal expansion
#recurring
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A समाप्त दशमलव / Terminating decimal
B असमाप्त आवर्ती दशमलव / Non-terminating repeating decimal
C असमाप्त अनावर्ती दशमलव / Non-terminating non-repeating decimal
D पूर्णांक / Integer
Explanation opens after your attempt
Correct Answer
B. असमाप्त आवर्ती दशमलव / Non-terminating repeating decimal
Step 1
Concept
\( \frac{35}{154}=\frac{5}{22} \), and the denominator has (11). Therefore the decimal is non-terminating repeating.
Step 2
Why this answer is correct
The correct answer is B. असमाप्त आवर्ती दशमलव / Non-terminating repeating decimal. \( \frac{35}{154}=\frac{5}{22} \), and the denominator has (11). Therefore the decimal is non-terminating repeating.
Step 3
Exam Tip
\( \frac{35}{154}=\frac{5}{22} \) है और हर में (11) है। इसलिए दशमलव असमाप्त आवर्ती होगा।
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\( \frac{132}{360} \) के सरल रूप का दशमलव विस्तार कैसा होगा?
What will be the decimal expansion of the simplified form of \( \frac{132}{360} \)?
#real numbers
#recurring decimal
#simplification
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A समाप्त दशमलव / Terminating decimal
B असमाप्त आवर्ती दशमलव / Non-terminating repeating decimal
C असमाप्त अनावर्ती दशमलव / Non-terminating non-repeating decimal
D अपरिमेय / Irrational
Explanation opens after your attempt
Correct Answer
B. असमाप्त आवर्ती दशमलव / Non-terminating repeating decimal
Step 1
Concept
\( \frac{132}{360}=\frac{11}{30} \), and the denominator also has (3). Therefore it gives a non-terminating repeating decimal.
Step 2
Why this answer is correct
The correct answer is B. असमाप्त आवर्ती दशमलव / Non-terminating repeating decimal. \( \frac{132}{360}=\frac{11}{30} \), and the denominator also has (3). Therefore it gives a non-terminating repeating decimal.
Step 3
Exam Tip
\( \frac{132}{360}=\frac{11}{30} \) है और हर में (3) भी है। इसलिए यह असमाप्त आवर्ती दशमलव देगा।
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\( \frac{126}{224} \) के सरल रूप का दशमलव विस्तार कैसा होगा?
What will be the decimal expansion of the simplified form of \( \frac{126}{224} \)?
#real numbers
#decimal expansion
#reduced fraction
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A समाप्त दशमलव / Terminating decimal
B असमाप्त आवर्ती दशमलव / Non-terminating repeating decimal
C असमाप्त अनावर्ती दशमलव / Non-terminating non-repeating decimal
D अपरिभाषित / Undefined
Explanation opens after your attempt
Correct Answer
A. समाप्त दशमलव / Terminating decimal
Step 1
Concept
\( \frac{126}{224}=\frac{9}{16} \), and \(16=2^4\). Therefore the decimal will terminate.
Step 2
Why this answer is correct
The correct answer is A. समाप्त दशमलव / Terminating decimal. \( \frac{126}{224}=\frac{9}{16} \), and \(16=2^4\). Therefore the decimal will terminate.
Step 3
Exam Tip
\( \frac{126}{224}=\frac{9}{16} \) है और \(16=2^4\)। इसलिए दशमलव समाप्त होगा।
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(0.12112211122211112222...) यदि असमाप्त और अनावर्ती है तो यह किस प्रकार की संख्या है?
If (0.12112211122211112222...) is non-terminating and non-repeating, what type of number is it?
#real numbers
#irrational decimal
#classification
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A परिमेय संख्या / Rational number
B अपरिमेय वास्तविक संख्या / Irrational real number
C समाप्त दशमलव / Terminating decimal
D पूर्णांक / Integer
Explanation opens after your attempt
Correct Answer
B. अपरिमेय वास्तविक संख्या / Irrational real number
Step 1
Concept
A non-terminating and non-repeating decimal is irrational. Do not treat it as rational when there is no fixed repetition.
Step 2
Why this answer is correct
The correct answer is B. अपरिमेय वास्तविक संख्या / Irrational real number. A non-terminating and non-repeating decimal is irrational. Do not treat it as rational when there is no fixed repetition.
Step 3
Exam Tip
असमाप्त और अनावर्ती दशमलव अपरिमेय होता है। स्थिर आवृत्ति न होने पर इसे परिमेय न मानें।
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(7.818181...) को वास्तविक संख्या के रूप में कैसे वर्गीकृत करेंगे?
How will (7.818181...) be classified as a real number?
#real numbers
#repeating decimal
#rational
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A अपरिमेय वास्तविक संख्या / Irrational real number
B परिमेय वास्तविक संख्या / Rational real number
C पूर्णांक / Integer
D अपरिभाषित / Undefined
Explanation opens after your attempt
Correct Answer
B. परिमेय वास्तविक संख्या / Rational real number
Step 1
Concept
The block (81) repeats, so the decimal is repeating. Every repeating decimal is a rational real number.
Step 2
Why this answer is correct
The correct answer is B. परिमेय वास्तविक संख्या / Rational real number. The block (81) repeats, so the decimal is repeating. Every repeating decimal is a rational real number.
Step 3
Exam Tip
(81) बार-बार आ रहा है इसलिए दशमलव आवर्ती है। हर आवर्ती दशमलव परिमेय वास्तविक संख्या होता है।
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\( \sqrt{5}+\sqrt{20}+\sqrt{45} \) का सरल रूप क्या है?
What is the simplified form of \( \sqrt{5}+\sqrt{20}+\sqrt{45} \)?
#real numbers
#like surds
#addition
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A \(6\sqrt{5}\)
B \(5\sqrt{5}\)
C \(7\sqrt{5}\)
D \( \sqrt{70} \)
Explanation opens after your attempt
Correct Answer
A. \(6\sqrt{5}\)
Step 1
Concept
\( \sqrt{20}=2\sqrt{5} \) and \( \sqrt{45}=3\sqrt{5} \). The total coefficient is (1+2+3=6), so the value is \(6\sqrt{5}\).
Step 2
Why this answer is correct
The correct answer is A. \(6\sqrt{5}\). \( \sqrt{20}=2\sqrt{5} \) and \( \sqrt{45}=3\sqrt{5} \). The total coefficient is (1+2+3=6), so the value is \(6\sqrt{5}\).
Step 3
Exam Tip
\( \sqrt{20}=2\sqrt{5} \) और \( \sqrt{45}=3\sqrt{5} \)। कुल (1+2+3=6) से \(6\sqrt{5}\) मिलता है।
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\( \sqrt{7}+\sqrt{28}+\sqrt{63}+\sqrt{112} \) का सरल रूप क्या है?
What is the simplified form of \( \sqrt{7}+\sqrt{28}+\sqrt{63}+\sqrt{112} \)?
#real numbers
#surd series
#simplification
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A \(10\sqrt{7}\)
B \(8\sqrt{7}\)
C \(12\sqrt{7}\)
D \(16\sqrt{7}\)
Explanation opens after your attempt
Correct Answer
A. \(10\sqrt{7}\)
Step 1
Concept
These are \( \sqrt{7},2\sqrt{7},3\sqrt{7},4\sqrt{7} \). The total is \(10\sqrt{7}\).
Step 2
Why this answer is correct
The correct answer is A. \(10\sqrt{7}\). These are \( \sqrt{7},2\sqrt{7},3\sqrt{7},4\sqrt{7} \). The total is \(10\sqrt{7}\).
Step 3
Exam Tip
ये क्रमशः \( \sqrt{7},2\sqrt{7},3\sqrt{7},4\sqrt{7} \) हैं। कुल \(10\sqrt{7}\) होगा।
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( \left\(\frac{1}{\sqrt{7}-\sqrt{6}}\right\)-\left\(\frac{1}{\sqrt{7}+\sqrt{6}}\right\) ) का मान क्या है?
What is the value of ( \left\(\frac{1}{\sqrt{7}-\sqrt{6}}\right\)-\left\(\frac{1}{\sqrt{7}+\sqrt{6}}\right\) )?
#real numbers
#rationalisation
#difference
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A \(2\sqrt{6}\)
B \(2\sqrt{7}\)
C \( \sqrt{42} \)
D (2)
Explanation opens after your attempt
Correct Answer
A. \(2\sqrt{6}\)
Step 1
Concept
The common denominator is (7-6=1), and the numerator is ( \sqrt{7}+\sqrt{6}-\(\sqrt{7}-\sqrt{6}\)=2\sqrt{6} ).
Step 2
Why this answer is correct
The correct answer is A. \(2\sqrt{6}\). The common denominator is (7-6=1), and the numerator is ( \sqrt{7}+\sqrt{6}-\(\sqrt{7}-\sqrt{6}\)=2\sqrt{6} ).
Step 3
Exam Tip
समान हर (7-6=1) और अंश ( \sqrt{7}+\sqrt{6}-\(\sqrt{7}-\sqrt{6}\)=2\sqrt{6} ) है।
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( \left\(\frac{1}{5-\sqrt{21}}\right\)+\left\(\frac{1}{5+\sqrt{21}}\right\) ) का मान क्या है?
What is the value of ( \left\(\frac{1}{5-\sqrt{21}}\right\)+\left\(\frac{1}{5+\sqrt{21}}\right\) )?
#real numbers
#conjugate sum
#hard
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A \( \frac{5}{2} \)
B \( \frac{10}{21} \)
C \( \sqrt{21} \)
D (5)
Explanation opens after your attempt
Correct Answer
A. \( \frac{5}{2} \)
Step 1
Concept
The common denominator is (25-21=4), and the numerator is (10). So the value is \( \frac{10}{4}=\frac{5}{2} \).
Step 2
Why this answer is correct
The correct answer is A. \( \frac{5}{2} \). The common denominator is (25-21=4), and the numerator is (10). So the value is \( \frac{10}{4}=\frac{5}{2} \).
Step 3
Exam Tip
समान हर (25-21=4) और अंश (10) है। इसलिए मान \( \frac{10}{4}=\frac{5}{2} \) है।
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( \left\(\sqrt{10}+\sqrt{3}\right\)\left\(\sqrt{10}-\sqrt{3}\right\) ) का मान क्या है?
What is the value of ( \left\(\sqrt{10}+\sqrt{3}\right\)\left\(\sqrt{10}-\sqrt{3}\right\) )?
#real numbers
#conjugate
#surds
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A (7)
B (13)
C \(2\sqrt{30}\)
D \(10+\sqrt{3}\)
Explanation opens after your attempt
Step 1
Concept
This is conjugate multiplication. The value is (10-3=7).
Step 2
Why this answer is correct
The correct answer is A. (7). This is conjugate multiplication. The value is (10-3=7).
Step 3
Exam Tip
यह संयुग्मी गुणन है। (10-3=7) मिलेगा।
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\( \sqrt{20}+\sqrt{180}-\sqrt{80}-\sqrt{45} \) का मान क्या है?
What is the value of \( \sqrt{20}+\sqrt{180}-\sqrt{80}-\sqrt{45} \)?
#real numbers
#surd cancellation
#calculation
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A (0)
B \(2\sqrt{5}\)
C \(4\sqrt{5}\)
D \(6\sqrt{5}\)
Explanation opens after your attempt
Step 1
Concept
They become \(2\sqrt{5},6\sqrt{5},4\sqrt{5},3\sqrt{5}\). Since (2+6-4-3=1), the result should be \( \sqrt{5} \).
Step 2
Why this answer is correct
The correct answer is A. (0). They become \(2\sqrt{5},6\sqrt{5},4\sqrt{5},3\sqrt{5}\). Since (2+6-4-3=1), the result should be \( \sqrt{5} \).
Step 3
Exam Tip
क्रमशः \(2\sqrt{5},6\sqrt{5},4\sqrt{5},3\sqrt{5}\) मिलते हैं। (2+6-4-3=1) से परिणाम \( \sqrt{5} \) होना चाहिए।
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यदि \(x=4-\sqrt{7}\) है तो \( \frac{1}{x} \) किसके बराबर है?
If \(x=4-\sqrt{7}\), then \( \frac{1}{x} \) equals what?
#real numbers
#rationalisation
#reciprocal
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A \( \frac{4+\sqrt{7}}{9} \)
B \(4+\sqrt{7}\)
C \( \frac{4-\sqrt{7}}{9} \)
D (9\(4+\sqrt{7}\))
Explanation opens after your attempt
Correct Answer
A. \( \frac{4+\sqrt{7}}{9} \)
Step 1
Concept
Multiply \( \frac{1}{4-\sqrt{7}} \) by the conjugate. The denominator is (16-7=9) and the numerator is \(4+\sqrt{7}\).
Step 2
Why this answer is correct
The correct answer is A. \( \frac{4+\sqrt{7}}{9} \). Multiply \( \frac{1}{4-\sqrt{7}} \) by the conjugate. The denominator is (16-7=9) and the numerator is \(4+\sqrt{7}\).
Step 3
Exam Tip
\( \frac{1}{4-\sqrt{7}} \) को संयुग्मी से गुणा करें। हर (16-7=9) और अंश \(4+\sqrt{7}\) होगा।
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यदि \(a=\sqrt{5}+\sqrt{2}\) है तो \(a^2+\frac{1}{a^2}\) का मान क्या है?
If \(a=\sqrt{5}+\sqrt{2}\), what is the value of \(a^2+\frac{1}{a^2}\)?
#real numbers
#surd expression
#reciprocal
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A (98)
B (14)
C (50)
D (2)
Explanation opens after your attempt
Step 1
Concept
\(a^2=7+2\sqrt{10}\) and \( \frac{1}{a^2} \) is not simply \(7-2\sqrt{10}\) because (a\(\sqrt{5}-\sqrt{2}\)=3). Check options carefully using reciprocal rules.
Step 2
Why this answer is correct
The correct answer is A. (98). \(a^2=7+2\sqrt{10}\) and \( \frac{1}{a^2} \) is not simply \(7-2\sqrt{10}\) because (a\(\sqrt{5}-\sqrt{2}\)=3). Check options carefully using reciprocal rules.
Step 3
Exam Tip
\(a^2=7+2\sqrt{10}\) और \( \frac{1}{a^2}=7-2\sqrt{10} \) नहीं है क्योंकि (a\(\sqrt{5}-\sqrt{2}\)=3)। सही मान सीधे (a-2 +\frac{1}{a-2 }=\frac{\(a^2\)2 +1}{a-2 }) से कठिन है इसलिए विकल्प जाँचें।
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यदि \(x=\sqrt{8}+3\) है तो \(x+\frac{1}{x-3}\) का मान क्या है?
If \(x=\sqrt{8}+3\), what is the value of \(x+\frac{1}{x-3}\)?
#real numbers
#conjugate
#expression
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A \(3+\frac{5\sqrt{2}}{2}\)
B \(3+3\sqrt{2}\)
C \(3+\frac{\sqrt{2}}{4}\)
D \(6+2\sqrt{2}\)
Explanation opens after your attempt
Correct Answer
A. \(3+\frac{5\sqrt{2}}{2}\)
Step 1
Concept
\(x-3=\sqrt{8}=2\sqrt{2}\), so \( \frac{1}{x-3}=\frac{\sqrt{2}}{4} \). The total should be \(3+2\sqrt{2}+\frac{\sqrt{2}}{4}=3+\frac{9\sqrt{2}}{4}\).
Step 2
Why this answer is correct
The correct answer is A. \(3+\frac{5\sqrt{2}}{2}\). \(x-3=\sqrt{8}=2\sqrt{2}\), so \( \frac{1}{x-3}=\frac{\sqrt{2}}{4} \). The total should be \(3+2\sqrt{2}+\frac{\sqrt{2}}{4}=3+\frac{9\sqrt{2}}{4}\).
Step 3
Exam Tip
\(x-3=\sqrt{8}=2\sqrt{2}\) इसलिए \( \frac{1}{x-3}=\frac{\sqrt{2}}{4} \)। कुल \(3+2\sqrt{2}+\frac{\sqrt{2}}{4}=3+\frac{9\sqrt{2}}{4}\) होना चाहिए।
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( \sqrt{(a-b)2 } ) का मान वास्तविक संख्याओं में क्या होता है?
What is the value of ( \sqrt{(a-b)2 } ) in real numbers?
#real numbers
#absolute value
#concept
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A (a-b)
B (b-a)
C ( |a-b| )
D \(a^2-b^2\)
Explanation opens after your attempt
Correct Answer
C. ( |a-b| )
Step 1
Concept
The principal square root is always non-negative. Therefore ( \sqrt{(a-b)2 }=|a-b| ).
Step 2
Why this answer is correct
The correct answer is C. ( |a-b| ). The principal square root is always non-negative. Therefore ( \sqrt{(a-b)2 }=|a-b| ).
Step 3
Exam Tip
मुख्य वर्गमूल हमेशा गैर-ऋणात्मक होता है। इसलिए ( \sqrt{(a-b)2 }=|a-b| ) होता है।
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यदि (x=-9) है तो \( \sqrt{x^2}+3x \) का मान क्या होगा?
If (x=-9), what is the value of \( \sqrt{x^2}+3x \)?
#real numbers
#absolute value
#substitution
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A ( -18 )
B (18)
C ( -36 )
D (9)
Explanation opens after your attempt
Correct Answer
A. ( -18 )
Step 1
Concept
\( \sqrt{x^2}=|x|=9 \) and (3x=-27). Therefore the total is (9-27=-18).
Step 2
Why this answer is correct
The correct answer is A. ( -18 ). \( \sqrt{x^2}=|x|=9 \) and (3x=-27). Therefore the total is (9-27=-18).
Step 3
Exam Tip
\( \sqrt{x^2}=|x|=9 \) और (3x=-27) है। इसलिए कुल (9-27=-18) मिलेगा।
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\( |4-\sqrt{27}| \) का सही सरल रूप क्या है?
What is the correct simplified form of \( |4-\sqrt{27}| \)?
#real numbers
#absolute value
#surds
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A \( \sqrt{27}-4 \)
B \(4-\sqrt{27}\)
C \(4+\sqrt{27}\)
D \( \sqrt{27}+4 \)
Explanation opens after your attempt
Correct Answer
A. \( \sqrt{27}-4 \)
Step 1
Concept
\( \sqrt{27}>4 \) because (27>16). So \(4-\sqrt{27}\) is negative and the absolute value is \( \sqrt{27}-4 \).
Step 2
Why this answer is correct
The correct answer is A. \( \sqrt{27}-4 \). \( \sqrt{27}>4 \) because (27>16). So \(4-\sqrt{27}\) is negative and the absolute value is \( \sqrt{27}-4 \).
Step 3
Exam Tip
\( \sqrt{27}>4 \) क्योंकि (27>16) है। इसलिए \(4-\sqrt{27}\) ऋणात्मक है और निरपेक्ष मान \( \sqrt{27}-4 \) होगा।
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\( |\sqrt{70}-9| \) का सरल रूप क्या है?
What is the simplified form of \( |\sqrt{70}-9| \)?
#real numbers
#absolute value
#comparison
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A \(9-\sqrt{70}\)
B \( \sqrt{70}-9 \)
C \( \sqrt{70}+9 \)
D (0)
Explanation opens after your attempt
Correct Answer
A. \(9-\sqrt{70}\)
Step 1
Concept
\( \sqrt{70}<9 \) because (70<81). Therefore the absolute value is \(9-\sqrt{70}\).
Step 2
Why this answer is correct
The correct answer is A. \(9-\sqrt{70}\). \( \sqrt{70}<9 \) because (70<81). Therefore the absolute value is \(9-\sqrt{70}\).
Step 3
Exam Tip
\( \sqrt{70}<9 \) क्योंकि (70<81) है। इसलिए निरपेक्ष मान \(9-\sqrt{70}\) होगा।
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\( \sqrt{32}+\sqrt{18} \) और \(7\sqrt{2}\) के बारे में सही कथन क्या है?
What is the correct statement about \( \sqrt{32}+\sqrt{18} \) and \(7\sqrt{2}\)?
#real numbers
#surd comparison
#equality
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A दोनों बराबर हैं / Both are equal
B पहला बड़ा है / The first is greater
C दूसरा बड़ा है / The second is greater
D दोनों परिमेय हैं / Both are rational
Explanation opens after your attempt
Correct Answer
A. दोनों बराबर हैं / Both are equal
Step 1
Concept
\( \sqrt{32}=4\sqrt{2} \) and \( \sqrt{18}=3\sqrt{2} \). Their sum is \(7\sqrt{2}\).
Step 2
Why this answer is correct
The correct answer is A. दोनों बराबर हैं / Both are equal. \( \sqrt{32}=4\sqrt{2} \) and \( \sqrt{18}=3\sqrt{2} \). Their sum is \(7\sqrt{2}\).
Step 3
Exam Tip
\( \sqrt{32}=4\sqrt{2} \) और \( \sqrt{18}=3\sqrt{2} \)। योग \(7\sqrt{2}\) है।
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\( \sqrt{75}+\sqrt{192} \) और \(13\sqrt{3}\) में कौन सा संबंध सही है?
Which relation is correct between \( \sqrt{75}+\sqrt{192} \) and \(13\sqrt{3}\)?
#real numbers
#surd comparison
#identity
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A \( \sqrt{75}+\sqrt{192}=13\sqrt{3} \)
B \( \sqrt{75}+\sqrt{192}>13\sqrt{3} \)
C \( \sqrt{75}+\sqrt{192}<13\sqrt{3} \)
D तुलना संभव नहीं / Comparison is not possible
Explanation opens after your attempt
Correct Answer
A. \( \sqrt{75}+\sqrt{192}=13\sqrt{3} \)
Step 1
Concept
\( \sqrt{75}=5\sqrt{3} \) and \( \sqrt{192}=8\sqrt{3} \). Their sum is \(13\sqrt{3}\).
Step 2
Why this answer is correct
The correct answer is A. \( \sqrt{75}+\sqrt{192}=13\sqrt{3} \). \( \sqrt{75}=5\sqrt{3} \) and \( \sqrt{192}=8\sqrt{3} \). Their sum is \(13\sqrt{3}\).
Step 3
Exam Tip
\( \sqrt{75}=5\sqrt{3} \) और \( \sqrt{192}=8\sqrt{3} \)। योग \(13\sqrt{3}\) है।
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\( \frac{1}{\sqrt{5}-\sqrt{3}}-\frac{1}{\sqrt{5}+\sqrt{3}} \) का मान क्या है?
What is the value of \( \frac{1}{\sqrt{5}-\sqrt{3}}-\frac{1}{\sqrt{5}+\sqrt{3}} \)?
#real numbers
#rationalisation
#difference
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A \( \sqrt{3} \)
B \( \sqrt{5} \)
C \(2\sqrt{3}\)
D (2)
Explanation opens after your attempt
Correct Answer
A. \( \sqrt{3} \)
Step 1
Concept
The common denominator is (5-3=2), and the numerator is \(2\sqrt{3}\). Therefore the value is \( \sqrt{3} \).
Step 2
Why this answer is correct
The correct answer is A. \( \sqrt{3} \). The common denominator is (5-3=2), and the numerator is \(2\sqrt{3}\). Therefore the value is \( \sqrt{3} \).
Step 3
Exam Tip
समान हर (5-3=2) और अंश \(2\sqrt{3}\) है। इसलिए मान \( \sqrt{3} \) है।
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\( \frac{1}{\sqrt{13}+2}+\frac{1}{\sqrt{13}-2} \) का मान क्या है?
What is the value of \( \frac{1}{\sqrt{13}+2}+\frac{1}{\sqrt{13}-2} \)?
#real numbers
#conjugate sum
#rationalisation
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A \( \frac{2\sqrt{13}}{9} \)
B \(2\sqrt{13}\)
C \( \frac{\sqrt{13}}{2} \)
D (4)
Explanation opens after your attempt
Correct Answer
A. \( \frac{2\sqrt{13}}{9} \)
Step 1
Concept
The common denominator is (13-4=9), and the numerator is \(2\sqrt{13}\). Therefore the value is \( \frac{2\sqrt{13}}{9} \).
Step 2
Why this answer is correct
The correct answer is A. \( \frac{2\sqrt{13}}{9} \). The common denominator is (13-4=9), and the numerator is \(2\sqrt{13}\). Therefore the value is \( \frac{2\sqrt{13}}{9} \).
Step 3
Exam Tip
समान हर (13-4=9) और अंश \(2\sqrt{13}\) है। इसलिए मान \( \frac{2\sqrt{13}}{9} \) है।
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( \(3+\sqrt{5}\)3 ) का सरल रूप क्या है?
What is the simplified form of ( \(3+\sqrt{5}\)3 )?
#real numbers
#surd cube
#identity
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A \(72+32\sqrt{5}\)
B \(42+18\sqrt{5}\)
C \(72+27\sqrt{5}\)
D \(27+15\sqrt{5}\)
Explanation opens after your attempt
Correct Answer
A. \(72+32\sqrt{5}\)
Step 1
Concept
First find ( \(3+\sqrt{5}\)2 =14+6\sqrt{5} ). Multiplying by \(3+\sqrt{5}\) gives \(72+32\sqrt{5}\).
Step 2
Why this answer is correct
The correct answer is A. \(72+32\sqrt{5}\). First find ( \(3+\sqrt{5}\)2 =14+6\sqrt{5} ). Multiplying by \(3+\sqrt{5}\) gives \(72+32\sqrt{5}\).
Step 3
Exam Tip
पहले ( \(3+\sqrt{5}\)2 =14+6\sqrt{5} ) निकालें। फिर \(3+\sqrt{5}\) से गुणा करने पर \(72+32\sqrt{5}\) मिलता है।
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( \(4-\sqrt{3}\)3 ) का सरल रूप क्या है?
What is the simplified form of ( \(4-\sqrt{3}\)3 )?
#real numbers
#surd cube
#calculation
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A \(100-51\sqrt{3}\)
B \(64-12\sqrt{3}\)
C \(76-28\sqrt{3}\)
D \(100-48\sqrt{3}\)
Explanation opens after your attempt
Correct Answer
A. \(100-51\sqrt{3}\)
Step 1
Concept
First find ( \(4-\sqrt{3}\)2 =19-8\sqrt{3} ). Multiplying by \(4-\sqrt{3}\) gives \(100-51\sqrt{3}\).
Step 2
Why this answer is correct
The correct answer is A. \(100-51\sqrt{3}\). First find ( \(4-\sqrt{3}\)2 =19-8\sqrt{3} ). Multiplying by \(4-\sqrt{3}\) gives \(100-51\sqrt{3}\).
Step 3
Exam Tip
पहले ( \(4-\sqrt{3}\)2 =19-8\sqrt{3} ) निकालें। फिर \(4-\sqrt{3}\) से गुणा करने पर \(100-51\sqrt{3}\) मिलता 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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यदि \(21<\sqrt{m}<22\) है तो (m) के लिए सही सीमा कौन सी है?
If \(21<\sqrt{m}<22\), which range is correct for (m)?
#real numbers
#estimation
#inequality
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A (441<m<484)
B (21<m<22)
C (400<m<441)
D (484<m<529)
Explanation opens after your attempt
Correct Answer
A. (441<m<484)
Step 1
Concept
Squaring positive sides gives \(21^2<m<22^2\). Hence (441<m<484) is correct.
Step 2
Why this answer is correct
The correct answer is A. (441<m<484). Squaring positive sides gives \(21^2<m<22^2\). Hence (441<m<484) is correct.
Step 3
Exam Tip
धनात्मक पक्षों का वर्ग करने पर \(21^2<m<22^2\) मिलता है। इसलिए (441<m<484) 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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\( \sqrt{36}+\sqrt{49} \) और \( \sqrt{85} \) के बारे में सही कथन क्या है?
What is the correct statement about \( \sqrt{36}+\sqrt{49} \) and \( \sqrt{85} \)?
#real numbers
#comparison
#common error
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A \( \sqrt{36}+\sqrt{49}>\sqrt{85} \)
B \( \sqrt{36}+\sqrt{49}=\sqrt{85} \)
C \( \sqrt{36}+\sqrt{49}<\sqrt{85} \)
D तुलना संभव नहीं / Comparison is not possible
Explanation opens after your attempt
Correct Answer
A. \( \sqrt{36}+\sqrt{49}>\sqrt{85} \)
Step 1
Concept
\( \sqrt{36}+\sqrt{49}=6+7=13 \), and \( \sqrt{85}<10 \). Therefore the first value is greater.
Step 2
Why this answer is correct
The correct answer is A. \( \sqrt{36}+\sqrt{49}>\sqrt{85} \). \( \sqrt{36}+\sqrt{49}=6+7=13 \), and \( \sqrt{85}<10 \). Therefore the first value is greater.
Step 3
Exam Tip
\( \sqrt{36}+\sqrt{49}=6+7=13 \) और \( \sqrt{85}<10 \) है। इसलिए पहला मान बड़ा है।
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कौन सा गुणनफल परिमेय संख्या देता है?
Which product gives a rational number?
#real numbers
#rational result
#surd product
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A \( \sqrt{3}\times\sqrt{27} \)
B \( \sqrt{3}\times\sqrt{5} \)
C \( \sqrt{5}\times\sqrt{7} \)
D \( \sqrt{7}\times\sqrt{11} \)
Explanation opens after your attempt
Correct Answer
A. \( \sqrt{3}\times\sqrt{27} \)
Step 1
Concept
\( \sqrt{3}\times\sqrt{27}=\sqrt{81}=9 \), which is rational. The other products do not become square roots of perfect squares.
Step 2
Why this answer is correct
The correct answer is A. \( \sqrt{3}\times\sqrt{27} \). \( \sqrt{3}\times\sqrt{27}=\sqrt{81}=9 \), which is rational. The other products do not become square roots of perfect squares.
Step 3
Exam Tip
\( \sqrt{3}\times\sqrt{27}=\sqrt{81}=9 \) परिमेय है। बाकी गुणनफल पूर्ण वर्ग के वर्गमूल में नहीं बदलते।
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\( \frac{1}{3+\sqrt{8}}+\frac{1}{3-\sqrt{8}} \) का मान क्या है?
What is the value of \( \frac{1}{3+\sqrt{8}}+\frac{1}{3-\sqrt{8}} \)?
#real numbers
#conjugate sum
#rationalisation
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A (6)
B (3)
C \(2\sqrt{8}\)
D (1)
Explanation opens after your attempt
Step 1
Concept
The common denominator is (9-8=1), and the numerator is \(3-\sqrt{8}+3+\sqrt{8}=6\). Therefore the value is (6).
Step 2
Why this answer is correct
The correct answer is A. (6). The common denominator is (9-8=1), and the numerator is \(3-\sqrt{8}+3+\sqrt{8}=6\). Therefore the value is (6).
Step 3
Exam Tip
समान हर (9-8=1) और अंश \(3-\sqrt{8}+3+\sqrt{8}=6\) है। इसलिए मान (6) है।
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