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( \(5+\sqrt{2}\)2 ) का विस्तार क्या है?
What is the expansion of ( \(5+\sqrt{2}\)2 )?
#real numbers
#identity
#surd square
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A \(25+2\sqrt{2}\)
B \(27+5\sqrt{2}\)
C \(27+10\sqrt{2}\)
D \(7+10\sqrt{2}\)
Explanation opens after your attempt
Correct Answer
C. \(27+10\sqrt{2}\)
Step 1
Concept
Use ( (a+b)2 ). Here \(25+10\sqrt{2}+2=27+10\sqrt{2}\).
Step 2
Why this answer is correct
The correct answer is C. \(27+10\sqrt{2}\). Use ( (a+b)2 ). Here \(25+10\sqrt{2}+2=27+10\sqrt{2}\).
Step 3
Exam Tip
( (a+b)2 ) का प्रयोग करें। यहाँ \(25+10\sqrt{2}+2=27+10\sqrt{2}\) मिलता है।
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( \(6+\sqrt{23}\)\(6-\sqrt{23}\) ) का मान क्या है?
What is the value of ( \(6+\sqrt{23}\)\(6-\sqrt{23}\) )?
#real numbers
#conjugate
#difference of squares
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A (59)
B (13)
C \(36+\sqrt{23}\)
D \(36-\sqrt{23}\)
Explanation opens after your attempt
Step 1
Concept
This is conjugate multiplication. (62 -\(\sqrt{23}\)2 =36-23=13).
Step 2
Why this answer is correct
The correct answer is B. (13). This is conjugate multiplication. (62 -\(\sqrt{23}\)2 =36-23=13).
Step 3
Exam Tip
यह संयुग्मी गुणन है। (62 -\(\sqrt{23}\)2 =36-23=13) होगा।
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\( \sqrt{45}\times\sqrt{80} \) का मान क्या है?
What is the value of \( \sqrt{45}\times\sqrt{80} \)?
#real numbers
#surd multiplication
#perfect square
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A (60)
B (30)
C \(20\sqrt{5}\)
D \( \sqrt{125} \)
Explanation opens after your attempt
Step 1
Concept
\( \sqrt{45}\times\sqrt{80}=\sqrt{3600}=60 \). In radical multiplication, multiply the radicands.
Step 2
Why this answer is correct
The correct answer is A. (60). \( \sqrt{45}\times\sqrt{80}=\sqrt{3600}=60 \). In radical multiplication, multiply the radicands.
Step 3
Exam Tip
\( \sqrt{45}\times\sqrt{80}=\sqrt{3600}=60 \)। करणी गुणन में अंदर की संख्याएँ गुणा करें।
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\( \sqrt{242}\div\sqrt{2} \) का मान क्या है?
What is the value of \( \sqrt{242}\div\sqrt{2} \)?
#real numbers
#surd division
#square root
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A (121)
B (11)
C \( \sqrt{240} \)
D (22)
Explanation opens after your attempt
Step 1
Concept
\( \frac{\sqrt{242}}{\sqrt{2}}=\sqrt{121}=11 \). In division of square roots, divide the radicands.
Step 2
Why this answer is correct
The correct answer is B. (11). \( \frac{\sqrt{242}}{\sqrt{2}}=\sqrt{121}=11 \). In division of square roots, divide the radicands.
Step 3
Exam Tip
\( \frac{\sqrt{242}}{\sqrt{2}}=\sqrt{121}=11 \)। वर्गमूल के भाग में अंदर की संख्याओं का भाग लें।
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\( \sqrt{3.24}+\sqrt{0.49} \) का मान क्या है?
What is the value of \( \sqrt{3.24}+\sqrt{0.49} \)?
#real numbers
#decimal square root
#addition
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A (2.5)
B (2.7)
C (3.1)
D (1.9)
Explanation opens after your attempt
Step 1
Concept
\( \sqrt{3.24}=1.8 \) and \( \sqrt{0.49}=0.7 \). The sum is (2.5).
Step 2
Why this answer is correct
The correct answer is A. (2.5). \( \sqrt{3.24}=1.8 \) and \( \sqrt{0.49}=0.7 \). The sum is (2.5).
Step 3
Exam Tip
\( \sqrt{3.24}=1.8 \) और \( \sqrt{0.49}=0.7 \) है। योग (2.5) होगा।
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\( \sqrt{\frac{25}{49}}+\sqrt{\frac{16}{81}} \) का मान क्या है?
What is the value of \( \sqrt{\frac{25}{49}}+\sqrt{\frac{16}{81}} \)?
#real numbers
#fraction square roots
#addition
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A \( \frac{73}{63} \)
B \( \frac{41}{63} \)
C \( \frac{31}{63} \)
D \( \frac{9}{16} \)
Explanation opens after your attempt
Correct Answer
A. \( \frac{73}{63} \)
Step 1
Concept
The first term is \( \frac{5}{7} \) and the second is \( \frac{4}{9} \). The sum is \( \frac{45}{63}+\frac{28}{63}=\frac{73}{63} \).
Step 2
Why this answer is correct
The correct answer is A. \( \frac{73}{63} \). The first term is \( \frac{5}{7} \) and the second is \( \frac{4}{9} \). The sum is \( \frac{45}{63}+\frac{28}{63}=\frac{73}{63} \).
Step 3
Exam Tip
पहला पद \( \frac{5}{7} \) और दूसरा \( \frac{4}{9} \) है। योग \( \frac{45}{63}+\frac{28}{63}=\frac{73}{63} \) है।
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\( \sqrt{\frac{100}{169}}-\sqrt{\frac{9}{64}} \) का मान क्या है?
What is the value of \( \sqrt{\frac{100}{169}}-\sqrt{\frac{9}{64}} \)?
#real numbers
#fraction roots
#subtraction
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A \( \frac{41}{104} \)
B \( \frac{53}{104} \)
C \( \frac{71}{104} \)
D \( \frac{37}{104} \)
Explanation opens after your attempt
Correct Answer
A. \( \frac{41}{104} \)
Step 1
Concept
\( \sqrt{\frac{100}{169}}=\frac{10}{13} \) and \( \sqrt{\frac{9}{64}}=\frac{3}{8} \). The difference is \( \frac{80}{104}-\frac{39}{104}=\frac{41}{104} \).
Step 2
Why this answer is correct
The correct answer is A. \( \frac{41}{104} \). \( \sqrt{\frac{100}{169}}=\frac{10}{13} \) and \( \sqrt{\frac{9}{64}}=\frac{3}{8} \). The difference is \( \frac{80}{104}-\frac{39}{104}=\frac{41}{104} \).
Step 3
Exam Tip
\( \sqrt{\frac{100}{169}}=\frac{10}{13} \) और \( \sqrt{\frac{9}{64}}=\frac{3}{8} \) है। अंतर \( \frac{80}{104}-\frac{39}{104}=\frac{41}{104} \) है।
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\( \sqrt{101} \) किस दो पूर्णांकों के बीच है?
Between which two integers does \( \sqrt{101} \) lie?
#real numbers
#square root estimation
#number line
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A (8) और (9) / (8) and (9)
B (9) और (10) / (9) and (10)
C (10) और (11) / (10) and (11)
D (11) और (12) / (11) and (12)
Explanation opens after your attempt
Correct Answer
C. (10) और (11) / (10) and (11)
Step 1
Concept
\(10^2=100\) and \(11^2=121\), so \( \sqrt{101} \) lies between (10) and (11). Compare nearby perfect squares.
Step 2
Why this answer is correct
The correct answer is C. (10) और (11) / (10) and (11). \(10^2=100\) and \(11^2=121\), so \( \sqrt{101} \) lies between (10) and (11). Compare nearby perfect squares.
Step 3
Exam Tip
\(10^2=100\) और \(11^2=121\) है इसलिए \( \sqrt{101} \) (10) और (11) के बीच है। निकट पूर्ण वर्गों की तुलना करें।
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\( \sqrt{130} \) का स्थान किन दो पूर्णांकों के बीच होगा?
Between which two integers will \( \sqrt{130} \) lie?
#real numbers
#estimation
#roots
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A (9) और (10) / (9) and (10)
B (10) और (11) / (10) and (11)
C (11) और (12) / (11) and (12)
D (12) और (13) / (12) and (13)
Explanation opens after your attempt
Correct Answer
C. (11) और (12) / (11) and (12)
Step 1
Concept
\(11^2=121\) and \(12^2=144\), so \( \sqrt{130} \) lies between (11) and (12). Check the range by squaring.
Step 2
Why this answer is correct
The correct answer is C. (11) और (12) / (11) and (12). \(11^2=121\) and \(12^2=144\), so \( \sqrt{130} \) lies between (11) and (12). Check the range by squaring.
Step 3
Exam Tip
\(11^2=121\) और \(12^2=144\) है इसलिए \( \sqrt{130} \) (11) और (12) के बीच है। सीमा वर्ग करके जाँचें।
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\( |-\sqrt{100}+6| \) का मान क्या है?
What is the value of \( |-\sqrt{100}+6| \)?
#real numbers
#absolute value
#square root
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A (4)
B ( -4 )
C (16)
D (10)
Explanation opens after your attempt
Step 1
Concept
\( -\sqrt{100}+6=-10+6=-4 \) and ( |-4|=4 ). Absolute value gives distance.
Step 2
Why this answer is correct
The correct answer is A. (4). \( -\sqrt{100}+6=-10+6=-4 \) and ( |-4|=4 ). Absolute value gives distance.
Step 3
Exam Tip
\( -\sqrt{100}+6=-10+6=-4 \) है और ( |-4|=4 )। निरपेक्ष मान दूरी देता है।
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