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( \(5-\sqrt{6}\)2 ) का सरल रूप क्या है?
What is the simplified form of ( \(5-\sqrt{6}\)2 )?
#real numbers
#algebraic identity
#surd square
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A \(31-10\sqrt{6}\)
B \(19-5\sqrt{6}\)
C \(25-\sqrt{6}\)
D \(30-2\sqrt{6}\)
Explanation opens after your attempt
Correct Answer
A. \(31-10\sqrt{6}\)
Step 1
Concept
Using ( (a-b)2 =a-2 -2ab+b-2 ), we get \(25-10\sqrt{6}+6=31-10\sqrt{6}\). Pay special attention to signs.
Step 2
Why this answer is correct
The correct answer is A. \(31-10\sqrt{6}\). Using ( (a-b)2 =a-2 -2ab+b-2 ), we get \(25-10\sqrt{6}+6=31-10\sqrt{6}\). Pay special attention to signs.
Step 3
Exam Tip
( (a-b)2 =a-2 -2ab+b-2 ) से \(25-10\sqrt{6}+6=31-10\sqrt{6}\) मिलता है। संकेतों पर विशेष ध्यान दें।
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( \(4+\sqrt{11}\)\(4-\sqrt{11}\) ) का मान क्या है?
What is the value of ( \(4+\sqrt{11}\)\(4-\sqrt{11}\) )?
#real numbers
#conjugate
#difference of squares
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A (27)
B (5)
C \(16+\sqrt{11}\)
D \(16-\sqrt{11}\)
Explanation opens after your attempt
Step 1
Concept
This is conjugate multiplication. (42 -\(\sqrt{11}\)2 =16-11=5).
Step 2
Why this answer is correct
The correct answer is B. (5). This is conjugate multiplication. (42 -\(\sqrt{11}\)2 =16-11=5).
Step 3
Exam Tip
यह संयुग्मी गुणन है। (42 -\(\sqrt{11}\)2 =16-11=5) होगा।
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\( \sqrt{27}\times\sqrt{12} \) का मान क्या है?
What is the value of \( \sqrt{27}\times\sqrt{12} \)?
#real numbers
#surd multiplication
#perfect square
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A (18)
B (36)
C \(9\sqrt{4}\)
D \(3\sqrt{39}\)
Explanation opens after your attempt
Step 1
Concept
\( \sqrt{27}\times\sqrt{12}=\sqrt{324}=18 \). In multiplication, multiply the numbers inside the radicals.
Step 2
Why this answer is correct
The correct answer is A. (18). \( \sqrt{27}\times\sqrt{12}=\sqrt{324}=18 \). In multiplication, multiply the numbers inside the radicals.
Step 3
Exam Tip
\( \sqrt{27}\times\sqrt{12}=\sqrt{324}=18 \)। गुणा में करणी के अंदर की संख्याएँ गुणा करें।
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\( \sqrt{90}\div\sqrt{10} \) का मान क्या है?
What is the value of \( \sqrt{90}\div\sqrt{10} \)?
#real numbers
#surd division
#square root
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A (9)
B (3)
C \( \sqrt{80} \)
D \( \sqrt{100} \)
Explanation opens after your attempt
Step 1
Concept
\( \frac{\sqrt{90}}{\sqrt{10}}=\sqrt{9}=3 \). In radical division, divide the radicands.
Step 2
Why this answer is correct
The correct answer is B. (3). \( \frac{\sqrt{90}}{\sqrt{10}}=\sqrt{9}=3 \). In radical division, divide the radicands.
Step 3
Exam Tip
\( \frac{\sqrt{90}}{\sqrt{10}}=\sqrt{9}=3 \)। करणी भाग में अंदर की संख्याओं का भाग लें।
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\( \sqrt{0.81}+\sqrt{0.04} \) का मान क्या है?
What is the value of \( \sqrt{0.81}+\sqrt{0.04} \)?
#real numbers
#decimal square root
#addition
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A (0.92)
B (1.1)
C (1.01)
D (0.11)
Explanation opens after your attempt
Step 1
Concept
\( \sqrt{0.81}=0.9 \) and \( \sqrt{0.04}=0.2 \). The sum is (1.1).
Step 2
Why this answer is correct
The correct answer is B. (1.1). \( \sqrt{0.81}=0.9 \) and \( \sqrt{0.04}=0.2 \). The sum is (1.1).
Step 3
Exam Tip
\( \sqrt{0.81}=0.9 \) और \( \sqrt{0.04}=0.2 \) है। योग (1.1) होगा।
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\( \sqrt{\frac{9}{16}}+\sqrt{\frac{25}{36}} \) का मान क्या है?
What is the value of \( \sqrt{\frac{9}{16}}+\sqrt{\frac{25}{36}} \)?
#real numbers
#fraction square roots
#addition
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A \( \frac{19}{12} \)
B \( \frac{17}{12} \)
C \( \frac{11}{12} \)
D \( \frac{7}{12} \)
Explanation opens after your attempt
Correct Answer
A. \( \frac{19}{12} \)
Step 1
Concept
The first term is \( \frac{3}{4} \) and the second is \( \frac{5}{6} \). The sum is \( \frac{9}{12}+\frac{10}{12}=\frac{19}{12} \).
Step 2
Why this answer is correct
The correct answer is A. \( \frac{19}{12} \). The first term is \( \frac{3}{4} \) and the second is \( \frac{5}{6} \). The sum is \( \frac{9}{12}+\frac{10}{12}=\frac{19}{12} \).
Step 3
Exam Tip
पहला पद \( \frac{3}{4} \) और दूसरा \( \frac{5}{6} \) है। योग \( \frac{9}{12}+\frac{10}{12}=\frac{19}{12} \) मिलता है।
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\( \sqrt{\frac{49}{100}}-\sqrt{\frac{4}{25}} \) का मान क्या है?
What is the value of \( \sqrt{\frac{49}{100}}-\sqrt{\frac{4}{25}} \)?
#real numbers
#fraction roots
#subtraction
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A \( \frac{7}{10} \)
B \( \frac{3}{10} \)
C \( \frac{11}{10} \)
D \( \frac{1}{10} \)
Explanation opens after your attempt
Correct Answer
B. \( \frac{3}{10} \)
Step 1
Concept
\( \sqrt{\frac{49}{100}}=\frac{7}{10} \) and \( \sqrt{\frac{4}{25}}=\frac{2}{5} \). The difference is \( \frac{3}{10} \).
Step 2
Why this answer is correct
The correct answer is B. \( \frac{3}{10} \). \( \sqrt{\frac{49}{100}}=\frac{7}{10} \) and \( \sqrt{\frac{4}{25}}=\frac{2}{5} \). The difference is \( \frac{3}{10} \).
Step 3
Exam Tip
\( \sqrt{\frac{49}{100}}=\frac{7}{10} \) और \( \sqrt{\frac{4}{25}}=\frac{2}{5} \) है। अंतर \( \frac{3}{10} \) है।
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\( \sqrt{26} \) किस दो पूर्णांकों के बीच है?
Between which two integers does \( \sqrt{26} \) lie?
#real numbers
#square root estimation
#number line
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A (4) और (5) / (4) and (5)
B (5) और (6) / (5) and (6)
C (6) और (7) / (6) and (7)
D (7) और (8) / (7) and (8)
Explanation opens after your attempt
Correct Answer
B. (5) और (6) / (5) and (6)
Step 1
Concept
\(5^2=25\) and \(6^2=36\), so \( \sqrt{26} \) lies between (5) and (6). Compare nearby perfect squares.
Step 2
Why this answer is correct
The correct answer is B. (5) और (6) / (5) and (6). \(5^2=25\) and \(6^2=36\), so \( \sqrt{26} \) lies between (5) and (6). Compare nearby perfect squares.
Step 3
Exam Tip
\(5^2=25\) और \(6^2=36\) है इसलिए \( \sqrt{26} \) (5) और (6) के बीच है। निकट पूर्ण वर्गों की तुलना करें।
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\( \sqrt{53} \) का स्थान किन दो पूर्णांकों के बीच होगा?
Between which two integers will \( \sqrt{53} \) lie?
#real numbers
#estimation
#roots
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A (5) और (6) / (5) and (6)
B (6) और (7) / (6) and (7)
C (7) और (8) / (7) and (8)
D (8) और (9) / (8) and (9)
Explanation opens after your attempt
Correct Answer
C. (7) और (8) / (7) and (8)
Step 1
Concept
\(7^2=49\) and \(8^2=64\), so \( \sqrt{53} \) lies between (7) and (8). Check limits by squaring.
Step 2
Why this answer is correct
The correct answer is C. (7) और (8) / (7) and (8). \(7^2=49\) and \(8^2=64\), so \( \sqrt{53} \) lies between (7) and (8). Check limits by squaring.
Step 3
Exam Tip
\(7^2=49\) और \(8^2=64\) है इसलिए \( \sqrt{53} \) (7) और (8) के बीच है। वर्ग करके सीमा जाँचें।
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\( |-\sqrt{49}+3| \) का मान क्या है?
What is the value of \( |-\sqrt{49}+3| \)?
#real numbers
#absolute value
#square root
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A (4)
B ( -4 )
C (10)
D (7)
Explanation opens after your attempt
Step 1
Concept
\( -\sqrt{49}+3=-7+3=-4 \) and ( |-4|=4 ). Absolute value gives distance.
Step 2
Why this answer is correct
The correct answer is A. (4). \( -\sqrt{49}+3=-7+3=-4 \) and ( |-4|=4 ). Absolute value gives distance.
Step 3
Exam Tip
\( -\sqrt{49}+3=-7+3=-4 \) है और ( |-4|=4 )। निरपेक्ष मान दूरी देता है।
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