\( \sqrt{64} \) किस प्रकार की वास्तविक संख्या है?
What type of real number is \( \sqrt{64} \)?
#real numbers
#square root
#rational
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A परिमेय वास्तविक संख्या / Rational real number
B अपरिमेय वास्तविक संख्या / Irrational real number
C अपरिभाषित संख्या / Undefined number
D असमाप्त अनावर्ती दशमलव / Non-terminating non-repeating decimal
Explanation opens after your attempt
Correct Answer
A. परिमेय वास्तविक संख्या / Rational real number
Step 1
Concept
\( \sqrt{64}=8 \) and (8) is rational. The square root of a perfect square is rational.
Step 2
Why this answer is correct
The correct answer is A. परिमेय वास्तविक संख्या / Rational real number. \( \sqrt{64}=8 \) and (8) is rational. The square root of a perfect square is rational.
Step 3
Exam Tip
\( \sqrt{64}=8 \) है और (8) परिमेय संख्या है। पूर्ण वर्ग का वर्गमूल परिमेय होता है।
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कौन सा दशमलव वास्तविक परिमेय संख्या है?
Which decimal is a rational real number?
#real numbers
#repeating decimal
#rational
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A (0.123456...) बिना आवृत्ति / (0.123456...) without repetition
B (0.272727...)
C \( \sqrt{10} \)
D \( \pi \)
Explanation opens after your attempt
Correct Answer
B. (0.272727...)
Step 1
Concept
(0.272727...) is repeating so it is rational. A repeating decimal can be converted into a fraction.
Step 2
Why this answer is correct
The correct answer is B. (0.272727...). (0.272727...) is repeating so it is rational. A repeating decimal can be converted into a fraction.
Step 3
Exam Tip
(0.272727...) आवर्ती दशमलव है इसलिए परिमेय है। आवर्ती दशमलव को भिन्न में बदला जा सकता है।
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\( \sqrt{11} \) संख्या रेखा पर किन दो पूर्णांकों के बीच है?
Between which two integers does \( \sqrt{11} \) lie on the number line?
#real numbers
#number line
#estimation
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A (1) और (2) / (1) and (2)
B (2) और (3) / (2) and (3)
C (3) और (4) / (3) and (4)
D (4) और (5) / (4) and (5)
Explanation opens after your attempt
Correct Answer
C. (3) और (4) / (3) and (4)
Step 1
Concept
\(3^2=9\) and \(4^2=16\) so \( \sqrt{11} \) lies between (3) and (4). Use squares to locate square roots.
Step 2
Why this answer is correct
The correct answer is C. (3) और (4) / (3) and (4). \(3^2=9\) and \(4^2=16\) so \( \sqrt{11} \) lies between (3) and (4). Use squares to locate square roots.
Step 3
Exam Tip
\(3^2=9\) और \(4^2=16\) है इसलिए \( \sqrt{11} \) (3) और (4) के बीच है। वर्गों से वर्गमूल का स्थान पहचानें।
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\( \sqrt{98} \) का सरल करणी रूप क्या है?
What is the simplified surd form of \( \sqrt{98} \)?
#real numbers
#surd simplification
#radicals
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A \(7\sqrt{2}\)
B \(14\sqrt{2}\)
C \(2\sqrt{49}\)
D \(49\sqrt{2}\)
Explanation opens after your attempt
Correct Answer
A. \(7\sqrt{2}\)
Step 1
Concept
Since \(98=49\times2\), \( \sqrt{98}=7\sqrt{2} \). Choose the largest perfect-square factor.
Step 2
Why this answer is correct
The correct answer is A. \(7\sqrt{2}\). Since \(98=49\times2\), \( \sqrt{98}=7\sqrt{2} \). Choose the largest perfect-square factor.
Step 3
Exam Tip
\(98=49\times2\) इसलिए \( \sqrt{98}=7\sqrt{2} \)। सबसे बड़ा पूर्ण वर्ग गुणनखंड चुनें।
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\( \sqrt{72} \) को सरल करने पर क्या मिलेगा?
What is obtained by simplifying \( \sqrt{72} \)?
#real numbers
#surd simplification
#class 9
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A \(12\sqrt{2}\)
B \(6\sqrt{2}\)
C \(8\sqrt{3}\)
D \(9\sqrt{2}\)
Explanation opens after your attempt
Correct Answer
B. \(6\sqrt{2}\)
Step 1
Concept
Since \(72=36\times2\), \( \sqrt{72}=6\sqrt{2} \). Take the perfect square outside the square root.
Step 2
Why this answer is correct
The correct answer is B. \(6\sqrt{2}\). Since \(72=36\times2\), \( \sqrt{72}=6\sqrt{2} \). Take the perfect square outside the square root.
Step 3
Exam Tip
\(72=36\times2\) इसलिए \( \sqrt{72}=6\sqrt{2} \)। पूर्ण वर्ग को वर्गमूल से बाहर निकालें।
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\( \sqrt{63} \) का सरल रूप कौन सा है?
Which is the simplified form of \( \sqrt{63} \)?
#real numbers
#surd form
#simplification
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A \(7\sqrt{3}\)
B \(21\sqrt{3}\)
C \(3\sqrt{7}\)
D \(9\sqrt{7}\)
Explanation opens after your attempt
Correct Answer
C. \(3\sqrt{7}\)
Step 1
Concept
Since \(63=9\times7\), \( \sqrt{63}=3\sqrt{7} \). Identifying perfect-square factors is important.
Step 2
Why this answer is correct
The correct answer is C. \(3\sqrt{7}\). Since \(63=9\times7\), \( \sqrt{63}=3\sqrt{7} \). Identifying perfect-square factors is important.
Step 3
Exam Tip
\(63=9\times7\) इसलिए \( \sqrt{63}=3\sqrt{7} \)। पूर्ण वर्ग गुणनखंड पहचानना जरूरी है।
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\( \sqrt{2}\times\sqrt{50} \) का मान क्या है?
What is the value of \( \sqrt{2}\times\sqrt{50} \)?
#real numbers
#surd multiplication
#square root
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A (25)
B \(5\sqrt{2}\)
C \( \sqrt{52} \)
D (10)
Explanation opens after your attempt
Step 1
Concept
\( \sqrt{2}\times\sqrt{50}=\sqrt{100}=10 \). In multiplication, multiply the numbers inside square roots.
Step 2
Why this answer is correct
The correct answer is D. (10). \( \sqrt{2}\times\sqrt{50}=\sqrt{100}=10 \). In multiplication, multiply the numbers inside square roots.
Step 3
Exam Tip
\( \sqrt{2}\times\sqrt{50}=\sqrt{100}=10 \)। गुणा में वर्गमूल के अंदर की संख्याएँ गुणा करें।
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\( \sqrt{80}\div\sqrt{5} \) का मान क्या है?
What is the value of \( \sqrt{80}\div\sqrt{5} \)?
#real numbers
#surd division
#radicals
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A (4)
B (8)
C (16)
D (20)
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Step 1
Concept
\( \frac{\sqrt{80}}{\sqrt{5}}=\sqrt{16}=4 \). During division, divide the numbers inside square roots.
Step 2
Why this answer is correct
The correct answer is A. (4). \( \frac{\sqrt{80}}{\sqrt{5}}=\sqrt{16}=4 \). During division, divide the numbers inside square roots.
Step 3
Exam Tip
\( \frac{\sqrt{80}}{\sqrt{5}}=\sqrt{16}=4 \)। भाग करते समय वर्गमूल के अंदर का भाग लें।
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\(4\sqrt{2}+5\sqrt{2}\) का सरल रूप क्या है?
What is the simplified form of \(4\sqrt{2}+5\sqrt{2}\)?
#real numbers
#like surds
#addition
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A \(20\sqrt{2}\)
B \(9\sqrt{2}\)
C \(9\sqrt{4}\)
D \( \sqrt{18} \)
Explanation opens after your attempt
Correct Answer
B. \(9\sqrt{2}\)
Step 1
Concept
Coefficients of like surd terms are added. Thus \(4\sqrt{2}+5\sqrt{2}=9\sqrt{2}\).
Step 2
Why this answer is correct
The correct answer is B. \(9\sqrt{2}\). Coefficients of like surd terms are added. Thus \(4\sqrt{2}+5\sqrt{2}=9\sqrt{2}\).
Step 3
Exam Tip
समान करणी पदों के गुणांक जोड़े जाते हैं। इसलिए \(4\sqrt{2}+5\sqrt{2}=9\sqrt{2}\)।
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\(9\sqrt{7}-4\sqrt{7}\) का सरल रूप क्या है?
What is the simplified form of \(9\sqrt{7}-4\sqrt{7}\)?
#real numbers
#like surds
#subtraction
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A \(13\sqrt{7}\)
B \(5\sqrt{14}\)
C \(5\sqrt{7}\)
D \( \sqrt{35} \)
Explanation opens after your attempt
Correct Answer
C. \(5\sqrt{7}\)
Step 1
Concept
For like surd terms, subtract the coefficients. Hence \(9\sqrt{7}-4\sqrt{7}=5\sqrt{7}\).
Step 2
Why this answer is correct
The correct answer is C. \(5\sqrt{7}\). For like surd terms, subtract the coefficients. Hence \(9\sqrt{7}-4\sqrt{7}=5\sqrt{7}\).
Step 3
Exam Tip
समान करणी पदों में गुणांक घटते हैं। इसलिए \(9\sqrt{7}-4\sqrt{7}=5\sqrt{7}\)।
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\( \sqrt{48}+\sqrt{27} \) का सरल रूप क्या है?
What is the simplified form of \( \sqrt{48}+\sqrt{27} \)?
#real numbers
#surd addition
#simplification
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A \( \sqrt{75} \)
B \(7\sqrt{3}\)
C \(4\sqrt{3}\)
D \(3\sqrt{7}\)
Explanation opens after your attempt
Correct Answer
B. \(7\sqrt{3}\)
Step 1
Concept
\( \sqrt{48}=4\sqrt{3} \) and \( \sqrt{27}=3\sqrt{3} \). Therefore the sum is \(7\sqrt{3}\).
Step 2
Why this answer is correct
The correct answer is B. \(7\sqrt{3}\). \( \sqrt{48}=4\sqrt{3} \) and \( \sqrt{27}=3\sqrt{3} \). Therefore the sum is \(7\sqrt{3}\).
Step 3
Exam Tip
\( \sqrt{48}=4\sqrt{3} \) और \( \sqrt{27}=3\sqrt{3} \) हैं। इसलिए योग \(7\sqrt{3}\) है।
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\( \sqrt{75}-\sqrt{12} \) का सरल रूप क्या है?
What is the simplified form of \( \sqrt{75}-\sqrt{12} \)?
#real numbers
#surd subtraction
#class 9
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A \(3\sqrt{3}\)
B \(7\sqrt{3}\)
C \( \sqrt{63} \)
D \(5\sqrt{3}\)
Explanation opens after your attempt
Correct Answer
A. \(3\sqrt{3}\)
Step 1
Concept
\( \sqrt{75}=5\sqrt{3} \) and \( \sqrt{12}=2\sqrt{3} \). The difference is \(3\sqrt{3}\).
Step 2
Why this answer is correct
The correct answer is A. \(3\sqrt{3}\). \( \sqrt{75}=5\sqrt{3} \) and \( \sqrt{12}=2\sqrt{3} \). The difference is \(3\sqrt{3}\).
Step 3
Exam Tip
\( \sqrt{75}=5\sqrt{3} \) और \( \sqrt{12}=2\sqrt{3} \) हैं। अंतर \(3\sqrt{3}\) है।
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\( \frac{3}{\sqrt{2}} \) का परिमेय हर वाला रूप क्या है?
What is the form of \( \frac{3}{\sqrt{2}} \) with rational denominator?
#real numbers
#rationalisation
#denominator
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A \( \frac{3}{2} \)
B \( \frac{3\sqrt{2}}{2} \)
C \( \frac{\sqrt{2}}{3} \)
D \(3\sqrt{2}\)
Explanation opens after your attempt
Correct Answer
B. \( \frac{3\sqrt{2}}{2} \)
Step 1
Concept
Multiply numerator and denominator by \( \sqrt{2} \). This makes the denominator (2).
Step 2
Why this answer is correct
The correct answer is B. \( \frac{3\sqrt{2}}{2} \). Multiply numerator and denominator by \( \sqrt{2} \). This makes the denominator (2).
Step 3
Exam Tip
अंश और हर को \( \sqrt{2} \) से गुणा करें। इससे हर (2) हो जाता है।
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\( \frac{5}{\sqrt{7}} \) का हर परिमेय करने पर क्या मिलेगा?
What is obtained by rationalising the denominator of \( \frac{5}{\sqrt{7}} \)?
#real numbers
#rationalisation
#surds
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A \( \frac{\sqrt{7}}{5} \)
B \( \frac{5}{7} \)
C \( \frac{5\sqrt{7}}{7} \)
D \(5\sqrt{7}\)
Explanation opens after your attempt
Correct Answer
C. \( \frac{5\sqrt{7}}{7} \)
Step 1
Concept
Multiplying numerator and denominator by \( \sqrt{7} \) gives \( \frac{5\sqrt{7}}{7} \). Rationalising the denominator is a common exam question.
Step 2
Why this answer is correct
The correct answer is C. \( \frac{5\sqrt{7}}{7} \). Multiplying numerator and denominator by \( \sqrt{7} \) gives \( \frac{5\sqrt{7}}{7} \). Rationalising the denominator is a common exam question.
Step 3
Exam Tip
अंश और हर को \( \sqrt{7} \) से गुणा करने पर \( \frac{5\sqrt{7}}{7} \) मिलता है। हर को परिमेय करना परीक्षा में सामान्य प्रश्न है।
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\( \frac{1}{2+\sqrt{3}} \) का हर परिमेय करने पर क्या मिलेगा?
What is obtained by rationalising the denominator of \( \frac{1}{2+\sqrt{3}} \)?
#real numbers
#rationalisation
#conjugate
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A \(2+\sqrt{3}\)
B \( \frac{1}{2-\sqrt{3}} \)
C \( \sqrt{3}-2 \)
D \(2-\sqrt{3}\)
Explanation opens after your attempt
Correct Answer
D. \(2-\sqrt{3}\)
Step 1
Concept
Multiply by the conjugate \(2-\sqrt{3}\) and the denominator becomes (4-3=1). Hence the answer is \(2-\sqrt{3}\).
Step 2
Why this answer is correct
The correct answer is D. \(2-\sqrt{3}\). Multiply by the conjugate \(2-\sqrt{3}\) and the denominator becomes (4-3=1). Hence the answer is \(2-\sqrt{3}\).
Step 3
Exam Tip
संयुग्मी \(2-\sqrt{3}\) से गुणा करें और हर (4-3=1) बनेगा। इसलिए उत्तर \(2-\sqrt{3}\) है।
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\( \frac{1}{3-\sqrt{5}} \) का हर परिमेय करने पर अंश में क्या आएगा?
What will come in the numerator after rationalising \( \frac{1}{3-\sqrt{5}} \)?
#real numbers
#conjugate
#rationalisation
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A \(3+\sqrt{5}\)
B \(3-\sqrt{5}\)
C \( \sqrt{5}-3 \)
D (8)
Explanation opens after your attempt
Correct Answer
A. \(3+\sqrt{5}\)
Step 1
Concept
We multiply by the conjugate \(3+\sqrt{5}\). So the new numerator will contain \(3+\sqrt{5}\).
Step 2
Why this answer is correct
The correct answer is A. \(3+\sqrt{5}\). We multiply by the conjugate \(3+\sqrt{5}\). So the new numerator will contain \(3+\sqrt{5}\).
Step 3
Exam Tip
हर के संयुग्मी \(3+\sqrt{5}\) से गुणा किया जाता है। इसलिए नए अंश में \(3+\sqrt{5}\) आएगा।
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( \(2+\sqrt{5}\)\(2-\sqrt{5}\) ) का मान क्या है?
What is the value of ( \(2+\sqrt{5}\)\(2-\sqrt{5}\) )?
#real numbers
#conjugate
#multiplication
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A (9)
B ( -1 )
C (1)
D \(4+\sqrt{5}\)
Explanation opens after your attempt
Step 1
Concept
It is a difference of squares (22 -\(\sqrt{5}\)2 =4-5=-1). Middle terms cancel in conjugate multiplication.
Step 2
Why this answer is correct
The correct answer is B. ( -1 ). It is a difference of squares (22 -\(\sqrt{5}\)2 =4-5=-1). Middle terms cancel in conjugate multiplication.
Step 3
Exam Tip
यह अंतर के वर्ग का रूप है (22 -\(\sqrt{5}\)2 =4-5=-1)। संयुग्मी गुणा में मध्य पद कट जाते हैं।
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( \(3+\sqrt{2}\)\(3-\sqrt{2}\) ) का मान क्या है?
What is the value of ( \(3+\sqrt{2}\)\(3-\sqrt{2}\) )?
#real numbers
#conjugate
#difference of squares
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A (7)
B (11)
C \(6-\sqrt{2}\)
D \(9+\sqrt{2}\)
Explanation opens after your attempt
Step 1
Concept
(32 -\(\sqrt{2}\)2 =9-2=7). Multiplying conjugates often gives a rational answer.
Step 2
Why this answer is correct
The correct answer is A. (7). (32 -\(\sqrt{2}\)2 =9-2=7). Multiplying conjugates often gives a rational answer.
Step 3
Exam Tip
(32 -\(\sqrt{2}\)2 =9-2=7) होता है। संयुग्मी का गुणन अक्सर परिमेय उत्तर देता है।
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\( \sqrt{3} \) और \( \sqrt{12} \) में कौन बड़ी है?
Which is greater between \( \sqrt{3} \) and \( \sqrt{12} \)?
#real numbers
#square root comparison
#ordering
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A \( \sqrt{3} \)
B दोनों बराबर / Both are equal
C \( \sqrt{12} \)
D दोनों वास्तविक नहीं हैं / Both are not real
Explanation opens after your attempt
Correct Answer
C. \( \sqrt{12} \)
Step 1
Concept
Since (12>3), \( \sqrt{12}>\sqrt{3} \). For positive numbers, a larger radicand gives a larger square root.
Step 2
Why this answer is correct
The correct answer is C. \( \sqrt{12} \). Since (12>3), \( \sqrt{12}>\sqrt{3} \). For positive numbers, a larger radicand gives a larger square root.
Step 3
Exam Tip
क्योंकि (12>3) है इसलिए \( \sqrt{12}>\sqrt{3} \)। धनात्मक संख्याओं में बड़ा आधार बड़ा वर्गमूल देता है।
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\( \sqrt{35} \) और (6) में कौन छोटी है?
Which is smaller between \( \sqrt{35} \) and (6)?
#real numbers
#ordering
#estimation
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A (6)
B \( \sqrt{35} \)
C दोनों बराबर / Both are equal
D निर्धारित नहीं / Cannot be determined
Explanation opens after your attempt
Correct Answer
B. \( \sqrt{35} \)
Step 1
Concept
\( \sqrt{35}<\sqrt{36}=6 \). Therefore \( \sqrt{35} \) is smaller.
Step 2
Why this answer is correct
The correct answer is B. \( \sqrt{35} \). \( \sqrt{35}<\sqrt{36}=6 \). Therefore \( \sqrt{35} \) is smaller.
Step 3
Exam Tip
\( \sqrt{35}<\sqrt{36}=6 \) है। इसलिए \( \sqrt{35} \) छोटी है।
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\( -\sqrt{10} \) और ( -3 ) में कौन बड़ी संख्या है?
Which is greater between \( -\sqrt{10} \) and ( -3 )?
#real numbers
#negative comparison
#number line
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A \( -\sqrt{10} \)
B दोनों बराबर / Both are equal
C ( -3 )
D दोनों धनात्मक हैं / Both are positive
Explanation opens after your attempt
Step 1
Concept
\( \sqrt{10}\approx3.16 \), so \( -\sqrt{10} \) is less than ( -3 ). The negative number closer to zero is greater.
Step 2
Why this answer is correct
The correct answer is C. ( -3 ). \( \sqrt{10}\approx3.16 \), so \( -\sqrt{10} \) is less than ( -3 ). The negative number closer to zero is greater.
Step 3
Exam Tip
\( \sqrt{10}\approx3.16 \) इसलिए \( -\sqrt{10} \) ( -3 ) से छोटा है। शून्य के पास वाली ऋणात्मक संख्या बड़ी होती है।
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\( \sqrt{1.44} \) का मान क्या है?
What is the value of \( \sqrt{1.44} \)?
#real numbers
#decimal square root
#class 9
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A (0.12)
B (1.02)
C (1.2)
D (12)
Explanation opens after your attempt
Step 1
Concept
\(1.2^2=1.44\), so \( \sqrt{1.44}=1.2 \). Be careful with place value in decimal square roots.
Step 2
Why this answer is correct
The correct answer is C. (1.2). \(1.2^2=1.44\), so \( \sqrt{1.44}=1.2 \). Be careful with place value in decimal square roots.
Step 3
Exam Tip
\(1.2^2=1.44\) इसलिए \( \sqrt{1.44}=1.2 \)। दशमलव वर्गमूल में स्थान मान ध्यान रखें।
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\( \sqrt{2.25} \) का मान क्या है?
What is the value of \( \sqrt{2.25} \)?
#real numbers
#decimal square root
#perfect square
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A (0.15)
B (1.5)
C (2.5)
D (15)
Explanation opens after your attempt
Step 1
Concept
\(1.5^2=2.25\), so \( \sqrt{2.25}=1.5 \). Check the answer by squaring it.
Step 2
Why this answer is correct
The correct answer is B. (1.5). \(1.5^2=2.25\), so \( \sqrt{2.25}=1.5 \). Check the answer by squaring it.
Step 3
Exam Tip
\(1.5^2=2.25\) इसलिए \( \sqrt{2.25}=1.5 \)। उत्तर को वर्ग करके जाँचें।
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\( \sqrt{\frac{25}{36}} \) का मान क्या है?
What is the value of \( \sqrt{\frac{25}{36}} \)?
#real numbers
#fraction square root
#perfect squares
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A \( \frac{25}{6} \)
B \( \frac{6}{5} \)
C \( \frac{5}{6} \)
D \( \frac{5}{36} \)
Explanation opens after your attempt
Correct Answer
C. \( \frac{5}{6} \)
Step 1
Concept
Take the square roots of numerator and denominator separately. \( \sqrt{\frac{25}{36}}=\frac{5}{6} \).
Step 2
Why this answer is correct
The correct answer is C. \( \frac{5}{6} \). Take the square roots of numerator and denominator separately. \( \sqrt{\frac{25}{36}}=\frac{5}{6} \).
Step 3
Exam Tip
अंश और हर के वर्गमूल अलग-अलग लें। \( \sqrt{\frac{25}{36}}=\frac{5}{6} \) है।
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\( \sqrt{\frac{121}{144}} \) किसके बराबर है?
What is \( \sqrt{\frac{121}{144}} \) equal to?
#real numbers
#square root fraction
#class 9
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A \( \frac{11}{12} \)
B \( \frac{121}{12} \)
C \( \frac{12}{11} \)
D \( \frac{11}{144} \)
Explanation opens after your attempt
Correct Answer
A. \( \frac{11}{12} \)
Step 1
Concept
\( \sqrt{121}=11 \) and \( \sqrt{144}=12 \). Therefore the answer is \( \frac{11}{12} \).
Step 2
Why this answer is correct
The correct answer is A. \( \frac{11}{12} \). \( \sqrt{121}=11 \) and \( \sqrt{144}=12 \). Therefore the answer is \( \frac{11}{12} \).
Step 3
Exam Tip
\( \sqrt{121}=11 \) और \( \sqrt{144}=12 \) है। इसलिए उत्तर \( \frac{11}{12} \) है।
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(3.125) को भिन्न में बदलने पर क्या मिलेगा?
What is obtained by converting (3.125) into a fraction?
#real numbers
#decimal to fraction
#rational
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A \( \frac{125}{3} \)
B \( \frac{25}{8} \)
C \( \frac{31}{25} \)
D \( \frac{8}{25} \)
Explanation opens after your attempt
Correct Answer
B. \( \frac{25}{8} \)
Step 1
Concept
\(3.125=\frac{3125}{1000}=\frac{25}{8} \). Convert the terminating decimal into a fraction and simplify.
Step 2
Why this answer is correct
The correct answer is B. \( \frac{25}{8} \). \(3.125=\frac{3125}{1000}=\frac{25}{8} \). Convert the terminating decimal into a fraction and simplify.
Step 3
Exam Tip
\(3.125=\frac{3125}{1000}=\frac{25}{8} \)। समाप्त दशमलव को भिन्न बनाकर सरल करें।
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(4.5) किस भिन्न के बराबर है?
Which fraction is equal to (4.5)?
#real numbers
#decimal conversion
#fraction
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A \( \frac{9}{2} \)
B \( \frac{45}{100} \)
C \( \frac{2}{9} \)
D \( \frac{5}{4} \)
Explanation opens after your attempt
Correct Answer
A. \( \frac{9}{2} \)
Step 1
Concept
\(4.5=\frac{45}{10}=\frac{9}{2} \). Write the decimal with a denominator that is a power of (10).
Step 2
Why this answer is correct
The correct answer is A. \( \frac{9}{2} \). \(4.5=\frac{45}{10}=\frac{9}{2} \). Write the decimal with a denominator that is a power of (10).
Step 3
Exam Tip
\(4.5=\frac{45}{10}=\frac{9}{2} \)। दशमलव को (10) की घात वाले हर में लिखें।
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\( \frac{13}{20} \) का दशमलव रूप क्या है?
What is the decimal form of \( \frac{13}{20} \)?
#real numbers
#fraction to decimal
#rational
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A (0.13)
B (0.20)
C (0.65)
D (1.65)
Explanation opens after your attempt
Step 1
Concept
\( \frac{13}{20}=\frac{65}{100}=0.65 \). Changing the denominator to (100) is an easy method.
Step 2
Why this answer is correct
The correct answer is C. (0.65). \( \frac{13}{20}=\frac{65}{100}=0.65 \). Changing the denominator to (100) is an easy method.
Step 3
Exam Tip
\( \frac{13}{20}=\frac{65}{100}=0.65 \)। हर को (100) में बदलना आसान तरीका है।
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\( \frac{17}{25} \) का दशमलव रूप क्या है?
What is the decimal form of \( \frac{17}{25} \)?
#real numbers
#decimal form
#fractions
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A (0.17)
B (0.68)
C (1.25)
D (0.25)
Explanation opens after your attempt
Step 1
Concept
\( \frac{17}{25}=\frac{68}{100}=0.68 \). Multiply denominator (25) by (4) to make (100).
Step 2
Why this answer is correct
The correct answer is B. (0.68). \( \frac{17}{25}=\frac{68}{100}=0.68 \). Multiply denominator (25) by (4) to make (100).
Step 3
Exam Tip
\( \frac{17}{25}=\frac{68}{100}=0.68 \)। हर (25) को (100) बनाने के लिए (4) से गुणा करें।
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\(0.\overline{45}\) किस प्रकार की संख्या है?
What type of number is \(0.\overline{45}\)?
#real numbers
#repeating decimal
#rational
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A अपरिमेय संख्या / Irrational number
B अपरिभाषित संख्या / Undefined number
C परिमेय वास्तविक संख्या / Rational real number
D केवल पूर्णांक / Only integer
Explanation opens after your attempt
Correct Answer
C. परिमेय वास्तविक संख्या / Rational real number
Step 1
Concept
\(0.\overline{45}\) is a repeating decimal, so it is rational. Every rational number is also real.
Step 2
Why this answer is correct
The correct answer is C. परिमेय वास्तविक संख्या / Rational real number. \(0.\overline{45}\) is a repeating decimal, so it is rational. Every rational number is also real.
Step 3
Exam Tip
\(0.\overline{45}\) आवर्ती दशमलव है इसलिए परिमेय है। हर परिमेय संख्या वास्तविक भी होती है।
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(3.14159...) यदि असमाप्त और अनावर्ती है तो यह किस प्रकार की संख्या है?
If (3.14159...) 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 पूर्ण संख्या / Whole number
D अपरिभाषित संख्या / Undefined number
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. Such a decimal can still be a real number.
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. Such a decimal can still be a real number.
Step 3
Exam Tip
असमाप्त और अनावर्ती दशमलव अपरिमेय होता है। ऐसा दशमलव फिर भी वास्तविक संख्या हो सकता है।
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( \(4+\sqrt{6}\) ) किस प्रकार की संख्या है?
What type of number is ( \(4+\sqrt{6}\) )?
#real numbers
#irrational sum
#classification
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A पूर्णांक / Integer
B परिमेय संख्या / Rational number
C अपरिमेय वास्तविक संख्या / Irrational real number
D पूर्ण संख्या / Whole number
Explanation opens after your attempt
Correct Answer
C. अपरिमेय वास्तविक संख्या / Irrational real number
Step 1
Concept
Adding irrational \( \sqrt{6} \) to rational (4) gives an irrational number. It is also a real number.
Step 2
Why this answer is correct
The correct answer is C. अपरिमेय वास्तविक संख्या / Irrational real number. Adding irrational \( \sqrt{6} \) to rational (4) gives an irrational number. It is also a real number.
Step 3
Exam Tip
परिमेय (4) में अपरिमेय \( \sqrt{6} \) जोड़ने पर अपरिमेय संख्या मिलती है। यह वास्तविक संख्या भी है।
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( \(7-\sqrt{3}\) ) किस प्रकार की संख्या है?
What type of number is ( \(7-\sqrt{3}\) )?
#real numbers
#irrational difference
#class 9
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A अपरिमेय वास्तविक संख्या / Irrational real number
B परिमेय संख्या / Rational number
C प्राकृतिक संख्या / Natural number
D शून्य / Zero
Explanation opens after your attempt
Correct Answer
A. अपरिमेय वास्तविक संख्या / Irrational real number
Step 1
Concept
Subtracting an irrational number from a rational number gives an irrational result. Thus \(7-\sqrt{3}\) is an irrational real number.
Step 2
Why this answer is correct
The correct answer is A. अपरिमेय वास्तविक संख्या / Irrational real number. Subtracting an irrational number from a rational number gives an irrational result. Thus \(7-\sqrt{3}\) is an irrational real number.
Step 3
Exam Tip
परिमेय संख्या से अपरिमेय संख्या घटाने पर परिणाम अपरिमेय होता है। इसलिए \(7-\sqrt{3}\) अपरिमेय वास्तविक संख्या है।
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\( \sqrt{13}\times\sqrt{13} \) का मान क्या है?
What is the value of \( \sqrt{13}\times\sqrt{13} \)?
#real numbers
#surd multiplication
#square root
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A \( \sqrt{26} \)
B (26)
C (169)
D (13)
Explanation opens after your attempt
Step 1
Concept
Multiplying the same square root by itself gives the number inside. Therefore \( \sqrt{13}\times\sqrt{13}=13 \).
Step 2
Why this answer is correct
The correct answer is D. (13). Multiplying the same square root by itself gives the number inside. Therefore \( \sqrt{13}\times\sqrt{13}=13 \).
Step 3
Exam Tip
एक ही वर्गमूल को स्वयं से गुणा करने पर अंदर की संख्या मिलती है। इसलिए \( \sqrt{13}\times\sqrt{13}=13 \)।
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( \(\sqrt{15}\)2 ) का मान क्या है?
What is the value of ( \(\sqrt{15}\)2 )?
#real numbers
#square of square root
#class 9
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A (15)
B (30)
C (225)
D \( \sqrt{30} \)
Explanation opens after your attempt
Step 1
Concept
The square of the square root of a positive number gives the same number. Therefore ( \(\sqrt{15}\)2 =15 ).
Step 2
Why this answer is correct
The correct answer is A. (15). The square of the square root of a positive number gives the same number. Therefore ( \(\sqrt{15}\)2 =15 ).
Step 3
Exam Tip
किसी धनात्मक संख्या के वर्गमूल का वर्ग वही संख्या देता है। इसलिए ( \(\sqrt{15}\)2 =15 )।
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( | -18 | ) का मान क्या है?
What is the value of ( | -18 | )?
#real numbers
#absolute value
#distance
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A ( -18 )
B (18)
C (0)
D (36)
Explanation opens after your attempt
Step 1
Concept
Absolute value shows the distance of a number from (0). Therefore ( | -18 |=18 ).
Step 2
Why this answer is correct
The correct answer is B. (18). Absolute value shows the distance of a number from (0). Therefore ( | -18 |=18 ).
Step 3
Exam Tip
निरपेक्ष मान संख्या की (0) से दूरी बताता है। इसलिए ( | -18 |=18 )।
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( |6-14| ) का मान क्या है?
What is the value of ( |6-14| )?
#real numbers
#absolute value
#calculation
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A ( -8 )
B (20)
C (8)
D (0)
Explanation opens after your attempt
Step 1
Concept
(6-14=-8) and ( |-8|=8 ). Absolute value is never negative.
Step 2
Why this answer is correct
The correct answer is C. (8). (6-14=-8) and ( |-8|=8 ). Absolute value is never negative.
Step 3
Exam Tip
(6-14=-8) और ( |-8|=8 )। निरपेक्ष मान कभी ऋणात्मक नहीं होता।
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वास्तविक संख्या ( -1.25 ) संख्या रेखा पर कहाँ स्थित है?
Where is the real number ( -1.25 ) located on the number line?
#real numbers
#number line
#negative decimal
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A (0) और (1) के बीच / Between (0) and (1)
B ( -1 ) और (0) के बीच / Between ( -1 ) and (0)
C (1) और (2) के बीच / Between (1) and (2)
D ( -2 ) और ( -1 ) के बीच / Between ( -2 ) and ( -1 )
Explanation opens after your attempt
Correct Answer
D. ( -2 ) और ( -1 ) के बीच / Between ( -2 ) and ( -1 )
Step 1
Concept
( -1.25 ) is greater than ( -2 ) and less than ( -1 ). So it lies between ( -2 ) and ( -1 ).
Step 2
Why this answer is correct
The correct answer is D. ( -2 ) और ( -1 ) के बीच / Between ( -2 ) and ( -1 ). ( -1.25 ) is greater than ( -2 ) and less than ( -1 ). So it lies between ( -2 ) and ( -1 ).
Step 3
Exam Tip
( -1.25 ) ( -2 ) से बड़ा और ( -1 ) से छोटा है। इसलिए यह ( -2 ) और ( -1 ) के बीच स्थित है।
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(3) और (4) के बीच एक अपरिमेय संख्या कौन सी है?
Which is an irrational number between (3) and (4)?
#real numbers
#irrational between
#interval
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A \( \frac{7}{2} \)
B \( \sqrt{10} \)
C (3.5)
D (4)
Explanation opens after your attempt
Correct Answer
B. \( \sqrt{10} \)
Step 1
Concept
Since \(3^2<10<4^2\), \( \sqrt{10} \) lies between (3) and (4). Since (10) is not a perfect square, it is irrational.
Step 2
Why this answer is correct
The correct answer is B. \( \sqrt{10} \). Since \(3^2<10<4^2\), \( \sqrt{10} \) lies between (3) and (4). Since (10) is not a perfect square, it is irrational.
Step 3
Exam Tip
\(3^2<10<4^2\) इसलिए \( \sqrt{10} \) (3) और (4) के बीच है। (10) पूर्ण वर्ग नहीं है इसलिए यह अपरिमेय है।
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(4) और (5) के बीच एक अपरिमेय संख्या कौन सी है?
Which is an irrational number between (4) and (5)?
#real numbers
#irrational number
#number line
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A (4.5)
B \( \frac{9}{2} \)
C \( \sqrt{22} \)
D (5)
Explanation opens after your attempt
Correct Answer
C. \( \sqrt{22} \)
Step 1
Concept
Since \(4^2<22<5^2\), \( \sqrt{22} \) lies between (4) and (5). Since (22) is not a perfect square, it is irrational.
Step 2
Why this answer is correct
The correct answer is C. \( \sqrt{22} \). Since \(4^2<22<5^2\), \( \sqrt{22} \) lies between (4) and (5). Since (22) is not a perfect square, it is irrational.
Step 3
Exam Tip
\(4^2<22<5^2\) इसलिए \( \sqrt{22} \) (4) और (5) के बीच है। (22) पूर्ण वर्ग नहीं है इसलिए यह अपरिमेय है।
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किसी भी दो अलग-अलग वास्तविक संख्याओं के बीच कितनी अपरिमेय संख्याएँ होती हैं?
How many irrational numbers are there between any two distinct real numbers?
#real numbers
#density
#irrational numbers
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A कोई नहीं / None
B केवल (1) / Only (1)
C केवल (2) / Only (2)
D अनंत / Infinitely many
Explanation opens after your attempt
Correct Answer
D. अनंत / Infinitely many
Step 1
Concept
There are infinitely many irrational numbers between two distinct real numbers. This is a density property of the real number line.
Step 2
Why this answer is correct
The correct answer is D. अनंत / Infinitely many. There are infinitely many irrational numbers between two distinct real numbers. This is a density property of the real number line.
Step 3
Exam Tip
दो अलग-अलग वास्तविक संख्याओं के बीच अनंत अपरिमेय संख्याएँ होती हैं। यह वास्तविक संख्या रेखा की घनत्व विशेषता है।
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किसी भी दो अलग-अलग वास्तविक संख्याओं के बीच कितनी वास्तविक संख्याएँ होती हैं?
How many real numbers are there between any two distinct real numbers?
#real numbers
#density
#number line
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A अनंत / Infinitely many
B केवल (10) / Only (10)
C केवल (100) / Only (100)
D कोई नहीं / None
Explanation opens after your attempt
Correct Answer
A. अनंत / Infinitely many
Step 1
Concept
The real number line is continuous, so infinitely many real numbers lie between two distinct points. Remember this basic property.
Step 2
Why this answer is correct
The correct answer is A. अनंत / Infinitely many. The real number line is continuous, so infinitely many real numbers lie between two distinct points. Remember this basic property.
Step 3
Exam Tip
वास्तविक संख्या रेखा सतत होती है इसलिए दो अलग-अलग बिंदुओं के बीच अनंत वास्तविक संख्याएँ होती हैं। यह मूल गुण याद रखें।
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\( \sqrt{0}+\sqrt{100} \) का मान क्या है?
What is the value of \( \sqrt{0}+\sqrt{100} \)?
#real numbers
#square roots
#calculation
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A (0)
B (10)
C (100)
D (110)
Explanation opens after your attempt
Step 1
Concept
\( \sqrt{0}=0 \) and \( \sqrt{100}=10 \). Therefore the sum is (10).
Step 2
Why this answer is correct
The correct answer is B. (10). \( \sqrt{0}=0 \) and \( \sqrt{100}=10 \). Therefore the sum is (10).
Step 3
Exam Tip
\( \sqrt{0}=0 \) और \( \sqrt{100}=10 \) है। इसलिए योग (10) है।
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\( \sqrt{144}-\sqrt{25} \) का मान क्या है?
What is the value of \( \sqrt{144}-\sqrt{25} \)?
#real numbers
#square root subtraction
#class 9
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A (17)
B (7)
C (12)
D (5)
Explanation opens after your attempt
Step 1
Concept
\( \sqrt{144}=12 \) and \( \sqrt{25}=5 \). Therefore the difference is (7).
Step 2
Why this answer is correct
The correct answer is B. (7). \( \sqrt{144}=12 \) and \( \sqrt{25}=5 \). Therefore the difference is (7).
Step 3
Exam Tip
\( \sqrt{144}=12 \) और \( \sqrt{25}=5 \) है। इसलिए अंतर (7) है।
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\( \sqrt{121}+\sqrt{169} \) का मान क्या है?
What is the value of \( \sqrt{121}+\sqrt{169} \)?
#real numbers
#perfect squares
#addition
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A (22)
B (24)
C (25)
D (26)
Explanation opens after your attempt
Step 1
Concept
\( \sqrt{121}=11 \) and \( \sqrt{169}=13 \). Therefore the sum is (24).
Step 2
Why this answer is correct
The correct answer is B. (24). \( \sqrt{121}=11 \) and \( \sqrt{169}=13 \). Therefore the sum is (24).
Step 3
Exam Tip
\( \sqrt{121}=11 \) और \( \sqrt{169}=13 \) है। इसलिए योग (24) है।
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\( \sqrt{225}\div\sqrt{9} \) का मान क्या है?
What is the value of \( \sqrt{225}\div\sqrt{9} \)?
#real numbers
#square root division
#perfect square
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A (3)
B (4)
C (5)
D (6)
Explanation opens after your attempt
Step 1
Concept
\( \sqrt{225}=15 \) and \( \sqrt{9}=3 \). \(15\div3=5\).
Step 2
Why this answer is correct
The correct answer is C. (5). \( \sqrt{225}=15 \) and \( \sqrt{9}=3 \). \(15\div3=5\).
Step 3
Exam Tip
\( \sqrt{225}=15 \) और \( \sqrt{9}=3 \) है। \(15\div3=5\) होता है।
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\(2\sqrt{3}\times3\sqrt{3}\) का मान क्या है?
What is the value of \(2\sqrt{3}\times3\sqrt{3}\)?
#real numbers
#surd multiplication
#calculation
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A \(6\sqrt{6}\)
B \(9\sqrt{3}\)
C (12)
D (18)
Explanation opens after your attempt
Step 1
Concept
\(2\sqrt{3}\times3\sqrt{3}=6\times3=18\). Multiply coefficients and surd parts separately.
Step 2
Why this answer is correct
The correct answer is D. (18). \(2\sqrt{3}\times3\sqrt{3}=6\times3=18\). Multiply coefficients and surd parts separately.
Step 3
Exam Tip
\(2\sqrt{3}\times3\sqrt{3}=6\times3=18\) होता है। गुणांक और करणी भाग अलग-अलग गुणा करें।
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\( \sqrt{196} \) का मान क्या है?
What is the value of \( \sqrt{196} \)?
#real numbers
#perfect squares
#square root
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A (12)
B (13)
C (14)
D (16)
Explanation opens after your attempt
Step 1
Concept
Since \(14^2=196\), \( \sqrt{196}=14 \). Recognising perfect squares saves time in exams.
Step 2
Why this answer is correct
The correct answer is C. (14). Since \(14^2=196\), \( \sqrt{196}=14 \). Recognising perfect squares saves time in exams.
Step 3
Exam Tip
\(14^2=196\) इसलिए \( \sqrt{196}=14 \)। पूर्ण वर्गों को पहचानना परीक्षा में समय बचाता है।
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\( \sqrt{108} \) का सरल करणी रूप क्या है?
What is the simplified surd form of \( \sqrt{108} \)?
#real numbers
#surd simplification
#radicals
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A \(6\sqrt{3}\)
B \(3\sqrt{12}\)
C \(9\sqrt{3}\)
D \(12\sqrt{3}\)
Explanation opens after your attempt
Correct Answer
A. \(6\sqrt{3}\)
Step 1
Concept
Since \(108=36\times3\), \( \sqrt{108}=6\sqrt{3} \). Choose the largest perfect-square factor.
Step 2
Why this answer is correct
The correct answer is A. \(6\sqrt{3}\). Since \(108=36\times3\), \( \sqrt{108}=6\sqrt{3} \). Choose the largest perfect-square factor.
Step 3
Exam Tip
\(108=36\times3\) इसलिए \( \sqrt{108}=6\sqrt{3} \)। सबसे बड़ा पूर्ण वर्ग गुणनखंड चुनें।
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\( \sqrt{2}+\sqrt{18} \) का सरल रूप क्या है?
What is the simplified form of \( \sqrt{2}+\sqrt{18} \)?
#real numbers
#surd addition
#like surds
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A \( \sqrt{20} \)
B \(4\sqrt{2}\)
C \(3\sqrt{2}\)
D \(2\sqrt{10}\)
Explanation opens after your attempt
Correct Answer
B. \(4\sqrt{2}\)
Step 1
Concept
\( \sqrt{18}=3\sqrt{2} \), so \( \sqrt{2}+3\sqrt{2}=4\sqrt{2} \). First simplify the surd and then add like terms.
Step 2
Why this answer is correct
The correct answer is B. \(4\sqrt{2}\). \( \sqrt{18}=3\sqrt{2} \), so \( \sqrt{2}+3\sqrt{2}=4\sqrt{2} \). First simplify the surd and then add like terms.
Step 3
Exam Tip
\( \sqrt{18}=3\sqrt{2} \) इसलिए \( \sqrt{2}+3\sqrt{2}=4\sqrt{2} \)। पहले करणी को सरल करें फिर समान पद जोड़ें।
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