\( \sqrt{125} \) का सरल करणी रूप क्या है?
What is the simplified surd form of \( \sqrt{125} \)?
#real numbers
#surds
#simplification
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A \(5\sqrt{5}\)
B \(25\sqrt{5}\)
C \(10\sqrt{5}\)
D \(5\sqrt{25}\)
Explanation opens after your attempt
Correct Answer
A. \(5\sqrt{5}\)
Step 1
Concept
Since \(125=25\times5\), \( \sqrt{125}=5\sqrt{5} \). Choose the largest perfect-square factor.
Step 2
Why this answer is correct
The correct answer is A. \(5\sqrt{5}\). Since \(125=25\times5\), \( \sqrt{125}=5\sqrt{5} \). Choose the largest perfect-square factor.
Step 3
Exam Tip
\(125=25\times5\) इसलिए \( \sqrt{125}=5\sqrt{5} \)। सबसे बड़ा पूर्ण वर्ग गुणनखंड चुनें।
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\( \sqrt{147} \) को सरल करने पर क्या मिलेगा?
What is obtained by simplifying \( \sqrt{147} \)?
#real numbers
#radicals
#class 9
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A \(21\sqrt{7}\)
B \(7\sqrt{3}\)
C \(3\sqrt{7}\)
D \(49\sqrt{3}\)
Explanation opens after your attempt
Correct Answer
B. \(7\sqrt{3}\)
Step 1
Concept
Since \(147=49\times3\), \( \sqrt{147}=7\sqrt{3} \). Taking out the perfect square is the main step.
Step 2
Why this answer is correct
The correct answer is B. \(7\sqrt{3}\). Since \(147=49\times3\), \( \sqrt{147}=7\sqrt{3} \). Taking out the perfect square is the main step.
Step 3
Exam Tip
\(147=49\times3\) इसलिए \( \sqrt{147}=7\sqrt{3} \)। पूर्ण वर्ग को बाहर निकालना मुख्य कदम है।
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\( \sqrt{192} \) का सरल रूप कौन सा है?
Which is the simplified form of \( \sqrt{192} \)?
#real numbers
#surd form
#simplification
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A \(4\sqrt{12}\)
B \(12\sqrt{2}\)
C \(8\sqrt{3}\)
D \(16\sqrt{3}\)
Explanation opens after your attempt
Correct Answer
C. \(8\sqrt{3}\)
Step 1
Concept
Since \(192=64\times3\), \( \sqrt{192}=8\sqrt{3} \). Find the largest perfect square inside the radical.
Step 2
Why this answer is correct
The correct answer is C. \(8\sqrt{3}\). Since \(192=64\times3\), \( \sqrt{192}=8\sqrt{3} \). Find the largest perfect square inside the radical.
Step 3
Exam Tip
\(192=64\times3\) इसलिए \( \sqrt{192}=8\sqrt{3} \)। करणी में सबसे बड़ा पूर्ण वर्ग खोजें।
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\(3\sqrt{8}+2\sqrt{18}\) का सरल रूप क्या है?
What is the simplified form of \(3\sqrt{8}+2\sqrt{18}\)?
#real numbers
#like surds
#addition
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A \(12\sqrt{2}\)
B \(6\sqrt{26}\)
C \(10\sqrt{2}\)
D \(8\sqrt{3}\)
Explanation opens after your attempt
Correct Answer
A. \(12\sqrt{2}\)
Step 1
Concept
\( \sqrt{8}=2\sqrt{2} \) and \( \sqrt{18}=3\sqrt{2} \). So the sum is \(6\sqrt{2}+6\sqrt{2}=12\sqrt{2}\).
Step 2
Why this answer is correct
The correct answer is A. \(12\sqrt{2}\). \( \sqrt{8}=2\sqrt{2} \) and \( \sqrt{18}=3\sqrt{2} \). So the sum is \(6\sqrt{2}+6\sqrt{2}=12\sqrt{2}\).
Step 3
Exam Tip
\( \sqrt{8}=2\sqrt{2} \) और \( \sqrt{18}=3\sqrt{2} \) हैं। इसलिए योग \(6\sqrt{2}+6\sqrt{2}=12\sqrt{2}\) है।
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\(5\sqrt{12}-\sqrt{75}\) का सरल रूप क्या है?
What is the simplified form of \(5\sqrt{12}-\sqrt{75}\)?
#real numbers
#surd subtraction
#medium
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A \(5\sqrt{3}\)
B \(10\sqrt{3}\)
C \(15\sqrt{3}\)
D \(20\sqrt{3}\)
Explanation opens after your attempt
Correct Answer
A. \(5\sqrt{3}\)
Step 1
Concept
\(5\sqrt{12}=10\sqrt{3}\) and \( \sqrt{75}=5\sqrt{3} \). The difference is \(5\sqrt{3}\).
Step 2
Why this answer is correct
The correct answer is A. \(5\sqrt{3}\). \(5\sqrt{12}=10\sqrt{3}\) and \( \sqrt{75}=5\sqrt{3} \). The difference is \(5\sqrt{3}\).
Step 3
Exam Tip
\(5\sqrt{12}=10\sqrt{3}\) और \( \sqrt{75}=5\sqrt{3} \) है। अंतर \(5\sqrt{3}\) होगा।
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( \sqrt{3}\(2+\sqrt{3}\) ) का मान क्या है?
What is the value of ( \sqrt{3}\(2+\sqrt{3}\) )?
#real numbers
#distribution
#surds
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A \(2\sqrt{3}+3\)
B \(5\sqrt{3}\)
C \(2+\sqrt{6}\)
D \(3\sqrt{3}+2\)
Explanation opens after your attempt
Correct Answer
A. \(2\sqrt{3}+3\)
Step 1
Concept
By distributive law, \( \sqrt{3}\times2+\sqrt{3}\times\sqrt{3}=2\sqrt{3}+3 \). Remember \( \sqrt{a}\sqrt{a}=a \) in surd multiplication.
Step 2
Why this answer is correct
The correct answer is A. \(2\sqrt{3}+3\). By distributive law, \( \sqrt{3}\times2+\sqrt{3}\times\sqrt{3}=2\sqrt{3}+3 \). Remember \( \sqrt{a}\sqrt{a}=a \) in surd multiplication.
Step 3
Exam Tip
वितरण नियम से \( \sqrt{3}\times2+\sqrt{3}\times\sqrt{3}=2\sqrt{3}+3 \)। करणी गुणा में \(\sqrt{a}\sqrt{a}=a\) याद रखें।
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( \(2+\sqrt{7}\)2 ) का विस्तार क्या है?
What is the expansion of ( \(2+\sqrt{7}\)2 )?
#real numbers
#identity
#surds
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A \(11+4\sqrt{7}\)
B \(9+2\sqrt{7}\)
C \(4+7\sqrt{2}\)
D \(7+4\sqrt{2}\)
Explanation opens after your attempt
Correct Answer
A. \(11+4\sqrt{7}\)
Step 1
Concept
Use ( (a+b)2 =a-2 +2ab+b-2 ). Here \(4+4\sqrt{7}+7=11+4\sqrt{7}\).
Step 2
Why this answer is correct
The correct answer is A. \(11+4\sqrt{7}\). Use ( (a+b)2 =a-2 +2ab+b-2 ). Here \(4+4\sqrt{7}+7=11+4\sqrt{7}\).
Step 3
Exam Tip
( (a+b)2 =a-2 +2ab+b-2 ) लगाएँ। यहाँ \(4+4\sqrt{7}+7=11+4\sqrt{7}\) मिलता है।
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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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( \(3+\sqrt{10}\)\(3-\sqrt{10}\) ) का मान क्या है?
What is the value of ( \(3+\sqrt{10}\)\(3-\sqrt{10}\) )?
#real numbers
#conjugate
#surds
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A (1)
B ( -1 )
C (19)
D \(6-\sqrt{10}\)
Explanation opens after your attempt
Step 1
Concept
Conjugate multiplication gives (32 -\(\sqrt{10}\)2 =9-10=-1). The middle terms cancel.
Step 2
Why this answer is correct
The correct answer is B. ( -1 ). Conjugate multiplication gives (32 -\(\sqrt{10}\)2 =9-10=-1). The middle terms cancel.
Step 3
Exam Tip
संयुग्मी गुणन से (32 -\(\sqrt{10}\)2 =9-10=-1) मिलता है। मध्य पद कट जाते हैं।
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\( \frac{4}{\sqrt{5}} \) का परिमेय हर वाला रूप क्या है?
What is the rationalised form of \( \frac{4}{\sqrt{5}} \)?
#real numbers
#rationalisation
#denominator
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A \( \frac{4\sqrt{5}}{5} \)
B \( \frac{\sqrt{5}}{4} \)
C \( \frac{4}{5} \)
D \(4\sqrt{5}\)
Explanation opens after your attempt
Correct Answer
A. \( \frac{4\sqrt{5}}{5} \)
Step 1
Concept
Multiply numerator and denominator by \( \sqrt{5} \). This makes the denominator (5).
Step 2
Why this answer is correct
The correct answer is A. \( \frac{4\sqrt{5}}{5} \). Multiply numerator and denominator by \( \sqrt{5} \). This makes the denominator (5).
Step 3
Exam Tip
अंश और हर को \( \sqrt{5} \) से गुणा करें। इससे हर (5) बनता है।
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\( \frac{7}{2\sqrt{3}} \) का परिमेय हर वाला रूप क्या है?
What is the rationalised form of \( \frac{7}{2\sqrt{3}} \)?
#real numbers
#rationalisation
#surds
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A \( \frac{7\sqrt{3}}{6} \)
B \( \frac{7\sqrt{3}}{2} \)
C \( \frac{7}{6} \)
D \( \frac{14\sqrt{3}}{3} \)
Explanation opens after your attempt
Correct Answer
A. \( \frac{7\sqrt{3}}{6} \)
Step 1
Concept
Multiplying numerator and denominator by \( \sqrt{3} \) gives \( \frac{7\sqrt{3}}{6} \). The radical should be removed from the denominator.
Step 2
Why this answer is correct
The correct answer is A. \( \frac{7\sqrt{3}}{6} \). Multiplying numerator and denominator by \( \sqrt{3} \) gives \( \frac{7\sqrt{3}}{6} \). The radical should be removed from the denominator.
Step 3
Exam Tip
अंश और हर को \( \sqrt{3} \) से गुणा करने पर \( \frac{7\sqrt{3}}{6} \) मिलता है। हर में करणी हटनी चाहिए।
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\( \frac{1}{\sqrt{6}+\sqrt{5}} \) का परिमेय हर वाला रूप क्या है?
What is the rationalised form of \( \frac{1}{\sqrt{6}+\sqrt{5}} \)?
#real numbers
#rationalisation
#conjugate
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A \( \sqrt{6}-\sqrt{5} \)
B \( \sqrt{6}+\sqrt{5} \)
C \( \frac{\sqrt{6}-\sqrt{5}}{11} \)
D \( \frac{1}{\sqrt{6}-\sqrt{5}} \)
Explanation opens after your attempt
Correct Answer
A. \( \sqrt{6}-\sqrt{5} \)
Step 1
Concept
Multiply by the conjugate \( \sqrt{6}-\sqrt{5} \) and the denominator becomes (6-5=1). So the answer is \( \sqrt{6}-\sqrt{5} \).
Step 2
Why this answer is correct
The correct answer is A. \( \sqrt{6}-\sqrt{5} \). Multiply by the conjugate \( \sqrt{6}-\sqrt{5} \) and the denominator becomes (6-5=1). So the answer is \( \sqrt{6}-\sqrt{5} \).
Step 3
Exam Tip
संयुग्मी \( \sqrt{6}-\sqrt{5} \) से गुणा करें और हर (6-5=1) बनेगा। इसलिए उत्तर \( \sqrt{6}-\sqrt{5} \) है।
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\( \frac{1}{\sqrt{7}-\sqrt{3}} \) का परिमेय हर वाला रूप क्या है?
What is the rationalised form of \( \frac{1}{\sqrt{7}-\sqrt{3}} \)?
#real numbers
#rationalisation
#binomial surd
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A \( \frac{\sqrt{7}+\sqrt{3}}{4} \)
B \( \sqrt{7}+\sqrt{3} \)
C \( \frac{\sqrt{7}-\sqrt{3}}{10} \)
D \( \frac{1}{4} \)
Explanation opens after your attempt
Correct Answer
A. \( \frac{\sqrt{7}+\sqrt{3}}{4} \)
Step 1
Concept
Multiply by the conjugate \( \sqrt{7}+\sqrt{3} \). The denominator becomes (7-3=4).
Step 2
Why this answer is correct
The correct answer is A. \( \frac{\sqrt{7}+\sqrt{3}}{4} \). Multiply by the conjugate \( \sqrt{7}+\sqrt{3} \). The denominator becomes (7-3=4).
Step 3
Exam Tip
संयुग्मी \( \sqrt{7}+\sqrt{3} \) से गुणा करें। हर (7-3=4) मिलेगा।
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\( \sqrt{45}+\sqrt{80}-\sqrt{20} \) का सरल रूप क्या है?
What is the simplified form of \( \sqrt{45}+\sqrt{80}-\sqrt{20} \)?
#real numbers
#surd simplification
#combined
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A \(8\sqrt{5}\)
B \(6\sqrt{5}\)
C \(10\sqrt{5}\)
D \(4\sqrt{5}\)
Explanation opens after your attempt
Correct Answer
B. \(6\sqrt{5}\)
Step 1
Concept
\( \sqrt{45}=3\sqrt{5} \), \( \sqrt{80}=4\sqrt{5} \), and \( \sqrt{20}=2\sqrt{5} \). So the value is \(3\sqrt{5}+4\sqrt{5}-2\sqrt{5}=5\sqrt{5}\).
Step 2
Why this answer is correct
The correct answer is B. \(6\sqrt{5}\). \( \sqrt{45}=3\sqrt{5} \), \( \sqrt{80}=4\sqrt{5} \), and \( \sqrt{20}=2\sqrt{5} \). So the value is \(3\sqrt{5}+4\sqrt{5}-2\sqrt{5}=5\sqrt{5}\).
Step 3
Exam Tip
\( \sqrt{45}=3\sqrt{5} \), \( \sqrt{80}=4\sqrt{5} \), और \( \sqrt{20}=2\sqrt{5} \)। इसलिए \(3\sqrt{5}+4\sqrt{5}-2\sqrt{5}=5\sqrt{5}\) नहीं बल्कि \(5\sqrt{5}\) होगा।
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\( \sqrt{45}+\sqrt{80}-\sqrt{20} \) का सही सरल रूप चुनिए।
Choose the correct simplified form of \( \sqrt{45}+\sqrt{80}-\sqrt{20} \).
#real numbers
#like radicals
#calculation
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A \(3\sqrt{5}\)
B \(5\sqrt{5}\)
C \(7\sqrt{5}\)
D \(9\sqrt{5}\)
Explanation opens after your attempt
Correct Answer
B. \(5\sqrt{5}\)
Step 1
Concept
Convert all surds into terms of \( \sqrt{5} \). \(3\sqrt{5}+4\sqrt{5}-2\sqrt{5}=5\sqrt{5}\) is correct.
Step 2
Why this answer is correct
The correct answer is B. \(5\sqrt{5}\). Convert all surds into terms of \( \sqrt{5} \). \(3\sqrt{5}+4\sqrt{5}-2\sqrt{5}=5\sqrt{5}\) is correct.
Step 3
Exam Tip
तीनों करणी को \( \sqrt{5} \) के पदों में बदलें। \(3\sqrt{5}+4\sqrt{5}-2\sqrt{5}=5\sqrt{5}\) सही है।
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\( \sqrt{28}+2\sqrt{63} \) का सरल रूप क्या है?
What is the simplified form of \( \sqrt{28}+2\sqrt{63} \)?
#real numbers
#surd addition
#medium
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A \(16\sqrt{7}\)
B \(8\sqrt{7}\)
C \(14\sqrt{7}\)
D \(2\sqrt{91}\)
Explanation opens after your attempt
Correct Answer
B. \(8\sqrt{7}\)
Step 1
Concept
\( \sqrt{28}=2\sqrt{7} \) and \(2\sqrt{63}=6\sqrt{7}\). The sum is \(8\sqrt{7}\).
Step 2
Why this answer is correct
The correct answer is B. \(8\sqrt{7}\). \( \sqrt{28}=2\sqrt{7} \) and \(2\sqrt{63}=6\sqrt{7}\). The sum is \(8\sqrt{7}\).
Step 3
Exam Tip
\( \sqrt{28}=2\sqrt{7} \) और \(2\sqrt{63}=6\sqrt{7}\) है। योग \(8\sqrt{7}\) होगा।
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\(3\sqrt{27}-2\sqrt{12}\) का सरल रूप क्या है?
What is the simplified form of \(3\sqrt{27}-2\sqrt{12}\)?
#real numbers
#surds
#subtraction
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A \(5\sqrt{3}\)
B \(9\sqrt{3}\)
C \(13\sqrt{3}\)
D \(7\sqrt{3}\)
Explanation opens after your attempt
Correct Answer
A. \(5\sqrt{3}\)
Step 1
Concept
\(3\sqrt{27}=9\sqrt{3}\) and \(2\sqrt{12}=4\sqrt{3}\). The difference is \(5\sqrt{3}\).
Step 2
Why this answer is correct
The correct answer is A. \(5\sqrt{3}\). \(3\sqrt{27}=9\sqrt{3}\) and \(2\sqrt{12}=4\sqrt{3}\). The difference is \(5\sqrt{3}\).
Step 3
Exam Tip
\(3\sqrt{27}=9\sqrt{3}\) और \(2\sqrt{12}=4\sqrt{3}\) है। अंतर \(5\sqrt{3}\) मिलता है।
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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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\( \frac{\sqrt{72}}{\sqrt{2}}+\sqrt{9} \) का मान क्या है?
What is the value of \( \frac{\sqrt{72}}{\sqrt{2}}+\sqrt{9} \)?
#real numbers
#mixed surds
#calculation
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A (9)
B (12)
C (15)
D (18)
Explanation opens after your attempt
Step 1
Concept
\( \frac{\sqrt{72}}{\sqrt{2}}=\sqrt{36}=6 \) and \( \sqrt{9}=3 \). The total value is (9).
Step 2
Why this answer is correct
The correct answer is A. (9). \( \frac{\sqrt{72}}{\sqrt{2}}=\sqrt{36}=6 \) and \( \sqrt{9}=3 \). The total value is (9).
Step 3
Exam Tip
\( \frac{\sqrt{72}}{\sqrt{2}}=\sqrt{36}=6 \) और \( \sqrt{9}=3 \)। कुल मान (9) है।
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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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\( \sqrt{2.56}-\sqrt{0.36} \) का मान क्या है?
What is the value of \( \sqrt{2.56}-\sqrt{0.36} \)?
#real numbers
#decimal radicals
#subtraction
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A (1)
B (1.2)
C (1.4)
D (2.2)
Explanation opens after your attempt
Step 1
Concept
\( \sqrt{2.56}=1.6 \) and \( \sqrt{0.36}=0.6 \). The difference is (1).
Step 2
Why this answer is correct
The correct answer is A. (1). \( \sqrt{2.56}=1.6 \) and \( \sqrt{0.36}=0.6 \). The difference is (1).
Step 3
Exam Tip
\( \sqrt{2.56}=1.6 \) और \( \sqrt{0.36}=0.6 \) है। अंतर (1) है।
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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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कौन सा विकल्प (2) और (3) के बीच अपरिमेय संख्या है?
Which option is an irrational number between (2) and (3)?
#real numbers
#irrational between
#interval
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A \( \frac{5}{2} \)
B \( \sqrt{8} \)
C (2.75)
D \( \sqrt{9} \)
Explanation opens after your attempt
Correct Answer
B. \( \sqrt{8} \)
Step 1
Concept
Since \(2^2<8<3^2\), \( \sqrt{8} \) lies between (2) and (3). Since (8) is not a perfect square, it is irrational.
Step 2
Why this answer is correct
The correct answer is B. \( \sqrt{8} \). Since \(2^2<8<3^2\), \( \sqrt{8} \) lies between (2) and (3). Since (8) is not a perfect square, it is irrational.
Step 3
Exam Tip
\(2^2<8<3^2\) इसलिए \( \sqrt{8} \) (2) और (3) के बीच है। (8) पूर्ण वर्ग नहीं है इसलिए यह अपरिमेय है।
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\( \sqrt{18} \) और \( \frac{9}{2} \) में कौन बड़ा है?
Which is greater between \( \sqrt{18} \) and \( \frac{9}{2} \)?
#real numbers
#comparison
#ordering
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A \( \sqrt{18} \)
B \( \frac{9}{2} \)
C दोनों बराबर / Both are equal
D निर्धारित नहीं / Cannot be determined
Explanation opens after your attempt
Correct Answer
B. \( \frac{9}{2} \)
Step 1
Concept
\( \sqrt{18}\approx4.24 \) and \( \frac{9}{2}=4.5 \). Therefore \( \frac{9}{2} \) is greater.
Step 2
Why this answer is correct
The correct answer is B. \( \frac{9}{2} \). \( \sqrt{18}\approx4.24 \) and \( \frac{9}{2}=4.5 \). Therefore \( \frac{9}{2} \) is greater.
Step 3
Exam Tip
\( \sqrt{18}\approx4.24 \) और \( \frac{9}{2}=4.5 \) है। इसलिए \( \frac{9}{2} \) बड़ा 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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\( -\sqrt{20} \) और ( -4.4 ) में कौन बड़ी संख्या है?
Which is greater between \( -\sqrt{20} \) and ( -4.4 )?
#real numbers
#negative comparison
#number line
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A \( -\sqrt{20} \)
B ( -4.4 )
C दोनों बराबर / Both are equal
D दोनों धनात्मक / Both are positive
Explanation opens after your attempt
Correct Answer
B. ( -4.4 )
Step 1
Concept
\( \sqrt{20}\approx4.47 \), so \( -\sqrt{20}\approx-4.47 \). ( -4.4 ) is closer to zero, so it is greater.
Step 2
Why this answer is correct
The correct answer is B. ( -4.4 ). \( \sqrt{20}\approx4.47 \), so \( -\sqrt{20}\approx-4.47 \). ( -4.4 ) is closer to zero, so it is greater.
Step 3
Exam Tip
\( \sqrt{20}\approx4.47 \) इसलिए \( -\sqrt{20}\approx-4.47 \)। ( -4.4 ) शून्य के अधिक निकट है इसलिए बड़ी है।
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कौन सा विकल्प गलत है?
Which option is incorrect?
#real numbers
#undefined
#false statement
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A \( \sqrt{2} \) वास्तविक संख्या है / \( \sqrt{2} \) is a real number
B (0.333...) परिमेय है / (0.333...) is rational
C \( \frac{5}{0} \) वास्तविक संख्या है / \( \frac{5}{0} \) is a real number
D ( -7 ) वास्तविक संख्या है / ( -7 ) is a real number
Explanation opens after your attempt
Correct Answer
C. \( \frac{5}{0} \) वास्तविक संख्या है / \( \frac{5}{0} \) is a real number
Step 1
Concept
\( \frac{5}{0} \) is undefined because the denominator is zero. Such a number is not considered real.
Step 2
Why this answer is correct
The correct answer is C. \( \frac{5}{0} \) वास्तविक संख्या है / \( \frac{5}{0} \) is a real number. \( \frac{5}{0} \) is undefined because the denominator is zero. Such a number is not considered real.
Step 3
Exam Tip
\( \frac{5}{0} \) परिभाषित नहीं है क्योंकि हर शून्य है। ऐसी संख्या वास्तविक नहीं मानी जाती।
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(0.12122122212222...) यदि अनावर्ती है तो यह किस प्रकार की संख्या है?
If (0.12122122212222...) is 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 पूर्णांक / Integer
D समाप्त दशमलव / Terminating decimal
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. Identifying the non-repeating pattern is important.
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. Identifying the non-repeating pattern is important.
Step 3
Exam Tip
असमाप्त और अनावर्ती दशमलव अपरिमेय होता है। अनावर्ती पैटर्न पहचानना जरूरी है।
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(1.232323...) किस प्रकार की वास्तविक संख्या है?
What type of real number is (1.232323...)?
#real numbers
#repeating decimal
#rational
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A अपरिमेय संख्या / Irrational number
B परिमेय वास्तविक संख्या / Rational real number
C केवल पूर्णांक / Only integer
D अपरिभाषित संख्या / Undefined number
Explanation opens after your attempt
Correct Answer
B. परिमेय वास्तविक संख्या / Rational real number
Step 1
Concept
The block (23) repeats, so the decimal is repeating. Repeating decimals are rational.
Step 2
Why this answer is correct
The correct answer is B. परिमेय वास्तविक संख्या / Rational real number. The block (23) repeats, so the decimal is repeating. Repeating decimals are rational.
Step 3
Exam Tip
(23) बार-बार आ रहा है इसलिए दशमलव आवर्ती है। आवर्ती दशमलव परिमेय होते हैं।
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(0.040040004...) यदि कोई स्थिर आवृत्ति नहीं है तो यह क्या है?
If (0.040040004...) has no fixed repetition, what is it?
#real numbers
#non repeating decimal
#irrational
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A परिमेय संख्या / Rational number
B पूर्ण संख्या / Whole number
C अपरिमेय वास्तविक संख्या / Irrational real number
D प्राकृतिक संख्या / Natural number
Explanation opens after your attempt
Correct Answer
C. अपरिमेय वास्तविक संख्या / Irrational real number
Step 1
Concept
A non-terminating decimal without fixed repetition is irrational. Only repeating decimals are rational.
Step 2
Why this answer is correct
The correct answer is C. अपरिमेय वास्तविक संख्या / Irrational real number. A non-terminating decimal without fixed repetition is irrational. Only repeating decimals are rational.
Step 3
Exam Tip
स्थिर आवृत्ति न होने पर असमाप्त दशमलव अपरिमेय होता है। केवल आवर्ती दशमलव परिमेय होते हैं।
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\( \frac{7}{11} \) के दशमलव रूप के बारे में सही कथन क्या है?
What is the correct statement about the decimal form of \( \frac{7}{11} \)?
#real numbers
#decimal expansion
#rational
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A यह समाप्त दशमलव है / It is terminating
B यह आवर्ती दशमलव है / It is repeating
C यह अपरिभाषित है / It is undefined
D यह पूर्णांक है / It is an integer
Explanation opens after your attempt
Correct Answer
B. यह आवर्ती दशमलव है / It is repeating
Step 1
Concept
The denominator (11) does not have only factors (2) and (5). Therefore the decimal will repeat.
Step 2
Why this answer is correct
The correct answer is B. यह आवर्ती दशमलव है / It is repeating. The denominator (11) does not have only factors (2) and (5). Therefore the decimal will repeat.
Step 3
Exam Tip
हर (11) में केवल (2) और (5) के गुणनखंड नहीं हैं। इसलिए दशमलव आवर्ती होगा।
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\( \frac{13}{40} \) के दशमलव रूप के बारे में सही कथन क्या है?
What is the correct statement about the decimal form of \( \frac{13}{40} \)?
#real numbers
#terminating decimal
#denominator
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A यह समाप्त दशमलव है / It is terminating
B यह अपरिमेय है / It is irrational
C यह अपरिभाषित है / It is undefined
D यह असमाप्त अनावर्ती है / It is non-terminating non-repeating
Explanation opens after your attempt
Correct Answer
A. यह समाप्त दशमलव है / It is terminating
Step 1
Concept
\(40=2^3\times5\), so the denominator has only (2) and (5). Such a fraction gives a terminating decimal.
Step 2
Why this answer is correct
The correct answer is A. यह समाप्त दशमलव है / It is terminating. \(40=2^3\times5\), so the denominator has only (2) and (5). Such a fraction gives a terminating decimal.
Step 3
Exam Tip
\(40=2^3\times5\) है इसलिए हर में केवल (2) और (5) हैं। ऐसा भिन्न समाप्त दशमलव देता है।
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\( \frac{3}{28} \) के दशमलव रूप के बारे में सही कथन क्या है?
What is the correct statement about the decimal form of \( \frac{3}{28} \)?
#real numbers
#decimal expansion
#recurring
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A यह समाप्त दशमलव है / It is terminating
B यह असमाप्त आवर्ती दशमलव है / It is non-terminating repeating decimal
C यह अपरिमेय है / It is irrational
D यह पूर्णांक है / It is an integer
Explanation opens after your attempt
Correct Answer
B. यह असमाप्त आवर्ती दशमलव है / It is non-terminating repeating decimal
Step 1
Concept
\(28=2^2\times7\) has factor (7). So the decimal will not terminate but will repeat.
Step 2
Why this answer is correct
The correct answer is B. यह असमाप्त आवर्ती दशमलव है / It is non-terminating repeating decimal. \(28=2^2\times7\) has factor (7). So the decimal will not terminate but will repeat.
Step 3
Exam Tip
\(28=2^2\times7\) में (7) गुणनखंड है। इसलिए दशमलव समाप्त नहीं होगा लेकिन आवर्ती होगा।
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\( \frac{17}{125} \) दशमलव रूप में किस प्रकार का होगा?
What type will \( \frac{17}{125} \) be in decimal form?
#real numbers
#terminating decimal
#factorisation
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A समाप्त दशमलव / Terminating decimal
B असमाप्त अनावर्ती दशमलव / Non-terminating non-repeating decimal
C अपरिमेय संख्या / Irrational number
D अपरिभाषित संख्या / Undefined number
Explanation opens after your attempt
Correct Answer
A. समाप्त दशमलव / Terminating decimal
Step 1
Concept
\(125=5^3\), so the denominator has only factor (5). Such a fraction gives a terminating decimal.
Step 2
Why this answer is correct
The correct answer is A. समाप्त दशमलव / Terminating decimal. \(125=5^3\), so the denominator has only factor (5). Such a fraction gives a terminating decimal.
Step 3
Exam Tip
\(125=5^3\) है इसलिए हर में केवल (5) का गुणनखंड है। ऐसा भिन्न समाप्त दशमलव देता है।
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\( \frac{19}{30} \) का दशमलव विस्तार कैसा होगा?
What will be the decimal expansion of \( \frac{19}{30} \)?
#real numbers
#decimal expansion
#medium
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A समाप्त / Terminating
B असमाप्त आवर्ती / Non-terminating repeating
C असमाप्त अनावर्ती / Non-terminating non-repeating
D अपरिभाषित / Undefined
Explanation opens after your attempt
Correct Answer
B. असमाप्त आवर्ती / Non-terminating repeating
Step 1
Concept
\(30=2\times3\times5\) also has (3). Therefore it will be a non-terminating repeating decimal.
Step 2
Why this answer is correct
The correct answer is B. असमाप्त आवर्ती / Non-terminating repeating. \(30=2\times3\times5\) also has (3). Therefore it will be a non-terminating repeating decimal.
Step 3
Exam Tip
\(30=2\times3\times5\) में (3) भी है। इसलिए यह असमाप्त आवर्ती दशमलव होगा।
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\( \sqrt{2}+\sqrt{3} \) किस प्रकार की संख्या है?
What type of number is \( \sqrt{2}+\sqrt{3} \)?
#real numbers
#irrational sum
#surds
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A परिमेय संख्या / Rational number
B अपरिमेय वास्तविक संख्या / Irrational real number
C पूर्णांक / Integer
D प्राकृतिक संख्या / Natural number
Explanation opens after your attempt
Correct Answer
B. अपरिमेय वास्तविक संख्या / Irrational real number
Step 1
Concept
The sum of these two different irrational surds is irrational. It lies on the real number line.
Step 2
Why this answer is correct
The correct answer is B. अपरिमेय वास्तविक संख्या / Irrational real number. The sum of these two different irrational surds is irrational. It lies on the real number line.
Step 3
Exam Tip
दो अलग-अलग अपरिमेय करणी पदों का योग यहाँ अपरिमेय है। यह वास्तविक संख्या रेखा पर स्थित है।
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\( \sqrt{5}\times\sqrt{20} \) किस प्रकार की संख्या है?
What type of number is \( \sqrt{5}\times\sqrt{20} \)?
#real numbers
#surd product
#rational result
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A परिमेय वास्तविक संख्या / Rational real number
B अपरिमेय वास्तविक संख्या / Irrational real number
C अपरिभाषित संख्या / Undefined number
D केवल प्राकृतिक नहीं / Not only natural
Explanation opens after your attempt
Correct Answer
A. परिमेय वास्तविक संख्या / Rational real number
Step 1
Concept
\( \sqrt{5}\times\sqrt{20}=\sqrt{100}=10 \). Therefore the result is a rational real number.
Step 2
Why this answer is correct
The correct answer is A. परिमेय वास्तविक संख्या / Rational real number. \( \sqrt{5}\times\sqrt{20}=\sqrt{100}=10 \). Therefore the result is a rational real number.
Step 3
Exam Tip
\( \sqrt{5}\times\sqrt{20}=\sqrt{100}=10 \) है। इसलिए परिणाम परिमेय वास्तविक संख्या है।
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\( \sqrt{7}\times\sqrt{14} \) किस प्रकार की संख्या है?
What type of number is \( \sqrt{7}\times\sqrt{14} \)?
#real numbers
#surd multiplication
#classification
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A परिमेय संख्या / Rational number
B अपरिमेय वास्तविक संख्या / Irrational real number
C पूर्णांक / Integer
D समाप्त दशमलव / Terminating decimal
Explanation opens after your attempt
Correct Answer
B. अपरिमेय वास्तविक संख्या / Irrational real number
Step 1
Concept
\( \sqrt{7}\times\sqrt{14}=\sqrt{98}=7\sqrt{2} \). This is an irrational real number.
Step 2
Why this answer is correct
The correct answer is B. अपरिमेय वास्तविक संख्या / Irrational real number. \( \sqrt{7}\times\sqrt{14}=\sqrt{98}=7\sqrt{2} \). This is an irrational real number.
Step 3
Exam Tip
\( \sqrt{7}\times\sqrt{14}=\sqrt{98}=7\sqrt{2} \) है। यह अपरिमेय वास्तविक संख्या है।
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\(2+\sqrt{13}\) और \(2-\sqrt{13}\) का गुणनफल क्या है?
What is the product of \(2+\sqrt{13}\) and \(2-\sqrt{13}\)?
#real numbers
#conjugate
#product
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A (9)
B ( -9 )
C (17)
D \(4+\sqrt{13}\)
Explanation opens after your attempt
Step 1
Concept
Conjugate multiplication gives (22 -\(\sqrt{13}\)2 =4-13=-9). Use the difference of squares rule here.
Step 2
Why this answer is correct
The correct answer is B. ( -9 ). Conjugate multiplication gives (22 -\(\sqrt{13}\)2 =4-13=-9). Use the difference of squares rule here.
Step 3
Exam Tip
संयुग्मी गुणन से (22 -\(\sqrt{13}\)2 =4-13=-9) मिलता है। इस रूप में अंतर के वर्ग का नियम लगाएँ।
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\( \frac{2+\sqrt{3}}{2-\sqrt{3}} \) का परिमेय हर करने पर मान क्या होगा?
What is the value of \( \frac{2+\sqrt{3}}{2-\sqrt{3}} \) after rationalising?
#real numbers
#rationalisation
#advanced
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A \(7+4\sqrt{3}\)
B \(7-4\sqrt{3}\)
C (1)
D \(4+\sqrt{3}\)
Explanation opens after your attempt
Correct Answer
A. \(7+4\sqrt{3}\)
Step 1
Concept
Multiply by the conjugate \(2+\sqrt{3}\). The numerator becomes (\(2+\sqrt{3}\)2 =7+4\sqrt{3}) and the denominator becomes (1).
Step 2
Why this answer is correct
The correct answer is A. \(7+4\sqrt{3}\). Multiply by the conjugate \(2+\sqrt{3}\). The numerator becomes (\(2+\sqrt{3}\)2 =7+4\sqrt{3}) and the denominator becomes (1).
Step 3
Exam Tip
हर के संयुग्मी \(2+\sqrt{3}\) से गुणा करें। अंश (\(2+\sqrt{3}\)2 =7+4\sqrt{3}) और हर (1) होगा।
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\( \frac{\sqrt{5}-1}{\sqrt{5}+1} \) का हर परिमेय करने के बाद हर क्या होगा?
What will be the denominator after rationalising \( \frac{\sqrt{5}-1}{\sqrt{5}+1} \)?
#real numbers
#rationalisation
#denominator
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A (4)
B (6)
C (5)
D (1)
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Step 1
Concept
Multiplying by the conjugate \( \sqrt{5}-1 \) makes the denominator (5-1=4). Use difference of squares in the conjugate method.
Step 2
Why this answer is correct
The correct answer is A. (4). Multiplying by the conjugate \( \sqrt{5}-1 \) makes the denominator (5-1=4). Use difference of squares in the conjugate method.
Step 3
Exam Tip
हर के संयुग्मी \( \sqrt{5}-1 \) से गुणा करने पर हर (5-1=4) होगा। संयुग्मी विधि में अंतर के वर्ग का प्रयोग करें।
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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)
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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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\( |\sqrt{16}-\sqrt{81}| \) का मान क्या है?
What is the value of \( |\sqrt{16}-\sqrt{81}| \)?
#real numbers
#absolute value
#calculation
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A (5)
B (13)
C ( -5 )
D (9)
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Step 1
Concept
\( \sqrt{16}=4 \) and \( \sqrt{81}=9 \). So ( |4-9|=5 ).
Step 2
Why this answer is correct
The correct answer is A. (5). \( \sqrt{16}=4 \) and \( \sqrt{81}=9 \). So ( |4-9|=5 ).
Step 3
Exam Tip
\( \sqrt{16}=4 \) और \( \sqrt{81}=9 \) है। ( |4-9|=5 ) होगा।
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\( \sqrt{a^2} \) का मान वास्तविक संख्याओं में क्या होता है?
What is the value of \( \sqrt{a^2} \) in real numbers?
#real numbers
#absolute value
#concept
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A (a)
B ( -a )
C ( |a| )
D \(a^2\)
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Correct Answer
C. ( |a| )
Step 1
Concept
In real numbers, \( \sqrt{a^2}=|a| \) because the principal square root is non-negative. Pay attention to the sign.
Step 2
Why this answer is correct
The correct answer is C. ( |a| ). In real numbers, \( \sqrt{a^2}=|a| \) because the principal square root is non-negative. Pay attention to the sign.
Step 3
Exam Tip
वास्तविक संख्याओं में \( \sqrt{a^2}=|a| \) होता है क्योंकि वर्गमूल अमुख्य रूप से गैर-ऋणात्मक होता है। संकेत का ध्यान रखें।
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यदि (x=-5) है तो \( \sqrt{x^2} \) का मान क्या होगा?
If (x=-5), what is the value of \( \sqrt{x^2} \)?
#real numbers
#absolute value
#substitution
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A ( -5 )
B (5)
C (25)
D \( \sqrt{-25} \)
Explanation opens after your attempt
Step 1
Concept
\( \sqrt{x^2}=|x| \). When (x=-5), ( |-5|=5 ).
Step 2
Why this answer is correct
The correct answer is B. (5). \( \sqrt{x^2}=|x| \). When (x=-5), ( |-5|=5 ).
Step 3
Exam Tip
\( \sqrt{x^2}=|x| \) होता है। (x=-5) होने पर ( |-5|=5 ) मिलेगा।
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\( \frac{1}{\sqrt{3}+\sqrt{2}} \) का परिमेय हर वाला रूप क्या है?
What is the rationalised form of \( \frac{1}{\sqrt{3}+\sqrt{2}} \)?
#real numbers
#rationalisation
#conjugate
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A \( \sqrt{3}+\sqrt{2} \)
B \( \frac{\sqrt{3}+\sqrt{2}}{5} \)
C \( \sqrt{3}-\sqrt{2} \)
D \( \frac{1}{\sqrt{3}-\sqrt{2}} \)
Explanation opens after your attempt
Correct Answer
C. \( \sqrt{3}-\sqrt{2} \)
Step 1
Concept
Multiplying by the conjugate \( \sqrt{3}-\sqrt{2} \) makes the denominator (3-2=1). So the rationalised form is \( \sqrt{3}-\sqrt{2} \).
Step 2
Why this answer is correct
The correct answer is C. \( \sqrt{3}-\sqrt{2} \). Multiplying by the conjugate \( \sqrt{3}-\sqrt{2} \) makes the denominator (3-2=1). So the rationalised form is \( \sqrt{3}-\sqrt{2} \).
Step 3
Exam Tip
संयुग्मी \( \sqrt{3}-\sqrt{2} \) से गुणा करने पर हर (3-2=1) बनता है। इसलिए परिमेय हर वाला रूप \( \sqrt{3}-\sqrt{2} \) है।
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