कौन सा विकल्प \(\sqrt{180}\) का सरल रूप है?
Which option is the simplified form of \(\sqrt{180}\)?
#surds
#simplification
#square-root
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A \(6\sqrt{5}\)
B \(18\sqrt{5}\)
C \(3\sqrt{20}\)
D \(5\sqrt{6}\)
Explanation opens after your attempt
Correct Answer
A. \(6\sqrt{5}\)
Step 1
Concept
\(\sqrt{180}=\sqrt{36\times5}=6\sqrt{5}\). Take out the greatest perfect square.
Step 2
Why this answer is correct
The correct answer is A. \(6\sqrt{5}\). \(\sqrt{180}=\sqrt{36\times5}=6\sqrt{5}\). Take out the greatest perfect square.
Step 3
Exam Tip
\(\sqrt{180}=\sqrt{36\times5}=6\sqrt{5}\) है। सबसे बड़ा पूर्ण वर्ग बाहर निकालें।
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यदि \(x=\sqrt{17}\) है तो \(x^2-5\) किस प्रकार की संख्या है?
If \(x=\sqrt{17}\), what type of number is \(x^2-5\)?
#square-root
#expression
#rational-result
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A परिमेय संख्या / Rational number
B अपरिमेय संख्या / Irrational number
C अवास्तविक संख्या / Non real number
D अनावर्ती दशमलव / Non repeating decimal
Explanation opens after your attempt
Correct Answer
A. परिमेय संख्या / Rational number
Step 1
Concept
Here \(x^2=17\), so \(x^2-5=12\). This is a rational number.
Step 2
Why this answer is correct
The correct answer is A. परिमेय संख्या / Rational number. Here \(x^2=17\), so \(x^2-5=12\). This is a rational number.
Step 3
Exam Tip
\(x^2=17\) इसलिए \(x^2-5=12\) है। यह परिमेय संख्या है।
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कौन सा विकल्प \(4+\sqrt{13}\) की प्रकृति सही बताता है?
Which option correctly describes the nature of \(4+\sqrt{13}\)?
#rational-irrational
#addition
#classification
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A अपरिमेय संख्या / Irrational number
B परिमेय संख्या / Rational number
C पूर्णांक / Integer
D सांत दशमलव / Terminating decimal
Explanation opens after your attempt
Correct Answer
A. अपरिमेय संख्या / Irrational number
Step 1
Concept
(4) is rational and \(\sqrt{13}\) is irrational. The sum of a rational and an irrational number is irrational.
Step 2
Why this answer is correct
The correct answer is A. अपरिमेय संख्या / Irrational number. (4) is rational and \(\sqrt{13}\) is irrational. The sum of a rational and an irrational number is irrational.
Step 3
Exam Tip
(4) परिमेय है और \(\sqrt{13}\) अपरिमेय है। परिमेय और अपरिमेय का योग अपरिमेय होता है।
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कौन सा विकल्प \(7-\sqrt{19}\) के बारे में सही है?
Which option is correct about \(7-\sqrt{19}\)?
#subtraction
#irrational-numbers
#properties
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A यह अपरिमेय है / It is irrational
B यह परिमेय है / It is rational
C यह प्राकृतिक संख्या है / It is a natural number
D यह शून्य है / It is zero
Explanation opens after your attempt
Correct Answer
A. यह अपरिमेय है / It is irrational
Step 1
Concept
\(\sqrt{19}\) is irrational because (19) is not a perfect square. Subtracting an irrational from a rational gives an irrational result.
Step 2
Why this answer is correct
The correct answer is A. यह अपरिमेय है / It is irrational. \(\sqrt{19}\) is irrational because (19) is not a perfect square. Subtracting an irrational from a rational gives an irrational result.
Step 3
Exam Tip
\(\sqrt{19}\) अपरिमेय है क्योंकि (19) पूर्ण वर्ग नहीं है। परिमेय से अपरिमेय घटाने पर परिणाम अपरिमेय होता है।
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कौन सा विकल्प \(\sqrt{125}+\sqrt{45}\) का सरल रूप है?
Which option is the simplified form of \(\sqrt{125}+\sqrt{45}\)?
#surds
#addition
#like-terms
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A \(8\sqrt{5}\)
B \(10\sqrt{5}\)
C \(\sqrt{170}\)
D \(6\sqrt{10}\)
Explanation opens after your attempt
Correct Answer
A. \(8\sqrt{5}\)
Step 1
Concept
\(\sqrt{125}=5\sqrt{5}\) and \(\sqrt{45}=3\sqrt{5}\). Adding like terms gives \(8\sqrt{5}\).
Step 2
Why this answer is correct
The correct answer is A. \(8\sqrt{5}\). \(\sqrt{125}=5\sqrt{5}\) and \(\sqrt{45}=3\sqrt{5}\). Adding like terms gives \(8\sqrt{5}\).
Step 3
Exam Tip
\(\sqrt{125}=5\sqrt{5}\) और \(\sqrt{45}=3\sqrt{5}\) है। समान पद जोड़ने पर \(8\sqrt{5}\) मिलता है।
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कौन सा विकल्प \(\sqrt{192}-\sqrt{27}\) का सरल रूप है?
Which option is the simplified form of \(\sqrt{192}-\sqrt{27}\)?
#surds
#subtraction
#simplification
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A \(5\sqrt{3}\)
B \(11\sqrt{3}\)
C \(\sqrt{165}\)
D \(3\sqrt{5}\)
Explanation opens after your attempt
Correct Answer
A. \(5\sqrt{3}\)
Step 1
Concept
\(\sqrt{192}=8\sqrt{3}\) and \(\sqrt{27}=3\sqrt{3}\). The difference is \(5\sqrt{3}\).
Step 2
Why this answer is correct
The correct answer is A. \(5\sqrt{3}\). \(\sqrt{192}=8\sqrt{3}\) and \(\sqrt{27}=3\sqrt{3}\). The difference is \(5\sqrt{3}\).
Step 3
Exam Tip
\(\sqrt{192}=8\sqrt{3}\) और \(\sqrt{27}=3\sqrt{3}\) है। अंतर \(5\sqrt{3}\) है।
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कौन सा विकल्प \(\sqrt{10}\times\sqrt{40}\) का मान है?
Which option is the value of \(\sqrt{10}\times\sqrt{40}\)?
#multiplication
#irrational-numbers
#rational-result
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A (20)
B \(\sqrt{50}\)
C \(10\sqrt{40}\)
D \(40\sqrt{10}\)
Explanation opens after your attempt
Step 1
Concept
\(\sqrt{10}\times\sqrt{40}=\sqrt{400}=20\). The product of two irrational numbers can be rational.
Step 2
Why this answer is correct
The correct answer is A. (20). \(\sqrt{10}\times\sqrt{40}=\sqrt{400}=20\). The product of two irrational numbers can be rational.
Step 3
Exam Tip
\(\sqrt{10}\times\sqrt{40}=\sqrt{400}=20\) है। दो अपरिमेय संख्याओं का गुणनफल परिमेय हो सकता है।
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कौन सा विकल्प \(\sqrt{6}\times\sqrt{10}\) की प्रकृति सही बताता है?
Which option correctly describes the nature of \(\sqrt{6}\times\sqrt{10}\)?
#irrational-product
#square-root
#classification
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A अपरिमेय संख्या / Irrational number
B परिमेय संख्या / Rational number
C पूर्णांक / Integer
D सांत दशमलव / Terminating decimal
Explanation opens after your attempt
Correct Answer
A. अपरिमेय संख्या / Irrational number
Step 1
Concept
\(\sqrt{6}\times\sqrt{10}=\sqrt{60}=2\sqrt{15}\). Since (15) is not a perfect square the result is irrational.
Step 2
Why this answer is correct
The correct answer is A. अपरिमेय संख्या / Irrational number. \(\sqrt{6}\times\sqrt{10}=\sqrt{60}=2\sqrt{15}\). Since (15) is not a perfect square the result is irrational.
Step 3
Exam Tip
\(\sqrt{6}\times\sqrt{10}=\sqrt{60}=2\sqrt{15}\) है। (15) पूर्ण वर्ग नहीं है इसलिए परिणाम अपरिमेय है।
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यदि \(a=3+\sqrt{6}\) और \(b=3-\sqrt{6}\) हैं तो (a+b) का मान क्या है?
If \(a=3+\sqrt{6}\) and \(b=3-\sqrt{6}\), what is the value of (a+b)?
#conjugate
#addition
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A (6)
B \(2\sqrt{6}\)
C (0)
D (9)
Explanation opens after your attempt
Step 1
Concept
In the sum \(\sqrt{6}\) and \(-\sqrt{6}\) cancel. So (a+b=6).
Step 2
Why this answer is correct
The correct answer is A. (6). In the sum \(\sqrt{6}\) and \(-\sqrt{6}\) cancel. So (a+b=6).
Step 3
Exam Tip
योग में \(\sqrt{6}\) और \(-\sqrt{6}\) कट जाते हैं। इसलिए (a+b=6) है।
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यदि \(u=6+\sqrt{5}\) और \(v=6-\sqrt{5}\) हैं तो (uv) का मान क्या है?
If \(u=6+\sqrt{5}\) and \(v=6-\sqrt{5}\), what is the value of (uv)?
#conjugate
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A (31)
B \(36+\sqrt{5}\)
C \(12\sqrt{5}\)
D (41)
Explanation opens after your attempt
Step 1
Concept
Conjugate multiplication gives ((6)2 -\(\sqrt{5}\)2 =36-5=31). Use \(a^2-b^2\) in such questions.
Step 2
Why this answer is correct
The correct answer is A. (31). Conjugate multiplication gives ((6)2 -\(\sqrt{5}\)2 =36-5=31). Use \(a^2-b^2\) in such questions.
Step 3
Exam Tip
संयुग्मी गुणन से ((6)2 -\(\sqrt{5}\)2 =36-5=31) मिलता है। ऐसे प्रश्नों में \(a^2-b^2\) प्रयोग करें।
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कौन सा विकल्प (\(\sqrt{11}+2\)\(\sqrt{11}-2\)) का मान है?
Which option is the value of (\(\sqrt{11}+2\)\(\sqrt{11}-2\))?
#identity
#conjugate
#surds
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A (7)
B (13)
C \(\sqrt{11}\)
D \(11+2\sqrt{11}\)
Explanation opens after your attempt
Step 1
Concept
This is ((a+b)(a-b)=a-2 -b-2 ). The value is (11-4=7).
Step 2
Why this answer is correct
The correct answer is A. (7). This is ((a+b)(a-b)=a-2 -b-2 ). The value is (11-4=7).
Step 3
Exam Tip
यह ((a+b)(a-b)=a-2 -b-2 ) है। मान (11-4=7) होगा।
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कौन सा विकल्प (\(3+\sqrt{2}\)2 ) का सही विस्तार है?
Which option is the correct expansion of (\(3+\sqrt{2}\)2 )?
#surds
#identity
#expansion
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A \(11+6\sqrt{2}\)
B \(9+3\sqrt{2}\)
C \(11+3\sqrt{2}\)
D \(7+6\sqrt{2}\)
Explanation opens after your attempt
Correct Answer
A. \(11+6\sqrt{2}\)
Step 1
Concept
(\(3+\sqrt{2}\)2 =9+6\sqrt{2}+2=11+6\sqrt{2}). Do not miss the middle term in the square formula.
Step 2
Why this answer is correct
The correct answer is A. \(11+6\sqrt{2}\). (\(3+\sqrt{2}\)2 =9+6\sqrt{2}+2=11+6\sqrt{2}). Do not miss the middle term in the square formula.
Step 3
Exam Tip
(\(3+\sqrt{2}\)2 =9+6\sqrt{2}+2=11+6\sqrt{2}) है। वर्ग सूत्र में बीच का पद न छोड़ें।
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कौन सा विकल्प (7) और (8) के बीच की परिमेय संख्या है?
Which option is a rational number between (7) and (8)?
#rational-number
#number-line
#between-numbers
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A \(\frac{15}{2}\)
B \(\sqrt{53}\)
C \(\sqrt{60}\)
D \(\pi+4\)
Explanation opens after your attempt
Correct Answer
A. \(\frac{15}{2}\)
Step 1
Concept
\(\frac{15}{2}=7.5\), which lies between (7) and (8). Fraction form shows rationality.
Step 2
Why this answer is correct
The correct answer is A. \(\frac{15}{2}\). \(\frac{15}{2}=7.5\), which lies between (7) and (8). Fraction form shows rationality.
Step 3
Exam Tip
\(\frac{15}{2}=7.5\) है जो (7) और (8) के बीच है। भिन्न रूप परिमेयता बताता है।
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कौन सा विकल्प \(\sqrt{7}\) के निकटतम दो पूर्णांकों को सही बताता है?
Which option correctly gives the two nearest integers between which \(\sqrt{7}\) lies?
#estimation
#square-root
#number-line
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A (2) और (3) / (2) and (3)
B (1) और (2) / (1) and (2)
C (3) और (4) / (3) and (4)
D (7) और (8) / (7) and (8)
Explanation opens after your attempt
Correct Answer
A. (2) और (3) / (2) and (3)
Step 1
Concept
Since (4<7<9), \(2<\sqrt{7}<3\). Locate roots using squares.
Step 2
Why this answer is correct
The correct answer is A. (2) और (3) / (2) and (3). Since (4<7<9), \(2<\sqrt{7}<3\). Locate roots using squares.
Step 3
Exam Tip
क्योंकि (4<7<9) इसलिए \(2<\sqrt{7}<3\)। जड़ की स्थिति वर्गों से पहचानें।
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कौन सा विकल्प \(\sqrt{90}\) और \(\sqrt{99}\) की तुलना सही करता है?
Which option correctly compares \(\sqrt{90}\) and \(\sqrt{99}\)?
#comparison
#square-root
#number-line
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A \(\sqrt{99}>\sqrt{90}\)
B \(\sqrt{99}<\sqrt{90}\)
C \(\sqrt{99}=\sqrt{90}\)
D तुलना संभव नहीं / Comparison is not possible
Explanation opens after your attempt
Correct Answer
A. \(\sqrt{99}>\sqrt{90}\)
Step 1
Concept
For positive numbers a larger number inside the square root gives a larger value. Here (99>90).
Step 2
Why this answer is correct
The correct answer is A. \(\sqrt{99}>\sqrt{90}\). For positive numbers a larger number inside the square root gives a larger value. Here (99>90).
Step 3
Exam Tip
धनात्मक संख्याओं में अंदर की संख्या बड़ी हो तो वर्गमूल भी बड़ा होता है। (99>90) है।
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कौन सा विकल्प \(\sqrt{0.64}+\sqrt{0.09}\) का मान है?
Which option is the value of \(\sqrt{0.64}+\sqrt{0.09}\)?
#decimal-square-root
#rational-number
#calculation
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A (1.1)
B (0.11)
C (0.89)
D (1.7)
Explanation opens after your attempt
Step 1
Concept
\(\sqrt{0.64}=0.8\) and \(\sqrt{0.09}=0.3\). The sum is (1.1).
Step 2
Why this answer is correct
The correct answer is A. (1.1). \(\sqrt{0.64}=0.8\) and \(\sqrt{0.09}=0.3\). The sum is (1.1).
Step 3
Exam Tip
\(\sqrt{0.64}=0.8\) और \(\sqrt{0.09}=0.3\) है। योग (1.1) है।
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कौन सा विकल्प \(\frac{\sqrt{80}}{\sqrt{5}}\) का मान है?
Which option is the value of \(\frac{\sqrt{80}}{\sqrt{5}}\)?
#division
#square-root
#rational-result
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A (4)
B \(\sqrt{75}\)
C (16)
D \(4\sqrt{5}\)
Explanation opens after your attempt
Step 1
Concept
\(\frac{\sqrt{80}}{\sqrt{5}}=\sqrt{16}=4\). In division of roots simplify the quotient inside.
Step 2
Why this answer is correct
The correct answer is A. (4). \(\frac{\sqrt{80}}{\sqrt{5}}=\sqrt{16}=4\). In division of roots simplify the quotient inside.
Step 3
Exam Tip
\(\frac{\sqrt{80}}{\sqrt{5}}=\sqrt{16}=4\) है। जड़ों के भाग में अंदर का भागफल सरल करें।
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कौन सा विकल्प \(\frac{3}{\sqrt{3}}\) का सरल रूप है?
Which option is the simplified form of \(\frac{3}{\sqrt{3}}\)?
#division
#rationalisation
#irrational-number
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A \(\sqrt{3}\)
B \(3\sqrt{3}\)
C (1)
D \(\frac{1}{3}\)
Explanation opens after your attempt
Correct Answer
A. \(\sqrt{3}\)
Step 1
Concept
\(\frac{3}{\sqrt{3}}=\sqrt{3}\) because \(3=\sqrt{3}\times\sqrt{3}\). Simplify when a root is in the denominator.
Step 2
Why this answer is correct
The correct answer is A. \(\sqrt{3}\). \(\frac{3}{\sqrt{3}}=\sqrt{3}\) because \(3=\sqrt{3}\times\sqrt{3}\). Simplify when a root is in the denominator.
Step 3
Exam Tip
\(\frac{3}{\sqrt{3}}=\sqrt{3}\) क्योंकि \(3=\sqrt{3}\times\sqrt{3}\)। हर में जड़ हो तो सरल करें।
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कौन सा विकल्प (\sqrt{3}\(4+\sqrt{3}\)) का मान है?
Which option is the value of (\sqrt{3}\(4+\sqrt{3}\))?
#surds
#distribution
#expression
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A \(3+4\sqrt{3}\)
B \(7\sqrt{3}\)
C \(12+\sqrt{3}\)
D \(4+3\sqrt{3}\)
Explanation opens after your attempt
Correct Answer
A. \(3+4\sqrt{3}\)
Step 1
Concept
Distributing gives \(4\sqrt{3}+3\). Keep rational and irrational terms separate.
Step 2
Why this answer is correct
The correct answer is A. \(3+4\sqrt{3}\). Distributing gives \(4\sqrt{3}+3\). Keep rational and irrational terms separate.
Step 3
Exam Tip
वितरण करने पर \(4\sqrt{3}+3\) मिलता है। परिमेय और अपरिमेय पद अलग रखें।
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कौन सा विकल्प \(2\sqrt{5}\times3\sqrt{5}\) का मान है?
Which option is the value of \(2\sqrt{5}\times3\sqrt{5}\)?
#surds
#multiplication
#rational-result
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A (30)
B \(6\sqrt{5}\)
C \(30\sqrt{5}\)
D (15)
Explanation opens after your attempt
Step 1
Concept
\(2\sqrt{5}\times3\sqrt{5}=6\times5=30\). Multiplying same roots can give a rational result.
Step 2
Why this answer is correct
The correct answer is A. (30). \(2\sqrt{5}\times3\sqrt{5}=6\times5=30\). Multiplying same roots can give a rational result.
Step 3
Exam Tip
\(2\sqrt{5}\times3\sqrt{5}=6\times5=30\) है। समान जड़ का गुणन परिमेय परिणाम दे सकता है।
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कौन सा विकल्प \(5\sqrt{2}+3\sqrt{2}-\sqrt{2}\) का सरल रूप है?
Which option is the simplified form of \(5\sqrt{2}+3\sqrt{2}-\sqrt{2}\)?
#surds
#like-terms
#simplification
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A \(7\sqrt{2}\)
B \(8\sqrt{2}\)
C \(7\sqrt{6}\)
D \(\sqrt{14}\)
Explanation opens after your attempt
Correct Answer
A. \(7\sqrt{2}\)
Step 1
Concept
The coefficients of like radical terms add as (5+3-1=7). So the answer is \(7\sqrt{2}\).
Step 2
Why this answer is correct
The correct answer is A. \(7\sqrt{2}\). The coefficients of like radical terms add as (5+3-1=7). So the answer is \(7\sqrt{2}\).
Step 3
Exam Tip
समान जड़ वाले पदों के गुणांक (5+3-1=7) जुड़ते हैं। इसलिए उत्तर \(7\sqrt{2}\) है।
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कौन सा विकल्प \(\sqrt{50}+\sqrt{72}-\sqrt{32}\) का सरल रूप है?
Which option is the simplified form of \(\sqrt{50}+\sqrt{72}-\sqrt{32}\)?
#surds
#addition-subtraction
#simplification
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A \(7\sqrt{2}\)
B \(15\sqrt{2}\)
C \(\sqrt{90}\)
D \(3\sqrt{2}\)
Explanation opens after your attempt
Correct Answer
A. \(7\sqrt{2}\)
Step 1
Concept
\(\sqrt{50}=5\sqrt{2}\), \(\sqrt{72}=6\sqrt{2}\), and \(\sqrt{32}=4\sqrt{2}\). The result is \(7\sqrt{2}\).
Step 2
Why this answer is correct
The correct answer is A. \(7\sqrt{2}\). \(\sqrt{50}=5\sqrt{2}\), \(\sqrt{72}=6\sqrt{2}\), and \(\sqrt{32}=4\sqrt{2}\). The result is \(7\sqrt{2}\).
Step 3
Exam Tip
\(\sqrt{50}=5\sqrt{2}\), \(\sqrt{72}=6\sqrt{2}\) और \(\sqrt{32}=4\sqrt{2}\) है। परिणाम \(7\sqrt{2}\) है।
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कौन सा विकल्प \(\sqrt{200}\) का सही सरल रूप है?
Which option is the correct simplified form of \(\sqrt{200}\)?
#surds
#simplification
#square-root
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A \(10\sqrt{2}\)
B \(20\sqrt{2}\)
C \(5\sqrt{8}\)
D \(2\sqrt{100}\)
Explanation opens after your attempt
Correct Answer
A. \(10\sqrt{2}\)
Step 1
Concept
\(\sqrt{200}=\sqrt{100\times2}=10\sqrt{2}\). In simplest form no perfect square should remain inside the root.
Step 2
Why this answer is correct
The correct answer is A. \(10\sqrt{2}\). \(\sqrt{200}=\sqrt{100\times2}=10\sqrt{2}\). In simplest form no perfect square should remain inside the root.
Step 3
Exam Tip
\(\sqrt{200}=\sqrt{100\times2}=10\sqrt{2}\) है। सरल रूप में जड़ के अंदर पूर्ण वर्ग नहीं रहना चाहिए।
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कौन सा विकल्प \(0.\overline{123}\) की प्रकृति सही बताता है?
Which option correctly describes the nature of \(0.\overline{123}\)?
#bar-decimal
#repeating-decimal
#rational
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A परिमेय संख्या / Rational number
B अपरिमेय संख्या / Irrational number
C अवास्तविक संख्या / Non real number
D पूर्णांक / Integer
Explanation opens after your attempt
Correct Answer
A. परिमेय संख्या / Rational number
Step 1
Concept
The bar shows repetition of (123). A repeating decimal is rational.
Step 2
Why this answer is correct
The correct answer is A. परिमेय संख्या / Rational number. The bar shows repetition of (123). A repeating decimal is rational.
Step 3
Exam Tip
ऊपर की रेखा (123) के आवर्तन को बताती है। आवर्ती दशमलव परिमेय होता है।
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कौन सा विकल्प (3.010010001...) के बारे में सही है?
Which option is correct about (3.010010001...)?
#non-repeating-decimal
#irrational-number
#classification
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A यह अपरिमेय संख्या है / It is an irrational number
B यह सांत दशमलव है / It is a terminating decimal
C यह आवर्ती दशमलव है / It is a repeating decimal
D यह पूर्णांक है / It is an integer
Explanation opens after your attempt
Correct Answer
A. यह अपरिमेय संख्या है / It is an irrational number
Step 1
Concept
The decimal is infinite and has no fixed repeating block. So it is irrational.
Step 2
Why this answer is correct
The correct answer is A. यह अपरिमेय संख्या है / It is an irrational number. The decimal is infinite and has no fixed repeating block. So it is irrational.
Step 3
Exam Tip
दशमलव अनंत है और कोई निश्चित आवर्ती समूह नहीं है। इसलिए यह अपरिमेय है।
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यदि (m) धनात्मक पूर्णांक है और \(\sqrt{m}\) परिमेय है तो (m) क्या होना चाहिए?
If (m) is a positive integer and \(\sqrt{m}\) is rational, what must (m) be?
#perfect-square
#rational-root
#exam-rule
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A पूर्ण वर्ग / Perfect square
B हमेशा अभाज्य / Always prime
C हमेशा सम / Always even
D पूर्ण वर्ग नहीं / Not a perfect square
Explanation opens after your attempt
Correct Answer
A. पूर्ण वर्ग / Perfect square
Step 1
Concept
The square root of a positive integer is rational only when it is a perfect square. Apply this rule directly.
Step 2
Why this answer is correct
The correct answer is A. पूर्ण वर्ग / Perfect square. The square root of a positive integer is rational only when it is a perfect square. Apply this rule directly.
Step 3
Exam Tip
धनात्मक पूर्णांक की वर्गमूल परिमेय तभी होती है जब वह पूर्ण वर्ग हो। इस नियम को सीधे लागू करें।
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यदि \(\sqrt{k}\) अपरिमेय है और (k) धनात्मक पूर्णांक है तो (k) के बारे में सही कथन क्या है?
If \(\sqrt{k}\) is irrational and (k) is a positive integer, what is correct about (k)?
#perfect-square
#irrational-root
#reasoning
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A (k) पूर्ण वर्ग नहीं है / (k) is not a perfect square
B (k) हमेशा पूर्ण वर्ग है / (k) is always a perfect square
C (k=0) है / (k=0)
D (k) हमेशा ऋणात्मक है / (k) is always negative
Explanation opens after your attempt
Correct Answer
A. (k) पूर्ण वर्ग नहीं है / (k) is not a perfect square
Step 1
Concept
If a positive integer is not a perfect square its square root is irrational. So (k) is not a perfect square.
Step 2
Why this answer is correct
The correct answer is A. (k) पूर्ण वर्ग नहीं है / (k) is not a perfect square. If a positive integer is not a perfect square its square root is irrational. So (k) is not a perfect square.
Step 3
Exam Tip
धनात्मक पूर्णांक पूर्ण वर्ग न हो तो उसकी वर्गमूल अपरिमेय होती है। इसलिए (k) पूर्ण वर्ग नहीं होगा।
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कौन सा विकल्प \(\sqrt{289}\) और \(\sqrt{290}\) की प्रकृति सही बताता है?
Which option gives the correct nature of \(\sqrt{289}\) and \(\sqrt{290}\)?
#perfect-square
#comparison
#rational-irrational
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A \(\sqrt{289}\) परिमेय है और \(\sqrt{290}\) अपरिमेय है / \(\sqrt{289}\) is rational and \(\sqrt{290}\) is irrational
B दोनों परिमेय हैं / Both are rational
C दोनों अपरिमेय हैं / Both are irrational
D \(\sqrt{289}\) अपरिमेय है और \(\sqrt{290}\) परिमेय है / \(\sqrt{289}\) is irrational and \(\sqrt{290}\) is rational
Explanation opens after your attempt
Correct Answer
A. \(\sqrt{289}\) परिमेय है और \(\sqrt{290}\) अपरिमेय है / \(\sqrt{289}\) is rational and \(\sqrt{290}\) is irrational
Step 1
Concept
\(\sqrt{289}=17\), but (290) is not a perfect square. So the first root is rational and the second is irrational.
Step 2
Why this answer is correct
The correct answer is A. \(\sqrt{289}\) परिमेय है और \(\sqrt{290}\) अपरिमेय है / \(\sqrt{289}\) is rational and \(\sqrt{290}\) is irrational. \(\sqrt{289}=17\), but (290) is not a perfect square. So the first root is rational and the second is irrational.
Step 3
Exam Tip
\(\sqrt{289}=17\) है लेकिन (290) पूर्ण वर्ग नहीं है। इसलिए पहली जड़ परिमेय और दूसरी अपरिमेय है।
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कौन सा विकल्प \(\sqrt[3]{125}\) की प्रकृति सही बताता है?
Which option correctly describes the nature of \(\sqrt[3]{125}\)?
#cube-root
#perfect-cube
#rational-number
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A परिमेय संख्या / Rational number
B अपरिमेय संख्या / Irrational number
C अवास्तविक संख्या / Non real number
D अनावर्ती दशमलव / Non repeating decimal
Explanation opens after your attempt
Correct Answer
A. परिमेय संख्या / Rational number
Step 1
Concept
\(\sqrt[3]{125}=5\), which is rational. The cube root of a perfect cube is rational.
Step 2
Why this answer is correct
The correct answer is A. परिमेय संख्या / Rational number. \(\sqrt[3]{125}=5\), which is rational. The cube root of a perfect cube is rational.
Step 3
Exam Tip
\(\sqrt[3]{125}=5\) है जो परिमेय है। पूर्ण घन की घनमूल परिमेय होती है।
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कौन सा विकल्प \(\sqrt[3]{12}\) के लिए सही है?
Which option is correct for \(\sqrt[3]{12}\)?
#cube-root
#irrational-number
#classification
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A यह अपरिमेय है / It is irrational
B यह (4) है / It is (4)
C यह (3) है / It is (3)
D यह सांत दशमलव है / It is a terminating decimal
Explanation opens after your attempt
Correct Answer
A. यह अपरिमेय है / It is irrational
Step 1
Concept
(12) is not a perfect cube so \(\sqrt[3]{12}\) is irrational. Check perfect cubes in cube roots.
Step 2
Why this answer is correct
The correct answer is A. यह अपरिमेय है / It is irrational. (12) is not a perfect cube so \(\sqrt[3]{12}\) is irrational. Check perfect cubes in cube roots.
Step 3
Exam Tip
(12) पूर्ण घन नहीं है इसलिए \(\sqrt[3]{12}\) अपरिमेय है। घनमूल में पूर्ण घन देखें।
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कौन सा विकल्प \(2+\sqrt{m}\) को अपरिमेय बनाता है?
Which option makes \(2+\sqrt{m}\) irrational?
#perfect-square
#irrational-expression
#reasoning
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A (m=45)
B (m=49)
C (m=64)
D (m=81)
Explanation opens after your attempt
Step 1
Concept
(45) is not a perfect square so \(\sqrt{45}\) is irrational. Adding rational (2) keeps it irrational.
Step 2
Why this answer is correct
The correct answer is A. (m=45). (45) is not a perfect square so \(\sqrt{45}\) is irrational. Adding rational (2) keeps it irrational.
Step 3
Exam Tip
(45) पूर्ण वर्ग नहीं है इसलिए \(\sqrt{45}\) अपरिमेय है। परिमेय (2) जोड़ने पर परिणाम अपरिमेय रहता है।
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कौन सा विकल्प \(9-\sqrt{m}\) को परिमेय बनाता है?
Which option makes \(9-\sqrt{m}\) rational?
#perfect-square
#rational-expression
#reasoning
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A (m=100)
B (m=101)
C (m=102)
D (m=103)
Explanation opens after your attempt
Correct Answer
A. (m=100)
Step 1
Concept
\(\sqrt{100}=10\) is rational so \(9-\sqrt{100}\) will be rational. The root of a perfect square is rational.
Step 2
Why this answer is correct
The correct answer is A. (m=100). \(\sqrt{100}=10\) is rational so \(9-\sqrt{100}\) will be rational. The root of a perfect square is rational.
Step 3
Exam Tip
\(\sqrt{100}=10\) परिमेय है इसलिए \(9-\sqrt{100}\) परिमेय होगा। पूर्ण वर्ग वाली जड़ परिमेय होती है।
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कौन सा विकल्प \(1+\sqrt{7}\) और \(1-\sqrt{7}\) के गुणनफल का मान है?
Which option is the value of the product of \(1+\sqrt{7}\) and \(1-\sqrt{7}\)?
#conjugate
#surds
#rational-result
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A (-6)
B (6)
C \(1+\sqrt{7}\)
D (7)
Explanation opens after your attempt
Step 1
Concept
(\(1+\sqrt{7}\)\(1-\sqrt{7}\)=1-7=-6). In conjugate multiplication the irrational part cancels.
Step 2
Why this answer is correct
The correct answer is A. (-6). (\(1+\sqrt{7}\)\(1-\sqrt{7}\)=1-7=-6). In conjugate multiplication the irrational part cancels.
Step 3
Exam Tip
(\(1+\sqrt{7}\)\(1-\sqrt{7}\)=1-7=-6) है। संयुग्मी गुणन में अपरिमेय भाग हट जाता है।
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कौन सा विकल्प \(\sqrt{48}+\sqrt{108}-\sqrt{12}\) का सरल रूप है?
Which option is the simplified form of \(\sqrt{48}+\sqrt{108}-\sqrt{12}\)?
#surds
#addition-subtraction
#simplification
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A \(8\sqrt{3}\)
B \(12\sqrt{3}\)
C \(\sqrt{144}\)
D \(6\sqrt{3}\)
Explanation opens after your attempt
Correct Answer
A. \(8\sqrt{3}\)
Step 1
Concept
\(\sqrt{48}=4\sqrt{3}\), \(\sqrt{108}=6\sqrt{3}\), and \(\sqrt{12}=2\sqrt{3}\). The result is \(8\sqrt{3}\).
Step 2
Why this answer is correct
The correct answer is A. \(8\sqrt{3}\). \(\sqrt{48}=4\sqrt{3}\), \(\sqrt{108}=6\sqrt{3}\), and \(\sqrt{12}=2\sqrt{3}\). The result is \(8\sqrt{3}\).
Step 3
Exam Tip
\(\sqrt{48}=4\sqrt{3}\), \(\sqrt{108}=6\sqrt{3}\) और \(\sqrt{12}=2\sqrt{3}\) है। परिणाम \(8\sqrt{3}\) है।
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कौन सा विकल्प \(2+\sqrt{3}\) और \(2-\sqrt{3}\) के योग और गुणनफल को सही बताता है?
Which option correctly gives the sum and product of \(2+\sqrt{3}\) and \(2-\sqrt{3}\)?
#conjugate
#sum-product
#surds
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A योग (4), गुणनफल (1) / Sum (4), product (1)
B योग (0), गुणनफल (4) / Sum (0), product (4)
C योग \(2\sqrt{3}\), गुणनफल (7) / Sum \(2\sqrt{3}\), product (7)
D योग (4), गुणनफल (7) / Sum (4), product (7)
Explanation opens after your attempt
Correct Answer
A. योग (4), गुणनफल (1) / Sum (4), product (1)
Step 1
Concept
The radical terms cancel in the sum and the product is (4-3=1). This method is quick for conjugates.
Step 2
Why this answer is correct
The correct answer is A. योग (4), गुणनफल (1) / Sum (4), product (1). The radical terms cancel in the sum and the product is (4-3=1). This method is quick for conjugates.
Step 3
Exam Tip
योग में जड़ वाले पद कटते हैं और गुणनफल (4-3=1) है। संयुग्मी संख्याओं में यह तरीका तेज है।
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कौन सा विकल्प (\(\sqrt{5}-\sqrt{2}\)2 ) का सही विस्तार है?
Which option is the correct expansion of (\(\sqrt{5}-\sqrt{2}\)2 )?
#surds
#identity
#expansion
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A \(7-2\sqrt{10}\)
B \(3-2\sqrt{10}\)
C \(7-\sqrt{10}\)
D \(5-2\sqrt{2}\)
Explanation opens after your attempt
Correct Answer
A. \(7-2\sqrt{10}\)
Step 1
Concept
(\(\sqrt{5}-\sqrt{2}\)2 =5+2-2\sqrt{10}). Apply the (2ab) term carefully in the square formula.
Step 2
Why this answer is correct
The correct answer is A. \(7-2\sqrt{10}\). (\(\sqrt{5}-\sqrt{2}\)2 =5+2-2\sqrt{10}). Apply the (2ab) term carefully in the square formula.
Step 3
Exam Tip
(\(\sqrt{5}-\sqrt{2}\)2 =5+2-2\sqrt{10}) है। वर्ग सूत्र में (2ab) पद ध्यान से लगाएँ।
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यदि कोई दशमलव सांत या आवर्ती है तो वह किस प्रकार की संख्या है?
If a decimal is terminating or repeating, what type of number is it?
#decimal-expansion
#rational-number
#concept
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A परिमेय संख्या / Rational number
B अपरिमेय संख्या / Irrational number
C अवास्तविक संख्या / Non real number
D केवल पूर्णांक / Integer only
Explanation opens after your attempt
Correct Answer
A. परिमेय संख्या / Rational number
Step 1
Concept
The decimal expansion of a rational number is terminating or repeating. This identification is very important.
Step 2
Why this answer is correct
The correct answer is A. परिमेय संख्या / Rational number. The decimal expansion of a rational number is terminating or repeating. This identification is very important.
Step 3
Exam Tip
परिमेय संख्या का दशमलव प्रसार सांत या आवर्ती होता है। यह पहचान बहुत महत्वपूर्ण है।
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यदि कोई दशमलव अनंत और अनावर्ती है तो वह किस प्रकार की संख्या है?
If a decimal is non terminating and non repeating, what type of number is it?
#decimal-expansion
#irrational-number
#concept
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A अपरिमेय संख्या / Irrational number
B परिमेय संख्या / Rational number
C पूर्णांक / Integer
D सांत दशमलव / Terminating decimal
Explanation opens after your attempt
Correct Answer
A. अपरिमेय संख्या / Irrational number
Step 1
Concept
A non terminating and non repeating decimal identifies an irrational number. Check carefully if no repeating block appears.
Step 2
Why this answer is correct
The correct answer is A. अपरिमेय संख्या / Irrational number. A non terminating and non repeating decimal identifies an irrational number. Check carefully if no repeating block appears.
Step 3
Exam Tip
अनंत और अनावर्ती दशमलव अपरिमेय संख्या की पहचान है। आवर्ती भाग न दिखे तो सावधानी से जाँचें।
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कौन सा विकल्प \(-\sqrt{47}\) की प्रकृति सही बताता है?
Which option correctly describes the nature of \(-\sqrt{47}\)?
#negative-irrational
#real-number
#classification
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A अपरिमेय वास्तविक संख्या / Irrational real number
B परिमेय संख्या / Rational number
C पूर्ण संख्या / Whole number
D प्राकृतिक संख्या / Natural number
Explanation opens after your attempt
Correct Answer
A. अपरिमेय वास्तविक संख्या / Irrational real number
Step 1
Concept
\(\sqrt{47}\) is irrational because (47) is not a perfect square. Its negative is also a real irrational number.
Step 2
Why this answer is correct
The correct answer is A. अपरिमेय वास्तविक संख्या / Irrational real number. \(\sqrt{47}\) is irrational because (47) is not a perfect square. Its negative is also a real irrational number.
Step 3
Exam Tip
\(\sqrt{47}\) अपरिमेय है क्योंकि (47) पूर्ण वर्ग नहीं है। उसका ऋण भी वास्तविक अपरिमेय है।
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कौन सा विकल्प \(\frac{1}{3}+\sqrt{11}\) की प्रकृति सही बताता है?
Which option correctly describes the nature of \(\frac{1}{3}+\sqrt{11}\)?
#rational-irrational
#addition
#classification
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A अपरिमेय संख्या / Irrational number
B परिमेय संख्या / Rational number
C पूर्णांक / Integer
D सांत दशमलव / Terminating decimal
Explanation opens after your attempt
Correct Answer
A. अपरिमेय संख्या / Irrational number
Step 1
Concept
\(\frac{1}{3}\) is rational and \(\sqrt{11}\) is irrational. Their sum is irrational.
Step 2
Why this answer is correct
The correct answer is A. अपरिमेय संख्या / Irrational number. \(\frac{1}{3}\) is rational and \(\sqrt{11}\) is irrational. Their sum is irrational.
Step 3
Exam Tip
\(\frac{1}{3}\) परिमेय है और \(\sqrt{11}\) अपरिमेय है। उनका योग अपरिमेय होता है।
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कौन सा विकल्प \(4\sqrt{7}-\sqrt{112}\) का मान है?
Which option is the value of \(4\sqrt{7}-\sqrt{112}\)?
#surds
#subtraction
#rational-result
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A (0)
B \(8\sqrt{7}\)
C \(4\sqrt{105}\)
D \(\sqrt{7}\)
Explanation opens after your attempt
Step 1
Concept
\(\sqrt{112}=\sqrt{16\times7}=4\sqrt{7}\). Therefore \(4\sqrt{7}-4\sqrt{7}=0\).
Step 2
Why this answer is correct
The correct answer is A. (0). \(\sqrt{112}=\sqrt{16\times7}=4\sqrt{7}\). Therefore \(4\sqrt{7}-4\sqrt{7}=0\).
Step 3
Exam Tip
\(\sqrt{112}=\sqrt{16\times7}=4\sqrt{7}\) है। इसलिए \(4\sqrt{7}-4\sqrt{7}=0\) है।
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कौन सा विकल्प \(\sqrt{245}\) का सरल रूप है?
Which option is the simplified form of \(\sqrt{245}\)?
#surds
#simplification
#square-root
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A \(7\sqrt{5}\)
B \(5\sqrt{7}\)
C \(49\sqrt{5}\)
D \(\sqrt{49}\)
Explanation opens after your attempt
Correct Answer
A. \(7\sqrt{5}\)
Step 1
Concept
\(\sqrt{245}=\sqrt{49\times5}=7\sqrt{5}\). Identify the perfect square factor inside the root.
Step 2
Why this answer is correct
The correct answer is A. \(7\sqrt{5}\). \(\sqrt{245}=\sqrt{49\times5}=7\sqrt{5}\). Identify the perfect square factor inside the root.
Step 3
Exam Tip
\(\sqrt{245}=\sqrt{49\times5}=7\sqrt{5}\) है। जड़ में पूर्ण वर्ग गुणनखंड पहचानें।
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कौन सा विकल्प (\(4+\sqrt{7}\)\(4-\sqrt{7}\)) का मान है?
Which option is the value of (\(4+\sqrt{7}\)\(4-\sqrt{7}\))?
#conjugate
#surds
#rational-result
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A (9)
B (23)
C (16+7)
D \(8\sqrt{7}\)
Explanation opens after your attempt
Step 1
Concept
Conjugate multiplication gives (42 -\(\sqrt{7}\)2 =16-7=9). Use the difference of squares formula in such questions.
Step 2
Why this answer is correct
The correct answer is A. (9). Conjugate multiplication gives (42 -\(\sqrt{7}\)2 =16-7=9). Use the difference of squares formula in such questions.
Step 3
Exam Tip
संयुग्मी गुणन से (42 -\(\sqrt{7}\)2 =16-7=9) मिलता है। ऐसे प्रश्नों में अंतर वर्ग सूत्र लगाएँ।
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कौन सा विकल्प \(\sqrt{72}+\sqrt{128}-\sqrt{50}\) का सरल रूप है?
Which option is the simplified form of \(\sqrt{72}+\sqrt{128}-\sqrt{50}\)?
#surds
#addition-subtraction
#simplification
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A \(9\sqrt{2}\)
B \(19\sqrt{2}\)
C \(\sqrt{150}\)
D \(3\sqrt{2}\)
Explanation opens after your attempt
Correct Answer
A. \(9\sqrt{2}\)
Step 1
Concept
\(\sqrt{72}=6\sqrt{2}\), \(\sqrt{128}=8\sqrt{2}\), and \(\sqrt{50}=5\sqrt{2}\). The result is \(9\sqrt{2}\).
Step 2
Why this answer is correct
The correct answer is A. \(9\sqrt{2}\). \(\sqrt{72}=6\sqrt{2}\), \(\sqrt{128}=8\sqrt{2}\), and \(\sqrt{50}=5\sqrt{2}\). The result is \(9\sqrt{2}\).
Step 3
Exam Tip
\(\sqrt{72}=6\sqrt{2}\), \(\sqrt{128}=8\sqrt{2}\) और \(\sqrt{50}=5\sqrt{2}\) है। परिणाम \(9\sqrt{2}\) है।
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कौन सा विकल्प (8) और (9) के बीच की अपरिमेय संख्या है?
Which option is an irrational number between (8) and (9)?
#number-line
#irrational-number
#between-numbers
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A \(\sqrt{70}\)
B \(\sqrt{64}\)
C \(\sqrt{81}\)
D \(\frac{17}{2}\)
Explanation opens after your attempt
Correct Answer
A. \(\sqrt{70}\)
Step 1
Concept
Since (64<70<81), \(\sqrt{70}\) lies between (8) and (9). (70) is not a perfect square so it is irrational.
Step 2
Why this answer is correct
The correct answer is A. \(\sqrt{70}\). Since (64<70<81), \(\sqrt{70}\) lies between (8) and (9). (70) is not a perfect square so it is irrational.
Step 3
Exam Tip
क्योंकि (64<70<81) इसलिए \(\sqrt{70}\) (8) और (9) के बीच है। (70) पूर्ण वर्ग नहीं है इसलिए यह अपरिमेय है।
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यदि \(x=2+\sqrt{10}\) और \(y=2-\sqrt{10}\) हैं तो (x-y) का सरल रूप क्या है?
If \(x=2+\sqrt{10}\) and \(y=2-\sqrt{10}\), what is the simplified form of (x-y)?
#surds
#subtraction
#expression
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A \(2\sqrt{10}\)
B (4)
C (0)
D (10)
Explanation opens after your attempt
Correct Answer
A. \(2\sqrt{10}\)
Step 1
Concept
On subtracting, the (2) terms cancel and (\sqrt{10}-\(-\sqrt{10}\)=2\sqrt{10}). Watch the signs carefully.
Step 2
Why this answer is correct
The correct answer is A. \(2\sqrt{10}\). On subtracting, the (2) terms cancel and (\sqrt{10}-\(-\sqrt{10}\)=2\sqrt{10}). Watch the signs carefully.
Step 3
Exam Tip
घटाने पर (2) पद कटते हैं और (\sqrt{10}-\(-\sqrt{10}\)=2\sqrt{10}) मिलता है। चिह्नों का ध्यान रखें।
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कौन सा विकल्प (\(\sqrt{13}-\sqrt{3}\)\(\sqrt{13}+\sqrt{3}\)) का मान है?
Which option is the value of (\(\sqrt{13}-\sqrt{3}\)\(\sqrt{13}+\sqrt{3}\))?
#conjugate
#identity
#rational-result
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A (10)
B (16)
C \(\sqrt{39}\)
D \(13+\sqrt{3}\)
Explanation opens after your attempt
Step 1
Concept
This is ((a-b)(a+b)=a-2 -b-2 ). The value is (13-3=10).
Step 2
Why this answer is correct
The correct answer is A. (10). This is ((a-b)(a+b)=a-2 -b-2 ). The value is (13-3=10).
Step 3
Exam Tip
यह ((a-b)(a+b)=a-2 -b-2 ) है। मान (13-3=10) होगा।
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कौन सा विकल्प (\(\sqrt{6}+\sqrt{2}\)2 ) का सही विस्तार है?
Which option is the correct expansion of (\(\sqrt{6}+\sqrt{2}\)2 )?
#surds
#identity
#expansion
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A \(8+4\sqrt{3}\)
B \(8+2\sqrt{3}\)
C \(4+4\sqrt{3}\)
D \(6+2\sqrt{2}\)
Explanation opens after your attempt
Correct Answer
A. \(8+4\sqrt{3}\)
Step 1
Concept
(\(\sqrt{6}+\sqrt{2}\)2 =6+2+2\sqrt{12}=8+4\sqrt{3}). Apply the (2ab) term correctly.
Step 2
Why this answer is correct
The correct answer is A. \(8+4\sqrt{3}\). (\(\sqrt{6}+\sqrt{2}\)2 =6+2+2\sqrt{12}=8+4\sqrt{3}). Apply the (2ab) term correctly.
Step 3
Exam Tip
(\(\sqrt{6}+\sqrt{2}\)2 =6+2+2\sqrt{12}=8+4\sqrt{3}) है। वर्ग सूत्र में (2ab) पद सही लगाएँ।
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कौन सा विकल्प \(\sqrt[3]{216}\) की प्रकृति सही बताता है?
Which option correctly describes the nature of \(\sqrt[3]{216}\)?
#cube-root
#perfect-cube
#rational-number
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A परिमेय संख्या / Rational number
B अपरिमेय संख्या / Irrational number
C अवास्तविक संख्या / Non real number
D अनंत अनावर्ती दशमलव / Non terminating non repeating decimal
Explanation opens after your attempt
Correct Answer
A. परिमेय संख्या / Rational number
Step 1
Concept
\(\sqrt[3]{216}=6\), which is rational. The cube root of a perfect cube is rational.
Step 2
Why this answer is correct
The correct answer is A. परिमेय संख्या / Rational number. \(\sqrt[3]{216}=6\), which is rational. The cube root of a perfect cube is rational.
Step 3
Exam Tip
\(\sqrt[3]{216}=6\) है जो परिमेय है। पूर्ण घन की घनमूल परिमेय होती है।
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कौन सा विकल्प \(5+\sqrt{m}\) को परिमेय बनाता है?
Which option makes \(5+\sqrt{m}\) rational?
#perfect-square
#rational-expression
#reasoning
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A (m=121)
B (m=122)
C (m=123)
D (m=124)
Explanation opens after your attempt
Correct Answer
A. (m=121)
Step 1
Concept
\(\sqrt{121}=11\) is rational so \(5+\sqrt{121}\) will be rational. The root of a perfect square is rational.
Step 2
Why this answer is correct
The correct answer is A. (m=121). \(\sqrt{121}=11\) is rational so \(5+\sqrt{121}\) will be rational. The root of a perfect square is rational.
Step 3
Exam Tip
\(\sqrt{121}=11\) परिमेय है इसलिए \(5+\sqrt{121}\) परिमेय होगा। पूर्ण वर्ग वाली जड़ परिमेय होती है।
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