यदि \(a=\sqrt{20}\) है तो (a) का सरल रूप क्या है?
If \(a=\sqrt{20}\), what is the simplified form of (a)?
#surds
#simplification
#irrational-numbers
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A \(2\sqrt{5}\)
B \(4\sqrt{5}\)
C \(\sqrt{10}\)
D \(5\sqrt{2}\)
Explanation opens after your attempt
Correct Answer
A. \(2\sqrt{5}\)
Step 1
Concept
\(\sqrt{20}=\sqrt{4\times5}=2\sqrt{5}\). Look for a perfect square factor inside the root.
Step 2
Why this answer is correct
The correct answer is A. \(2\sqrt{5}\). \(\sqrt{20}=\sqrt{4\times5}=2\sqrt{5}\). Look for a perfect square factor inside the root.
Step 3
Exam Tip
\(\sqrt{20}=\sqrt{4\times5}=2\sqrt{5}\) होता है। जड़ में पूर्ण वर्ग गुणनखंड खोजें।
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कौन सा कथन \(3+\sqrt{7}\) के लिए सही है?
Which statement is correct for \(3+\sqrt{7}\)?
#rational-irrational
#addition
#classification
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A यह अपरिमेय है / It is irrational
B यह परिमेय है / It is rational
C यह पूर्णांक है / It is an integer
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
Adding irrational \(\sqrt{7}\) to rational (3) gives an irrational result. In exams identify roots of non perfect squares.
Step 2
Why this answer is correct
The correct answer is A. यह अपरिमेय है / It is irrational. Adding irrational \(\sqrt{7}\) to rational (3) gives an irrational result. In exams identify roots of non perfect squares.
Step 3
Exam Tip
परिमेय (3) में अपरिमेय \(\sqrt{7}\) जोड़ने पर परिणाम अपरिमेय होता है। परीक्षा में पूर्ण वर्ग न होने वाली जड़ को पहचानें।
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कौन सा विकल्प अनंत आवर्ती दशमलव है?
Which option is a non terminating repeating decimal?
#decimal-expansion
#repeating-decimal
#rational
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A (1.272727...)
B (1.270270027...)
C (1.27)
D \(\sqrt{2}\)
Explanation opens after your attempt
Correct Answer
A. (1.272727...)
Step 1
Concept
The block (27) repeats so it is a repeating decimal. A repeating decimal is rational.
Step 2
Why this answer is correct
The correct answer is A. (1.272727...). The block (27) repeats so it is a repeating decimal. A repeating decimal is rational.
Step 3
Exam Tip
(27) बार बार दोहर रहा है इसलिए यह आवर्ती दशमलव है। आवर्ती दशमलव परिमेय होता है।
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कौन सी संख्या \(\frac{p}{q}\) रूप में नहीं लिखी जा सकती जहाँ \(q\neq0\)?
Which number cannot be written in the form \(\frac{p}{q}\) where \(q\neq0\)?
#p-by-q-form
#irrational-root
#definition
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A \(\sqrt{14}\)
B (2.75)
C (-9)
D \(\frac{5}{6}\)
Explanation opens after your attempt
Correct Answer
A. \(\sqrt{14}\)
Step 1
Concept
\(\sqrt{14}\) is irrational because (14) is not a perfect square. The other options can be written in rational form.
Step 2
Why this answer is correct
The correct answer is A. \(\sqrt{14}\). \(\sqrt{14}\) is irrational because (14) is not a perfect square. The other options can be written in rational form.
Step 3
Exam Tip
\(\sqrt{14}\) अपरिमेय है क्योंकि (14) पूर्ण वर्ग नहीं है। बाकी विकल्प परिमेय रूप में लिखे जा सकते हैं।
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यदि \(x=\sqrt{11}\) है तो \(x^2+1\) का मान किस प्रकार की संख्या है?
If \(x=\sqrt{11}\), what type of number is \(x^2+1\)?
#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 \(x^2=11\), so \(x^2+1=12\). This is a rational number.
Step 2
Why this answer is correct
The correct answer is A. परिमेय संख्या / Rational number. Here \(x^2=11\), so \(x^2+1=12\). This is a rational number.
Step 3
Exam Tip
\(x^2=11\) इसलिए \(x^2+1=12\) है। यह परिमेय संख्या है।
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कौन सा विकल्प \(\sqrt{75}-\sqrt{27}\) का सही मान है?
Which option is the correct value of \(\sqrt{75}-\sqrt{27}\)?
#surds
#subtraction
#simplification
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A \(2\sqrt{3}\)
B \(8\sqrt{3}\)
C \(\sqrt{48}\)
D \(3\sqrt{2}\)
Explanation opens after your attempt
Correct Answer
A. \(2\sqrt{3}\)
Step 1
Concept
\(\sqrt{75}=5\sqrt{3}\) and \(\sqrt{27}=3\sqrt{3}\). The difference is \(2\sqrt{3}\).
Step 2
Why this answer is correct
The correct answer is A. \(2\sqrt{3}\). \(\sqrt{75}=5\sqrt{3}\) and \(\sqrt{27}=3\sqrt{3}\). The difference is \(2\sqrt{3}\).
Step 3
Exam Tip
\(\sqrt{75}=5\sqrt{3}\) और \(\sqrt{27}=3\sqrt{3}\) है। अंतर \(2\sqrt{3}\) मिलेगा।
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कौन सा विकल्प दो अपरिमेय संख्याओं का गुणनफल परिमेय बनने का उदाहरण है?
Which option is an example where the product of two irrational numbers is rational?
#irrational-numbers
#multiplication
#rational-result
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A \(\sqrt{12}\times\sqrt{3}\)
B \(\sqrt{2}\times\sqrt{5}\)
C \(\sqrt{7}\times\sqrt{3}\)
D \(\sqrt{11}\times\sqrt{2}\)
Explanation opens after your attempt
Correct Answer
A. \(\sqrt{12}\times\sqrt{3}\)
Step 1
Concept
\(\sqrt{12}\times\sqrt{3}=\sqrt{36}=6\). The product of two irrational numbers is not always irrational.
Step 2
Why this answer is correct
The correct answer is A. \(\sqrt{12}\times\sqrt{3}\). \(\sqrt{12}\times\sqrt{3}=\sqrt{36}=6\). The product of two irrational numbers is not always irrational.
Step 3
Exam Tip
\(\sqrt{12}\times\sqrt{3}=\sqrt{36}=6\) है। दो अपरिमेय संख्याओं का गुणनफल हमेशा अपरिमेय नहीं होता।
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कौन सा दशमलव अपरिमेय संख्या दिखाता है?
Which decimal shows an irrational number?
#irrational-decimal
#non-repeating
#decimal
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A (0.3030030003...)
B (0.303030...)
C (0.303)
D (0.3000...)
Explanation opens after your attempt
Correct Answer
A. (0.3030030003...)
Step 1
Concept
The first decimal is non terminating and non repeating. A non terminating non repeating decimal is irrational.
Step 2
Why this answer is correct
The correct answer is A. (0.3030030003...). The first decimal is non terminating and non repeating. A non terminating non repeating decimal is irrational.
Step 3
Exam Tip
पहला दशमलव अनंत और अनावर्ती है। अनंत अनावर्ती दशमलव अपरिमेय होता है।
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\(\sqrt{2}+\sqrt{8}+\sqrt{18}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{2}+\sqrt{8}+\sqrt{18}\)?
#surds
#addition
#like-terms
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A \(6\sqrt{2}\)
B \(11\sqrt{2}\)
C \(\sqrt{28}\)
D \(3\sqrt{10}\)
Explanation opens after your attempt
Correct Answer
A. \(6\sqrt{2}\)
Step 1
Concept
\(\sqrt{8}=2\sqrt{2}\) and \(\sqrt{18}=3\sqrt{2}\). The total is \(6\sqrt{2}\).
Step 2
Why this answer is correct
The correct answer is A. \(6\sqrt{2}\). \(\sqrt{8}=2\sqrt{2}\) and \(\sqrt{18}=3\sqrt{2}\). The total is \(6\sqrt{2}\).
Step 3
Exam Tip
\(\sqrt{8}=2\sqrt{2}\) और \(\sqrt{18}=3\sqrt{2}\) है। कुल \(6\sqrt{2}\) मिलता है।
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कौन सा विकल्प \(\sqrt{3}\) और \(\sqrt{12}\) के बीच सही संबंध बताता है?
Which option gives the correct relation between \(\sqrt{3}\) and \(\sqrt{12}\)?
#surds
#comparison
#square-root
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A \(\sqrt{12}=2\sqrt{3}\)
B \(\sqrt{12}=4\sqrt{3}\)
C \(\sqrt{12}=3\sqrt{2}\)
D \(\sqrt{12}=\sqrt{3}\)
Explanation opens after your attempt
Correct Answer
A. \(\sqrt{12}=2\sqrt{3}\)
Step 1
Concept
\(\sqrt{12}=\sqrt{4\times3}=2\sqrt{3}\). Taking out the perfect square makes comparison easy.
Step 2
Why this answer is correct
The correct answer is A. \(\sqrt{12}=2\sqrt{3}\). \(\sqrt{12}=\sqrt{4\times3}=2\sqrt{3}\). Taking out the perfect square makes comparison easy.
Step 3
Exam Tip
\(\sqrt{12}=\sqrt{4\times3}=2\sqrt{3}\) है। पूर्ण वर्ग बाहर निकालने से तुलना आसान होती है।
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कौन सा विकल्प (6) और (7) के बीच की अपरिमेय संख्या है?
Which option is an irrational number between (6) and (7)?
#number-line
#between-numbers
#irrational
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A \(\sqrt{43}\)
B \(\sqrt{36}\)
C \(\sqrt{49}\)
D \(\frac{13}{2}\)
Explanation opens after your attempt
Correct Answer
A. \(\sqrt{43}\)
Step 1
Concept
Since (36<43<49), \(\sqrt{43}\) lies between (6) and (7). It is also irrational.
Step 2
Why this answer is correct
The correct answer is A. \(\sqrt{43}\). Since (36<43<49), \(\sqrt{43}\) lies between (6) and (7). It is also irrational.
Step 3
Exam Tip
क्योंकि (36<43<49) इसलिए \(\sqrt{43}\) (6) और (7) के बीच है। यह अपरिमेय भी है।
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यदि \(a=2-\sqrt{5}\) और \(b=2+\sqrt{5}\) हैं तो (a+b) किस प्रकार की संख्या है?
If \(a=2-\sqrt{5}\) and \(b=2+\sqrt{5}\), what type of number is (a+b)?
#irrational-terms
#addition
#rational-result
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A परिमेय संख्या / Rational number
B अपरिमेय संख्या / Irrational number
C अवास्तविक संख्या / Non real number
D हमेशा ऋणात्मक / Always negative
Explanation opens after your attempt
Correct Answer
A. परिमेय संख्या / Rational number
Step 1
Concept
In the sum \(-\sqrt{5}\) and \(\sqrt{5}\) cancel. (a+b=4) is rational.
Step 2
Why this answer is correct
The correct answer is A. परिमेय संख्या / Rational number. In the sum \(-\sqrt{5}\) and \(\sqrt{5}\) cancel. (a+b=4) is rational.
Step 3
Exam Tip
योग में \(-\sqrt{5}\) और \(\sqrt{5}\) कट जाते हैं। (a+b=4) परिमेय है।
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कौन सा विकल्प \(\sqrt{0.25}+\sqrt{0.04}\) का मान है?
Which option is the value of \(\sqrt{0.25}+\sqrt{0.04}\)?
#decimal-square-root
#rational-numbers
#calculation
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A (0.7)
B (0.3)
C (0.54)
D (0.29)
Explanation opens after your attempt
Step 1
Concept
\(\sqrt{0.25}=0.5\) and \(\sqrt{0.04}=0.2\). The sum is (0.7), which is rational.
Step 2
Why this answer is correct
The correct answer is A. (0.7). \(\sqrt{0.25}=0.5\) and \(\sqrt{0.04}=0.2\). The sum is (0.7), which is rational.
Step 3
Exam Tip
\(\sqrt{0.25}=0.5\) और \(\sqrt{0.04}=0.2\) है। योग (0.7) है जो परिमेय है।
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\(\frac{\sqrt{45}}{\sqrt{5}}\) का मान क्या है?
What is the value of \(\frac{\sqrt{45}}{\sqrt{5}}\)?
#division
#square-root
#rational-result
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A (3)
B \(\sqrt{40}\)
C (9)
D \(\sqrt{9}\sqrt{5}\)
Explanation opens after your attempt
Step 1
Concept
\(\frac{\sqrt{45}}{\sqrt{5}}=\sqrt{9}=3\). In division of roots simplify the ratio inside.
Step 2
Why this answer is correct
The correct answer is A. (3). \(\frac{\sqrt{45}}{\sqrt{5}}=\sqrt{9}=3\). In division of roots simplify the ratio inside.
Step 3
Exam Tip
\(\frac{\sqrt{45}}{\sqrt{5}}=\sqrt{9}=3\) है। जड़ों की भाग में अंदर के अनुपात को सरल करें।
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यदि \(x=0.\overline{12}\) है तो (x) किस प्रकार की संख्या है?
If \(x=0.\overline{12}\), what type of number is (x)?
#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 that (12) repeats. A repeating decimal is rational.
Step 2
Why this answer is correct
The correct answer is A. परिमेय संख्या / Rational number. The bar shows that (12) repeats. A repeating decimal is rational.
Step 3
Exam Tip
ऊपर की रेखा बताती है कि (12) दोहरता है। आवर्ती दशमलव परिमेय होता है।
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कौन सा विकल्प \(\sqrt{128}\) का सरल रूप है?
Which option is the simplified form of \(\sqrt{128}\)?
#surds
#simplification
#square-root
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A \(8\sqrt{2}\)
B \(16\sqrt{2}\)
C \(4\sqrt{8}\)
D \(2\sqrt{32}\)
Explanation opens after your attempt
Correct Answer
A. \(8\sqrt{2}\)
Step 1
Concept
\(\sqrt{128}=\sqrt{64\times2}=8\sqrt{2}\). Taking out the greatest perfect square is the better method.
Step 2
Why this answer is correct
The correct answer is A. \(8\sqrt{2}\). \(\sqrt{128}=\sqrt{64\times2}=8\sqrt{2}\). Taking out the greatest perfect square is the better method.
Step 3
Exam Tip
\(\sqrt{128}=\sqrt{64\times2}=8\sqrt{2}\) है। सबसे बड़ा पूर्ण वर्ग निकालना बेहतर तरीका है।
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किस विकल्प में केवल अपरिमेय संख्याएँ हैं?
Which option contains only irrational numbers?
#set-classification
#irrational-numbers
#square-root
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A \(\sqrt{6}\), \(\sqrt{10}\), \(\sqrt{15}\)
B \(\sqrt{4}\), \(\sqrt{6}\), \(\sqrt{10}\)
C \(\frac{1}{2}\), \(\sqrt{10}\), \(\pi\)
D (0), \(\sqrt{6}\), \(\sqrt{15}\)
Explanation opens after your attempt
Correct Answer
A. \(\sqrt{6}\), \(\sqrt{10}\), \(\sqrt{15}\)
Step 1
Concept
In the first option none is the root of a perfect square. So all are irrational.
Step 2
Why this answer is correct
The correct answer is A. \(\sqrt{6}\), \(\sqrt{10}\), \(\sqrt{15}\). In the first option none is the root of a perfect square. So all are irrational.
Step 3
Exam Tip
पहले विकल्प में कोई भी संख्या पूर्ण वर्ग की जड़ नहीं है। इसलिए सभी अपरिमेय हैं।
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किस विकल्प में केवल परिमेय संख्याएँ हैं?
Which option contains only rational numbers?
#rational-numbers
#set-classification
#real-numbers
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A (0.125), (-4), \(\sqrt{169}\)
B \(\sqrt{2}\), (5), (0.5)
C \(\pi\), (3), \(\frac{1}{3}\)
D \(\sqrt{18}\), (0), (7)
Explanation opens after your attempt
Correct Answer
A. (0.125), (-4), \(\sqrt{169}\)
Step 1
Concept
(0.125) is terminating and \(\sqrt{169}=13\). All numbers in the first option are rational.
Step 2
Why this answer is correct
The correct answer is A. (0.125), (-4), \(\sqrt{169}\). (0.125) is terminating and \(\sqrt{169}=13\). All numbers in the first option are rational.
Step 3
Exam Tip
(0.125) सांत है और \(\sqrt{169}=13\) है। पहले विकल्प की सभी संख्याएँ परिमेय हैं।
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कौन सा विकल्प \(\sqrt{3}\) और \(\sqrt{27}\) का गुणनफल बताता है?
Which option gives the product of \(\sqrt{3}\) and \(\sqrt{27}\)?
#surds
#multiplication
#rational-result
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A (9)
B \(3\sqrt{3}\)
C \(\sqrt{30}\)
D \(27\sqrt{3}\)
Explanation opens after your attempt
Step 1
Concept
\(\sqrt{3}\times\sqrt{27}=\sqrt{81}=9\). In multiplication multiply the numbers inside the roots.
Step 2
Why this answer is correct
The correct answer is A. (9). \(\sqrt{3}\times\sqrt{27}=\sqrt{81}=9\). In multiplication multiply the numbers inside the roots.
Step 3
Exam Tip
\(\sqrt{3}\times\sqrt{27}=\sqrt{81}=9\) है। गुणन में जड़ों के अंदर के संख्याओं को गुणा करें।
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यदि \(y=\sqrt{2}+\sqrt{32}\) है तो (y) का सरल रूप क्या है?
If \(y=\sqrt{2}+\sqrt{32}\), what is the simplified form of (y)?
#surds
#addition
#expression
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A \(5\sqrt{2}\)
B \(3\sqrt{2}\)
C \(\sqrt{34}\)
D \(17\sqrt{2}\)
Explanation opens after your attempt
Correct Answer
A. \(5\sqrt{2}\)
Step 1
Concept
\(\sqrt{32}=4\sqrt{2}\), so \(y=5\sqrt{2}\). Add like radical terms.
Step 2
Why this answer is correct
The correct answer is A. \(5\sqrt{2}\). \(\sqrt{32}=4\sqrt{2}\), so \(y=5\sqrt{2}\). Add like radical terms.
Step 3
Exam Tip
\(\sqrt{32}=4\sqrt{2}\) है इसलिए \(y=5\sqrt{2}\) होगा। समान जड़ वाले पदों को जोड़ें।
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कौन सा कथन दो अपरिमेय संख्याओं के योग के बारे में सही है?
Which statement is correct about the sum of two irrational numbers?
#irrational-numbers
#addition
#properties
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A योग परिमेय या अपरिमेय दोनों हो सकता है / The sum can be rational or irrational
B योग हमेशा परिमेय होता है / The sum is always rational
C योग हमेशा अपरिमेय होता है / The sum is always irrational
D योग हमेशा शून्य होता है / The sum is always zero
Explanation opens after your attempt
Correct Answer
A. योग परिमेय या अपरिमेय दोनों हो सकता है / The sum can be rational or irrational
Step 1
Concept
(\sqrt{2}+\(-\sqrt{2}\)=0) is rational but \(\sqrt{2}+\sqrt{3}\) is irrational. So there is no single fixed rule.
Step 2
Why this answer is correct
The correct answer is A. योग परिमेय या अपरिमेय दोनों हो सकता है / The sum can be rational or irrational. (\sqrt{2}+\(-\sqrt{2}\)=0) is rational but \(\sqrt{2}+\sqrt{3}\) is irrational. So there is no single fixed rule.
Step 3
Exam Tip
(\sqrt{2}+\(-\sqrt{2}\)=0) परिमेय है पर \(\sqrt{2}+\sqrt{3}\) अपरिमेय है। इसलिए एक ही स्थायी नियम नहीं है।
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कौन सा कथन दो अपरिमेय संख्याओं के गुणनफल के बारे में सही है?
Which statement is correct about the product of two irrational numbers?
#irrational-numbers
#multiplication
#properties
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A गुणनफल परिमेय या अपरिमेय दोनों हो सकता है / The product can be rational or irrational
B गुणनफल हमेशा अपरिमेय होता है / The product is always irrational
C गुणनफल हमेशा शून्य होता है / The product is always zero
D गुणनफल हमेशा ऋणात्मक होता है / The product is always negative
Explanation opens after your attempt
Correct Answer
A. गुणनफल परिमेय या अपरिमेय दोनों हो सकता है / The product can be rational or irrational
Step 1
Concept
\(\sqrt{5}\times\sqrt{5}=5\) is rational but \(\sqrt{5}\times\sqrt{2}=\sqrt{10}\) is irrational. So it depends on the case.
Step 2
Why this answer is correct
The correct answer is A. गुणनफल परिमेय या अपरिमेय दोनों हो सकता है / The product can be rational or irrational. \(\sqrt{5}\times\sqrt{5}=5\) is rational but \(\sqrt{5}\times\sqrt{2}=\sqrt{10}\) is irrational. So it depends on the case.
Step 3
Exam Tip
\(\sqrt{5}\times\sqrt{5}=5\) परिमेय है पर \(\sqrt{5}\times\sqrt{2}=\sqrt{10}\) अपरिमेय है। इसलिए स्थिति पर निर्भर करता है।
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कौन सा विकल्प (\sqrt{5}\(2+\sqrt{5}\)) का मान है?
Which option is the value of (\sqrt{5}\(2+\sqrt{5}\))?
#surds
#distribution
#expression
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A \(5+2\sqrt{5}\)
B \(7\sqrt{5}\)
C \(10+\sqrt{5}\)
D \(2+5\sqrt{5}\)
Explanation opens after your attempt
Correct Answer
A. \(5+2\sqrt{5}\)
Step 1
Concept
Distributing gives \(2\sqrt{5}+5\). Keep rational and irrational parts separate.
Step 2
Why this answer is correct
The correct answer is A. \(5+2\sqrt{5}\). Distributing gives \(2\sqrt{5}+5\). Keep rational and irrational parts separate.
Step 3
Exam Tip
वितरण करने पर \(2\sqrt{5}+5\) मिलता है। पदों को परिमेय और अपरिमेय भाग में अलग रखें।
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कौन सा विकल्प (\(\sqrt{7}+1\)\(\sqrt{7}-1\)) का मान है?
Which option is the value of (\(\sqrt{7}+1\)\(\sqrt{7}-1\))?
#surds
#identity
#rational-result
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A (6)
B (8)
C \(\sqrt{7}\)
D \(7+\sqrt{7}\)
Explanation opens after your attempt
Step 1
Concept
This is ((a+b)(a-b)=a-2 -b-2 ). The value is (7-1=6).
Step 2
Why this answer is correct
The correct answer is A. (6). This is ((a+b)(a-b)=a-2 -b-2 ). The value is (7-1=6).
Step 3
Exam Tip
यह ((a+b)(a-b)=a-2 -b-2 ) है। मान (7-1=6) मिलेगा।
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कौन सा विकल्प (\(2+\sqrt{3}\)2 ) का सही विस्तार है?
Which option is the correct expansion of (\(2+\sqrt{3}\)2 )?
#surds
#identity
#expansion
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A \(7+4\sqrt{3}\)
B \(7+2\sqrt{3}\)
C \(4+\sqrt{3}\)
D \(5+4\sqrt{3}\)
Explanation opens after your attempt
Correct Answer
A. \(7+4\sqrt{3}\)
Step 1
Concept
(\(2+\sqrt{3}\)2 =4+4\sqrt{3}+3=7+4\sqrt{3}). Do not forget the middle term in the square formula.
Step 2
Why this answer is correct
The correct answer is A. \(7+4\sqrt{3}\). (\(2+\sqrt{3}\)2 =4+4\sqrt{3}+3=7+4\sqrt{3}). Do not forget the middle term in the square formula.
Step 3
Exam Tip
(\(2+\sqrt{3}\)2 =4+4\sqrt{3}+3=7+4\sqrt{3}) है। वर्ग सूत्र में बीच का पद न भूलें।
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कौन सी संख्या (3) और (4) के बीच है और अपरिमेय है?
Which number lies between (3) and (4) and is irrational?
#number-line
#irrational-number
#between-numbers
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A \(\sqrt{13}\)
B \(\sqrt{9}\)
C \(\sqrt{16}\)
D \(\frac{7}{2}\)
Explanation opens after your attempt
Correct Answer
A. \(\sqrt{13}\)
Step 1
Concept
Since (9<13<16), \(\sqrt{13}\) lies between (3) and (4). (13) is not a perfect square.
Step 2
Why this answer is correct
The correct answer is A. \(\sqrt{13}\). Since (9<13<16), \(\sqrt{13}\) lies between (3) and (4). (13) is not a perfect square.
Step 3
Exam Tip
क्योंकि (9<13<16) इसलिए \(\sqrt{13}\) (3) और (4) के बीच है। (13) पूर्ण वर्ग नहीं है।
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कौन सा विकल्प (0) और (1) के बीच की अपरिमेय संख्या है?
Which option is an irrational number between (0) and (1)?
#between-zero-one
#irrational-number
#number-line
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A \(\frac{\sqrt{3}}{3}\)
B \(\frac{1}{3}\)
C (0.75)
D (1)
Explanation opens after your attempt
Correct Answer
A. \(\frac{\sqrt{3}}{3}\)
Step 1
Concept
\(\frac{\sqrt{3}}{3}\) is irrational and lies between (0) and (1). Dividing by a non zero rational keeps irrationality.
Step 2
Why this answer is correct
The correct answer is A. \(\frac{\sqrt{3}}{3}\). \(\frac{\sqrt{3}}{3}\) is irrational and lies between (0) and (1). Dividing by a non zero rational keeps irrationality.
Step 3
Exam Tip
\(\frac{\sqrt{3}}{3}\) अपरिमेय है और इसका मान (0) और (1) के बीच है। गैर शून्य परिमेय से भाग देने पर अपरिमेयता रहती है।
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यदि \(\sqrt{n}\) परिमेय है और (n) धनात्मक पूर्णांक है तो (n) के बारे में सही कथन क्या है?
If \(\sqrt{n}\) is rational and (n) is a positive integer, what is correct about (n)?
#perfect-square
#rational-root
#exam-rule
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A (n) पूर्ण वर्ग है / (n) is a perfect square
B (n) हमेशा अभाज्य है / (n) is always prime
C (n) हमेशा विषम है / (n) is always odd
D (n) पूर्ण वर्ग नहीं है / (n) is not a perfect square
Explanation opens after your attempt
Correct Answer
A. (n) पूर्ण वर्ग है / (n) is a perfect square
Step 1
Concept
The square root of a positive integer is rational only when the number is a perfect square. This is a direct exam rule.
Step 2
Why this answer is correct
The correct answer is A. (n) पूर्ण वर्ग है / (n) is a perfect square. The square root of a positive integer is rational only when the number is a perfect square. This is a direct exam rule.
Step 3
Exam Tip
धनात्मक पूर्णांक की वर्गमूल परिमेय तभी होती है जब संख्या पूर्ण वर्ग हो। यह सीधा परीक्षा नियम है।
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कौन सा विकल्प \(2.\overline{45}\) की प्रकृति सही बताता है?
Which option correctly describes the nature of \(2.\overline{45}\)?
#recurring-decimal
#rational-numbers
#classification
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A परिमेय संख्या / Rational number
B अपरिमेय संख्या / Irrational number
C अवास्तविक संख्या / Non real number
D पूर्ण संख्या / Whole number
Explanation opens after your attempt
Correct Answer
A. परिमेय संख्या / Rational number
Step 1
Concept
The bar shows repetition of (45). Every 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 (45). Every repeating decimal is rational.
Step 3
Exam Tip
ऊपर की रेखा (45) के आवर्तन को दिखाती है। हर आवर्ती दशमलव परिमेय होता है।
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कौन सा विकल्प \(\sqrt{162}\) का सरल रूप है?
Which option is the simplified form of \(\sqrt{162}\)?
#surds
#simplification
#square-root
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A \(9\sqrt{2}\)
B \(18\sqrt{2}\)
C \(3\sqrt{18}\)
D \(6\sqrt{3}\)
Explanation opens after your attempt
Correct Answer
A. \(9\sqrt{2}\)
Step 1
Concept
\(\sqrt{162}=\sqrt{81\times2}=9\sqrt{2}\). Take the greatest perfect square inside the root.
Step 2
Why this answer is correct
The correct answer is A. \(9\sqrt{2}\). \(\sqrt{162}=\sqrt{81\times2}=9\sqrt{2}\). Take the greatest perfect square inside the root.
Step 3
Exam Tip
\(\sqrt{162}=\sqrt{81\times2}=9\sqrt{2}\) है। जड़ में सबसे बड़ा पूर्ण वर्ग लें।
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कौन सा विकल्प \(4\sqrt{3}-\sqrt{27}\) का मान है?
Which option is the value of \(4\sqrt{3}-\sqrt{27}\)?
#surds
#subtraction
#like-terms
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A \(\sqrt{3}\)
B \(7\sqrt{3}\)
C \(\sqrt{24}\)
D (3)
Explanation opens after your attempt
Correct Answer
A. \(\sqrt{3}\)
Step 1
Concept
\(\sqrt{27}=3\sqrt{3}\). Hence \(4\sqrt{3}-3\sqrt{3}=\sqrt{3}\).
Step 2
Why this answer is correct
The correct answer is A. \(\sqrt{3}\). \(\sqrt{27}=3\sqrt{3}\). Hence \(4\sqrt{3}-3\sqrt{3}=\sqrt{3}\).
Step 3
Exam Tip
\(\sqrt{27}=3\sqrt{3}\) है। इसलिए \(4\sqrt{3}-3\sqrt{3}=\sqrt{3}\) होगा।
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कौन सा विकल्प \(\sqrt{5}+\sqrt{20}-\sqrt{45}\) का सरल रूप है?
Which option is the simplified form of \(\sqrt{5}+\sqrt{20}-\sqrt{45}\)?
#surds
#addition-subtraction
#rational-result
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A (0)
B \(6\sqrt{5}\)
C \(-\sqrt{5}\)
D \(2\sqrt{5}\)
Explanation opens after your attempt
Step 1
Concept
\(\sqrt{20}=2\sqrt{5}\) and \(\sqrt{45}=3\sqrt{5}\). So \(\sqrt{5}+2\sqrt{5}-3\sqrt{5}=0\).
Step 2
Why this answer is correct
The correct answer is A. (0). \(\sqrt{20}=2\sqrt{5}\) and \(\sqrt{45}=3\sqrt{5}\). So \(\sqrt{5}+2\sqrt{5}-3\sqrt{5}=0\).
Step 3
Exam Tip
\(\sqrt{20}=2\sqrt{5}\) और \(\sqrt{45}=3\sqrt{5}\) है। इसलिए \(\sqrt{5}+2\sqrt{5}-3\sqrt{5}=0\) है।
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कौन सा विकल्प \(\frac{2}{\sqrt{2}}\) का सरल रूप है?
Which option is the simplified form of \(\frac{2}{\sqrt{2}}\)?
#division
#rationalisation
#irrational-number
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A \(\sqrt{2}\)
B \(2\sqrt{2}\)
C (1)
D \(\frac{1}{2}\)
Explanation opens after your attempt
Correct Answer
A. \(\sqrt{2}\)
Step 1
Concept
\(\frac{2}{\sqrt{2}}=\sqrt{2}\). Simplify roots in the denominator to identify the nature.
Step 2
Why this answer is correct
The correct answer is A. \(\sqrt{2}\). \(\frac{2}{\sqrt{2}}=\sqrt{2}\). Simplify roots in the denominator to identify the nature.
Step 3
Exam Tip
\(\frac{2}{\sqrt{2}}=\sqrt{2}\) है। हर में जड़ हो तो सरल करके प्रकृति पहचानें।
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यदि \(a=\sqrt{6}+1\) है तो (a-1) किस प्रकार की संख्या है?
If \(a=\sqrt{6}+1\), what type of number is (a-1)?
#expression
#irrational-number
#simplification
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A अपरिमेय संख्या / Irrational number
B परिमेय संख्या / Rational number
C पूर्णांक / Integer
D शून्य / Zero
Explanation opens after your attempt
Correct Answer
A. अपरिमेय संख्या / Irrational number
Step 1
Concept
\(a-1=\sqrt{6}\), which is irrational. First simplify the expression.
Step 2
Why this answer is correct
The correct answer is A. अपरिमेय संख्या / Irrational number. \(a-1=\sqrt{6}\), which is irrational. First simplify the expression.
Step 3
Exam Tip
\(a-1=\sqrt{6}\) है जो अपरिमेय है। पहले अभिव्यक्ति को सरल करें।
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कौन सा विकल्प \(\sqrt{2}\) के निकटतम दो पूर्णांकों को सही बताता है?
Which option correctly gives the two nearest integers between which \(\sqrt{2}\) lies?
#number-line
#square-root
#estimation
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A (1) और (2) / (1) and (2)
B (2) और (3) / (2) and (3)
C (0) और (1) / (0) and (1)
D (3) और (4) / (3) and (4)
Explanation opens after your attempt
Correct Answer
A. (1) और (2) / (1) and (2)
Step 1
Concept
Since (1<2<4), \(1<\sqrt{2}<2\). Use squares to locate roots.
Step 2
Why this answer is correct
The correct answer is A. (1) और (2) / (1) and (2). Since (1<2<4), \(1<\sqrt{2}<2\). Use squares to locate roots.
Step 3
Exam Tip
क्योंकि (1<2<4) इसलिए \(1<\sqrt{2}<2\)। वर्गों से जड़ की स्थिति पहचानें।
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कौन सा विकल्प \(\sqrt{50}\) और \(\sqrt{72}\) की तुलना सही करता है?
Which option correctly compares \(\sqrt{50}\) and \(\sqrt{72}\)?
#comparison
#square-root
#number-line
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A \(\sqrt{72}>\sqrt{50}\)
B \(\sqrt{72}<\sqrt{50}\)
C \(\sqrt{72}=\sqrt{50}\)
D तुलना संभव नहीं / Comparison is not possible
Explanation opens after your attempt
Correct Answer
A. \(\sqrt{72}>\sqrt{50}\)
Step 1
Concept
For positive numbers a larger number inside the root gives a larger square root. Since (72>50), \(\sqrt{72}>\sqrt{50}\).
Step 2
Why this answer is correct
The correct answer is A. \(\sqrt{72}>\sqrt{50}\). For positive numbers a larger number inside the root gives a larger square root. Since (72>50), \(\sqrt{72}>\sqrt{50}\).
Step 3
Exam Tip
धनात्मक संख्याओं में अंदर की संख्या बड़ी हो तो वर्गमूल भी बड़ा होता है। (72>50) इसलिए \(\sqrt{72}>\sqrt{50}\)।
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कौन सा विकल्प \(\sqrt{0.81}\) का मान है?
Which option is the value of \(\sqrt{0.81}\)?
#decimal-square-root
#rational-number
#calculation
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A (0.9)
B (0.09)
C (9)
D (0.081)
Explanation opens after your attempt
Step 1
Concept
Since \(0.9\times0.9=0.81\), \(\sqrt{0.81}=0.9\). It is a terminating decimal.
Step 2
Why this answer is correct
The correct answer is A. (0.9). Since \(0.9\times0.9=0.81\), \(\sqrt{0.81}=0.9\). It is a terminating decimal.
Step 3
Exam Tip
\(0.9\times0.9=0.81\) इसलिए \(\sqrt{0.81}=0.9\)। यह सांत दशमलव है।
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यदि \(u=5+\sqrt{2}\) और \(v=5-\sqrt{2}\) हैं तो (uv) का मान क्या है?
If \(u=5+\sqrt{2}\) and \(v=5-\sqrt{2}\), what is the value of (uv)?
#conjugate
#surds
#rational-result
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A (23)
B (27)
C \(25+\sqrt{2}\)
D \(10\sqrt{2}\)
Explanation opens after your attempt
Step 1
Concept
(\(5+\sqrt{2}\)\(5-\sqrt{2}\)=25-2=23). In conjugate multiplication the irrational part cancels.
Step 2
Why this answer is correct
The correct answer is A. (23). (\(5+\sqrt{2}\)\(5-\sqrt{2}\)=25-2=23). In conjugate multiplication the irrational part cancels.
Step 3
Exam Tip
(\(5+\sqrt{2}\)\(5-\sqrt{2}\)=25-2=23) है। संयुग्मी गुणन में अपरिमेय भाग हट जाता है।
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कौन सा विकल्प \(\sqrt{24}\times\sqrt{6}\) का मान है?
Which option is the value of \(\sqrt{24}\times\sqrt{6}\)?
#surds
#multiplication
#rational-result
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A (12)
B \(6\sqrt{24}\)
C \(\sqrt{30}\)
D \(24\sqrt{6}\)
Explanation opens after your attempt
Step 1
Concept
\(\sqrt{24}\times\sqrt{6}=\sqrt{144}=12\). In root multiplication multiply the numbers inside.
Step 2
Why this answer is correct
The correct answer is A. (12). \(\sqrt{24}\times\sqrt{6}=\sqrt{144}=12\). In root multiplication multiply the numbers inside.
Step 3
Exam Tip
\(\sqrt{24}\times\sqrt{6}=\sqrt{144}=12\) है। जड़ों के गुणन में अंदर की संख्याएँ गुणा करें।
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कौन सा विकल्प \(\sqrt[3]{64}\) की प्रकृति सही बताता है?
Which option correctly describes the nature of \(\sqrt[3]{64}\)?
#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
\(\sqrt[3]{64}=4\), 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. \(\sqrt[3]{64}=4\), which is rational. The cube root of a perfect cube is rational.
Step 3
Exam Tip
\(\sqrt[3]{64}=4\) है जो परिमेय है। पूर्ण घन की घनमूल परिमेय होती है।
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कौन सा विकल्प \(\sqrt[3]{16}\) के लिए सही है?
Which option is correct for \(\sqrt[3]{16}\)?
#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 (8) है / It is (8)
D यह सांत दशमलव है / It is terminating decimal
Explanation opens after your attempt
Correct Answer
A. यह अपरिमेय है / It is irrational
Step 1
Concept
(16) is not a perfect cube so its cube root is irrational. Identify perfect cubes in cube roots.
Step 2
Why this answer is correct
The correct answer is A. यह अपरिमेय है / It is irrational. (16) is not a perfect cube so its cube root is irrational. Identify perfect cubes in cube roots.
Step 3
Exam Tip
(16) पूर्ण घन नहीं है इसलिए इसकी घनमूल अपरिमेय है। घनमूल में पूर्ण घन पहचानें।
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यदि \(2+\sqrt{m}\) अपरिमेय है और (m) धनात्मक पूर्णांक है तो कौन सा (m) हो सकता है?
If \(2+\sqrt{m}\) is irrational and (m) is a positive integer, which (m) can be correct?
#perfect-square
#irrational-expression
#reasoning
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A (18)
B (16)
C (25)
D (36)
Explanation opens after your attempt
Step 1
Concept
(18) is not a perfect square so \(\sqrt{18}\) is irrational. The roots of the other options are rational.
Step 2
Why this answer is correct
The correct answer is A. (18). (18) is not a perfect square so \(\sqrt{18}\) is irrational. The roots of the other options are rational.
Step 3
Exam Tip
(18) पूर्ण वर्ग नहीं है इसलिए \(\sqrt{18}\) अपरिमेय है। बाकी विकल्पों की जड़ परिमेय है।
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कौन सा विकल्प \(\sqrt{225}\) और \(\sqrt{226}\) की प्रकृति सही बताता है?
Which option gives the correct nature of \(\sqrt{225}\) and \(\sqrt{226}\)?
#perfect-square
#comparison
#rational-irrational
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A \(\sqrt{225}\) परिमेय है और \(\sqrt{226}\) अपरिमेय है / \(\sqrt{225}\) is rational and \(\sqrt{226}\) is irrational
B दोनों परिमेय हैं / Both are rational
C दोनों अपरिमेय हैं / Both are irrational
D \(\sqrt{225}\) अपरिमेय है और \(\sqrt{226}\) परिमेय है / \(\sqrt{225}\) is irrational and \(\sqrt{226}\) is rational
Explanation opens after your attempt
Correct Answer
A. \(\sqrt{225}\) परिमेय है और \(\sqrt{226}\) अपरिमेय है / \(\sqrt{225}\) is rational and \(\sqrt{226}\) is irrational
Step 1
Concept
\(\sqrt{225}=15\), but (226) 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. \(\sqrt{225}\) परिमेय है और \(\sqrt{226}\) अपरिमेय है / \(\sqrt{225}\) is rational and \(\sqrt{226}\) is irrational. \(\sqrt{225}=15\), but (226) is not a perfect square. So the first root is rational and the second is irrational.
Step 3
Exam Tip
\(\sqrt{225}=15\) है लेकिन (226) पूर्ण वर्ग नहीं है। इसलिए पहली जड़ परिमेय और दूसरी अपरिमेय है।
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कौन सा विकल्प (0.2020020002...) के बारे में सही है?
Which option is correct about (0.2020020002...)?
#non-repeating-decimal
#irrational-number
#decimal
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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
It has no fixed repeating block and the decimal is infinite. 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. It has no fixed repeating block and the decimal is infinite. So it is irrational.
Step 3
Exam Tip
इसमें कोई निश्चित आवर्ती समूह नहीं है और दशमलव अनंत है। इसलिए यह अपरिमेय है।
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यदि कोई संख्या सांत या आवर्ती दशमलव है तो वह कैसी संख्या होगी?
If a number has a terminating or repeating decimal, what type of number will it be?
#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 प्राकृतिक संख्या / Natural number only
Explanation opens after your attempt
Correct Answer
A. परिमेय संख्या / Rational number
Step 1
Concept
The decimal expansion of rational numbers is terminating or repeating. This identification is very useful in exams.
Step 2
Why this answer is correct
The correct answer is A. परिमेय संख्या / Rational number. The decimal expansion of rational numbers is terminating or repeating. This identification is very useful in exams.
Step 3
Exam Tip
परिमेय संख्याओं का दशमलव विस्तार सांत या आवर्ती होता है। यह पहचान परीक्षा में बहुत काम आती है।
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कौन सा विकल्प \(1+\sqrt{3}\) और \(1-\sqrt{3}\) के गुणनफल का मान है?
Which option is the value of the product of \(1+\sqrt{3}\) and \(1-\sqrt{3}\)?
#conjugate
#surds
#rational-result
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A (-2)
B (2)
C \(1+\sqrt{3}\)
D (3)
Explanation opens after your attempt
Step 1
Concept
(\(1+\sqrt{3}\)\(1-\sqrt{3}\)=1-3=-2). Multiplying conjugates gives a rational number.
Step 2
Why this answer is correct
The correct answer is A. (-2). (\(1+\sqrt{3}\)\(1-\sqrt{3}\)=1-3=-2). Multiplying conjugates gives a rational number.
Step 3
Exam Tip
(\(1+\sqrt{3}\)\(1-\sqrt{3}\)=1-3=-2) है। संयुग्मी जोड़े का गुणन परिमेय देता है।
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कौन सा विकल्प \(\sqrt{12}+\sqrt{75}-\sqrt{27}\) का सरल रूप है?
Which option is the simplified form of \(\sqrt{12}+\sqrt{75}-\sqrt{27}\)?
#surds
#addition-subtraction
#simplification
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A \(4\sqrt{3}\)
B \(10\sqrt{3}\)
C \(\sqrt{60}\)
D \(2\sqrt{3}\)
Explanation opens after your attempt
Correct Answer
A. \(4\sqrt{3}\)
Step 1
Concept
\(\sqrt{12}=2\sqrt{3}\), \(\sqrt{75}=5\sqrt{3}\), and \(\sqrt{27}=3\sqrt{3}\). The result is \(4\sqrt{3}\).
Step 2
Why this answer is correct
The correct answer is A. \(4\sqrt{3}\). \(\sqrt{12}=2\sqrt{3}\), \(\sqrt{75}=5\sqrt{3}\), and \(\sqrt{27}=3\sqrt{3}\). The result is \(4\sqrt{3}\).
Step 3
Exam Tip
\(\sqrt{12}=2\sqrt{3}\), \(\sqrt{75}=5\sqrt{3}\) और \(\sqrt{27}=3\sqrt{3}\) है। परिणाम \(4\sqrt{3}\) है।
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कौन सा विकल्प \( \frac{1}{2}+\sqrt{2}\) की प्रकृति सही बताता है?
Which option correctly describes the nature of \( \frac{1}{2}+\sqrt{2}\)?
#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
\(\frac{1}{2}\) is rational and \(\sqrt{2}\) is irrational. Their sum is irrational.
Step 2
Why this answer is correct
The correct answer is A. अपरिमेय संख्या / Irrational number. \(\frac{1}{2}\) is rational and \(\sqrt{2}\) is irrational. Their sum is irrational.
Step 3
Exam Tip
\(\frac{1}{2}\) परिमेय है और \(\sqrt{2}\) अपरिमेय है। उनका योग अपरिमेय होता है।
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कौन सा विकल्प \(\sqrt{300}\) का सरल रूप है?
Which option is the simplified form of \(\sqrt{300}\)?
#surds
#simplification
#square-root
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A \(10\sqrt{3}\)
B \(30\sqrt{10}\)
C \(5\sqrt{12}\)
D \(3\sqrt{100}\)
Explanation opens after your attempt
Correct Answer
A. \(10\sqrt{3}\)
Step 1
Concept
\(\sqrt{300}=\sqrt{100\times3}=10\sqrt{3}\). Take out the greatest perfect square.
Step 2
Why this answer is correct
The correct answer is A. \(10\sqrt{3}\). \(\sqrt{300}=\sqrt{100\times3}=10\sqrt{3}\). Take out the greatest perfect square.
Step 3
Exam Tip
\(\sqrt{300}=\sqrt{100\times3}=10\sqrt{3}\) है। सबसे बड़ा पूर्ण वर्ग बाहर निकालें।
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यदि \(x=4+\sqrt{7}\) और \(y=4-\sqrt{7}\) हैं तो (x-y) का सरल रूप क्या है?
If \(x=4+\sqrt{7}\) and \(y=4-\sqrt{7}\), what is the simplified form of (x-y)?
#surds
#subtraction
#expression
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A \(2\sqrt{7}\)
B (8)
C (0)
D (7)
Explanation opens after your attempt
Correct Answer
A. \(2\sqrt{7}\)
Step 1
Concept
On subtracting, the (4) terms cancel and (\sqrt{7}-\(-\sqrt{7}\)=2\sqrt{7}). Watch the signs carefully.
Step 2
Why this answer is correct
The correct answer is A. \(2\sqrt{7}\). On subtracting, the (4) terms cancel and (\sqrt{7}-\(-\sqrt{7}\)=2\sqrt{7}). Watch the signs carefully.
Step 3
Exam Tip
घटाने पर (4) पद कट जाते हैं और (\sqrt{7}-\(-\sqrt{7}\)=2\sqrt{7}) मिलता है। चिह्नों का ध्यान रखें।
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