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
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 \(1+\sqrt{3}\) 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
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 \(\sqrt{24}\times\sqrt{6}\) का मान है?
Which option is the value of \(\sqrt{24}\times\sqrt{6}\)?
#surds
#multiplication
#rational-result
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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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
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 \(\sqrt{5}+\sqrt{20}-\sqrt{45}\) का सरल रूप है?
Which option is the simplified form of \(\sqrt{5}+\sqrt{20}-\sqrt{45}\)?
#surds
#addition-subtraction
#rational-result
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 (\(\sqrt{7}+1\)\(\sqrt{7}-1\)) का मान है?
Which option is the value of (\(\sqrt{7}+1\)\(\sqrt{7}-1\))?
#surds
#identity
#rational-result
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 \(\sqrt{3}\) और \(\sqrt{27}\) का गुणनफल बताता है?
Which option gives the product of \(\sqrt{3}\) and \(\sqrt{27}\)?
#surds
#multiplication
#rational-result
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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\(\frac{\sqrt{45}}{\sqrt{5}}\) का मान क्या है?
What is the value of \(\frac{\sqrt{45}}{\sqrt{5}}\)?
#division
#square-root
#rational-result
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 \(a=2-\sqrt{5}\) 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
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 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
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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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
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 \(3\sqrt{2}\times2\sqrt{2}\) का मान है?
Which option is the value of \(3\sqrt{2}\times2\sqrt{2}\)?
#surds
#multiplication
#rational-result
A (12)
B \(6\sqrt{2}\)
C \(12\sqrt{2}\)
D (6)
Explanation opens after your attempt
Step 1
Concept
\(3\sqrt{2}\times2\sqrt{2}=6\times2=12\). Multiplying same roots can give a rational result.
Step 2
Why this answer is correct
The correct answer is A. (12). \(3\sqrt{2}\times2\sqrt{2}=6\times2=12\). Multiplying same roots can give a rational result.
Step 3
Exam Tip
\(3\sqrt{2}\times2\sqrt{2}=6\times2=12\) है। समान जड़ का गुणन परिमेय परिणाम दे सकता है।
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(\(5+\sqrt{7}\)-\(2+\sqrt{7}\)) का मान किस प्रकार की संख्या है?
What type of number is the value of (\(5+\sqrt{7}\)-\(2+\sqrt{7}\))?
#irrational-terms
#subtraction
#rational-result
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
On subtracting the \(\sqrt{7}\) terms cancel and the value is (3). So the result is rational.
Step 2
Why this answer is correct
The correct answer is A. परिमेय संख्या / Rational number. On subtracting the \(\sqrt{7}\) terms cancel and the value is (3). So the result is rational.
Step 3
Exam Tip
घटाने पर \(\sqrt{7}\) पद कट जाते हैं और मान (3) मिलता है। इसलिए परिणाम परिमेय है।
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\(\sqrt{5}\times\sqrt{45}\) का मान क्या है?
What is the value of \(\sqrt{5}\times\sqrt{45}\)?
#multiplication
#irrational-numbers
#rational-result
A (15)
B \(5\sqrt{45}\)
C \(\sqrt{50}\)
D \(45\sqrt{5}\)
Explanation opens after your attempt
Step 1
Concept
\(\sqrt{5}\times\sqrt{45}=\sqrt{225}=15\). The product of two irrational numbers can be rational.
Step 2
Why this answer is correct
The correct answer is A. (15). \(\sqrt{5}\times\sqrt{45}=\sqrt{225}=15\). The product of two irrational numbers can be rational.
Step 3
Exam Tip
\(\sqrt{5}\times\sqrt{45}=\sqrt{225}=15\) है। दो अपरिमेय संख्याओं का गुणनफल परिमेय हो सकता है।
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कौन सा विकल्प अपरिमेय संख्या को शून्य से गुणा करने का परिणाम दिखाता है?
Which option shows the result of multiplying an irrational number by zero?
#zero
#multiplication
#rational-result
A (0) जो परिमेय है / (0) which is rational
B हमेशा अपरिमेय / Always irrational
C हमेशा ऋणात्मक / Always negative
D हमेशा अवास्तविक / Always non real
Explanation opens after your attempt
Correct Answer
A. (0) जो परिमेय है / (0) which is rational
Step 1
Concept
Multiplying any real number by (0) gives (0). (0) is a rational number.
Step 2
Why this answer is correct
The correct answer is A. (0) जो परिमेय है / (0) which is rational. Multiplying any real number by (0) gives (0). (0) is a rational number.
Step 3
Exam Tip
किसी भी वास्तविक संख्या को (0) से गुणा करने पर (0) मिलता है। (0) परिमेय संख्या है।
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\(\sqrt{3}\times\sqrt{27}\) का मान क्या है?
What is the value of \(\sqrt{3}\times\sqrt{27}\)?
#multiplication
#irrational-numbers
#rational-result
A (9)
B \(3\sqrt{3}\)
C \(\sqrt{30}\)
D (27)
Explanation opens after your attempt
Step 1
Concept
\(\sqrt{3}\times\sqrt{27}=\sqrt{81}=9\). The product of two irrational numbers can be rational.
Step 2
Why this answer is correct
The correct answer is A. (9). \(\sqrt{3}\times\sqrt{27}=\sqrt{81}=9\). The product of two irrational numbers can be rational.
Step 3
Exam Tip
\(\sqrt{3}\times\sqrt{27}=\sqrt{81}=9\) है। दो अपरिमेय संख्याओं का गुणनफल परिमेय भी हो सकता है।
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यदि \(x=\sqrt{3}\) है तो \(x^2\) किस प्रकार की संख्या है?
If \(x=\sqrt{3}\), what type of number is \(x^2\)?
#square
#irrational-numbers
#rational-result
A परिमेय संख्या / Rational number
B अपरिमेय संख्या / Irrational number
C अवास्तविक संख्या / Non real number
D अपरिभाषित संख्या / Undefined number
Explanation opens after your attempt
Correct Answer
A. परिमेय संख्या / Rational number
Step 1
Concept
(\(\sqrt{3}\)2 =3) which is rational. The square of an irrational number can sometimes be rational.
Step 2
Why this answer is correct
The correct answer is A. परिमेय संख्या / Rational number. (\(\sqrt{3}\)2 =3) which is rational. The square of an irrational number can sometimes be rational.
Step 3
Exam Tip
(\(\sqrt{3}\)2 =3) है जो परिमेय है। अपरिमेय संख्या का वर्ग कभी-कभी परिमेय हो सकता है।
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कौन सी संख्या परिमेय है, जबकि उसमें अपरिमेय वर्गमूल दिखाई दे रहे हैं?
Which number is rational even though irrational square roots appear in it?
#conjugates
#irrational numbers
#rational result
#class 10
A (\(\sqrt{6}+\sqrt{2}\)\(\sqrt{6}-\sqrt{2}\))
B \(\sqrt{6}+\sqrt{2}\)
C \(\sqrt{6}-\sqrt{2}\)
D \(\sqrt{12}+\sqrt{2}\)
Explanation opens after your attempt
Correct Answer
A. (\(\sqrt{6}+\sqrt{2}\)\(\sqrt{6}-\sqrt{2}\))
Step 1
Concept
The first option is a product of conjugate terms.
Step 2
Why this answer is correct
(\(\sqrt{6}+\sqrt{2}\)\(\sqrt{6}-\sqrt{2}\)=6-2=4), which is rational.
Step 3
Exam Tip
Identifying conjugates helps remove radicals quickly. चरण 1: पहला विकल्प संयुग्मी पदों का गुणनफल है। चरण 2: (\(\sqrt{6}+\sqrt{2}\)\(\sqrt{6}-\sqrt{2}\)=6-2=4), जो परिमेय है। चरण 3: संयुग्मी पद पहचानने से वर्गमूल जल्दी हट जाते हैं।
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कौन सा विकल्प \(\sqrt{2}\sqrt{8}+\sqrt{3}\sqrt{12}\) का सही मान देता है?
Which option gives the correct value of \(\sqrt{2}\sqrt{8}+\sqrt{3}\sqrt{12}\)?
#radical products
#rational result
#class 10
A (10)
B \(\sqrt{10}\)
C \(4\sqrt{2}\)
D \(2\sqrt{6}\)
Explanation opens after your attempt
Step 1
Concept
\(\sqrt{2}\sqrt{8}=\sqrt{16}=4\).
Step 2
Why this answer is correct
\(\sqrt{3}\sqrt{12}=\sqrt{36}=6\), so the sum is (10).
Step 3
Exam Tip
In products combine radicals and check for perfect squares. चरण 1: \(\sqrt{2}\sqrt{8}=\sqrt{16}=4\)। चरण 2: \(\sqrt{3}\sqrt{12}=\sqrt{36}=6\) इसलिए योग (10) है। चरण 3: गुणनफल में वर्गमूलों को मिलाकर पूर्ण वर्ग देखें।
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यदि \(x=4+\sqrt{15}\) और \(y=4-\sqrt{15}\), तो \(x^2+y^2\) का मान क्या है?
If \(x=4+\sqrt{15}\) and \(y=4-\sqrt{15}\), what is the value of \(x^2+y^2\)?
#conjugate squares
#rational result
#class 10
A (62)
B (2)
C \(32\sqrt{15}\)
D (31)
Explanation opens after your attempt
Step 1
Concept
(x) and (y) are conjugates.
Step 2
Why this answer is correct
(x-2 +y-2 =2\(4^2+15\)=2(31)=62).
Step 3
Exam Tip
In the sum of squares of conjugates, irrational terms cancel. चरण 1: (x) और (y) संयुग्मी हैं। चरण 2: (x-2 +y-2 =2\(4^2+15\)=2(31)=62)। चरण 3: संयुग्मी वर्गों के योग में अपरिमेय पद कट जाते हैं।
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कौन-सा विकल्प \(\frac{\sqrt{12}+\sqrt{27}}{\sqrt{3}}\) का सही मान देता है?
Which option gives the correct value of \(\frac{\sqrt{12}+\sqrt{27}}{\sqrt{3}}\)?
#surd simplification
#rational result
#class 10
A (5)
B \(\sqrt{39}\)
C \(3\sqrt{3}\)
D (15)
Explanation opens after your attempt
Step 1
Concept
Write \(\sqrt{12}=2\sqrt{3}\) and \(\sqrt{27}=3\sqrt{3}\).
Step 2
Why this answer is correct
The numerator is \(5\sqrt{3}\), so \(\frac{5\sqrt{3}}{\sqrt{3}}=5\).
Step 3
Exam Tip
Combine like surds before division. चरण 1: \(\sqrt{12}=2\sqrt{3}\) और \(\sqrt{27}=3\sqrt{3}\) लिखें। चरण 2: ऊपर का योग \(5\sqrt{3}\) है, इसलिए \(\frac{5\sqrt{3}}{\sqrt{3}}=5\)। चरण 3: भाग से पहले समान मूल वाले पदों को जोड़ें।
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कौन-सा कथन \(\sqrt{5}+\sqrt{20}-\sqrt{45}\) के लिए सही है?
Which statement is correct for \(\sqrt{5}+\sqrt{20}-\sqrt{45}\)?
#cancellation of surds
#rational result
#class 10
A यह (0) है और परिमेय है / It is (0) and rational
B यह \(\sqrt{5}\) है और अपरिमेय है / It is \(\sqrt{5}\) and irrational
C यह \(6\sqrt{5}\) है और अपरिमेय है / It is \(6\sqrt{5}\) and irrational
D यह (10) है और परिमेय है / It is (10) and rational
Explanation opens after your attempt
Correct Answer
A. यह (0) है और परिमेय है / It is (0) and rational
Step 1
Concept
Write \(\sqrt{20}=2\sqrt{5}\) and \(\sqrt{45}=3\sqrt{5}\).
Step 2
Why this answer is correct
\(\sqrt{5}+2\sqrt{5}-3\sqrt{5}=0\), which is rational.
Step 3
Exam Tip
Terms that look irrational may cancel to give a rational result. चरण 1: \(\sqrt{20}=2\sqrt{5}\) और \(\sqrt{45}=3\sqrt{5}\) लिखें। चरण 2: \(\sqrt{5}+2\sqrt{5}-3\sqrt{5}=0\), जो परिमेय है। चरण 3: अपरिमेय दिखने वाले पद कटकर परिमेय उत्तर दे सकते हैं।
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कौन-सा विकल्प \(\frac{\sqrt{45}+\sqrt{20}}{\sqrt{5}}\) का सही मान देता है?
Which option gives the correct value of \(\frac{\sqrt{45}+\sqrt{20}}{\sqrt{5}}\)?
#surds
#simplification
#rational result
#class 10
A (5)
B (7)
C \(\sqrt{65}\)
D (13)
Explanation opens after your attempt
Step 1
Concept
\(\sqrt{45}=3\sqrt{5}\) and \(\sqrt{20}=2\sqrt{5}\).
Step 2
Why this answer is correct
The numerator becomes \(5\sqrt{5}\), so \(\frac{5\sqrt{5}}{\sqrt{5}}=5\).
Step 3
Exam Tip
Before division, convert the numerator surds into like terms. चरण 1: \(\sqrt{45}=3\sqrt{5}\) और \(\sqrt{20}=2\sqrt{5}\) हैं। चरण 2: ऊपर का योग \(5\sqrt{5}\) है, इसलिए \(\frac{5\sqrt{5}}{\sqrt{5}}=5\)। चरण 3: भाग से पहले ऊपर के मूलों को समान रूप में बदलें।
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किस विकल्प में (x+y) परिमेय है, जबकि (x) और (y) दोनों अपरिमेय हैं?
In which option is (x+y) rational while both (x) and (y) are irrational?
#sum of irrationals
#rational result
#class 10
A \(x=\sqrt{8},y=-2\sqrt{2}\)
B \(x=\sqrt{3},y=\sqrt{12}\)
C \(x=\sqrt{5},y=\sqrt{20}\)
D \(x=\sqrt{6},y=\sqrt{24}\)
Explanation opens after your attempt
Correct Answer
A. \(x=\sqrt{8},y=-2\sqrt{2}\)
Step 1
Concept
\(\sqrt{8}=2\sqrt{2}\), so (x) and \(y=-2\sqrt{2}\) are both irrational.
Step 2
Why this answer is correct
Their sum is \(2\sqrt{2}-2\sqrt{2}=0\), which is rational.
Step 3
Exam Tip
Opposite irrational terms can give a rational sum. चरण 1: \(\sqrt{8}=2\sqrt{2}\), इसलिए (x) और \(y=-2\sqrt{2}\) दोनों अपरिमेय हैं। चरण 2: उनका योग \(2\sqrt{2}-2\sqrt{2}=0\), जो परिमेय है। चरण 3: विपरीत अपरिमेय पदों के योग से परिमेय उत्तर मिल सकता है।
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कौन-सा विकल्प \(\frac{\sqrt{27}}{\sqrt{3}}\) का सही मान देता है?
Which option gives the correct value of \(\frac{\sqrt{27}}{\sqrt{3}}\)?
#division of radicals
#rational result
#class 10
A (3)
B \(\sqrt{9}\) और इसलिए (3) / \(\sqrt{9}\) and hence (3)
C \(9\sqrt{3}\)
D \(\sqrt{24}\)
Explanation opens after your attempt
Correct Answer
B. \(\sqrt{9}\) और इसलिए (3) / \(\sqrt{9}\) and hence (3)
Step 1
Concept
\(\frac{\sqrt{27}}{\sqrt{3}}=\sqrt{\frac{27}{3}}\).
Step 2
Why this answer is correct
This is \(\sqrt{9}=3\), which is rational.
Step 3
Exam Tip
In division, simplifying the radicals together is a quick method. चरण 1: \(\frac{\sqrt{27}}{\sqrt{3}}=\sqrt{\frac{27}{3}}\) लिखा जा सकता है। चरण 2: यह \(\sqrt{9}=3\) है, जो परिमेय है। चरण 3: भाग में मूलों को एक साथ सरल करना जल्दी तरीका है।
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कौन-सा युग्म दिखाता है कि दो अपरिमेय संख्याओं का भागफल परिमेय हो सकता है?
Which pair shows that the quotient of two irrational numbers can be rational?
#quotient of irrationals
#rational result
#class 10
A \(\sqrt{6}\) और \(\sqrt{3}\) / \(\sqrt{6}\) and \(\sqrt{3}\)
B \(\sqrt{12}\) और \(\sqrt{3}\) / \(\sqrt{12}\) and \(\sqrt{3}\)
C \(\sqrt{10}\) और \(\sqrt{2}\) / \(\sqrt{10}\) and \(\sqrt{2}\)
D \(\sqrt{7}\) और \(\sqrt{5}\) / \(\sqrt{7}\) and \(\sqrt{5}\)
Explanation opens after your attempt
Correct Answer
B. \(\sqrt{12}\) और \(\sqrt{3}\) / \(\sqrt{12}\) and \(\sqrt{3}\)
Step 1
Concept
\(\sqrt{12}=2\sqrt{3}\) and \(\sqrt{3}\) are both irrational.
Step 2
Why this answer is correct
\(\frac{\sqrt{12}}{\sqrt{3}}=\sqrt{4}=2\), which is rational.
Step 3
Exam Tip
In quotients, check whether the value inside the root becomes a perfect square. चरण 1: \(\sqrt{12}=2\sqrt{3}\) और \(\sqrt{3}\) दोनों अपरिमेय हैं। चरण 2: \(\frac{\sqrt{12}}{\sqrt{3}}=\sqrt{4}=2\), जो परिमेय है। चरण 3: भागफल में मूल के अंदर का भाग पूर्ण वर्ग बन रहा है या नहीं, यह देखें।
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यदि \(x=\sqrt{3}+2\) है, तो \(x-\sqrt{3}\) का मान और प्रकृति क्या होगी?
If \(x=\sqrt{3}+2\), what will be the value and nature of \(x-\sqrt{3}\)?
#cancellation of surds
#rational result
#class 10
#hard
A (2), परिमेय / (2), rational
B \(\sqrt{3}\), अपरिमेय / \(\sqrt{3}\), irrational
C \(2\sqrt{3}\), अपरिमेय / \(2\sqrt{3}\), irrational
D (5), परिमेय / (5), rational
Explanation opens after your attempt
Correct Answer
A. (2), परिमेय / (2), rational
Step 1
Concept
Substitute the given value of (x).
Step 2
Why this answer is correct
(x-\sqrt{3}=\(\sqrt{3}+2\)-\sqrt{3}=2), which is rational.
Step 3
Exam Tip
Like irrational terms may cancel, so decide the nature only after simplifying. चरण 1: दिए गए (x) का मान रखें। चरण 2: (x-\sqrt{3}=\(\sqrt{3}+2\)-\sqrt{3}=2), जो परिमेय है। चरण 3: समान अपरिमेय पद कट सकते हैं, इसलिए सरल करने के बाद ही प्रकृति तय करें।
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(\left\(\sqrt{13}-\sqrt{5}\right\)\left\(\sqrt{13}+\sqrt{5}\right\)) का मान क्या है?
What is the value of (\left\(\sqrt{13}-\sqrt{5}\right\)\left\(\sqrt{13}+\sqrt{5}\right\))?
#real-numbers
#conjugate-product
#rational-result
A (8)
B (18)
C \(\sqrt{65}\)
D \(13+\sqrt{5}\)
Explanation opens after your attempt
Step 1
Concept
This is of the form ((a-b)(a+b)=a-2 -b-2 ).
Step 2
Why this answer is correct
(\(\sqrt{13}\)2 -\(\sqrt{5}\)2 =13-5=8).
Step 3
Exam Tip
In conjugate multiplication, directly use the difference of squares. चरण 1: यह ((a-b)(a+b)=a-2 -b-2 ) का रूप है। चरण 2: (\(\sqrt{13}\)2 -\(\sqrt{5}\)2 =13-5=8)। चरण 3: संयुग्म गुणन में वर्गों का अंतर सीधे लगाएं।
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\(\sqrt{63}\times\sqrt{112}\) का मान क्या है?
What is the value of \(\sqrt{63}\times\sqrt{112}\)?
#real-numbers
#radical-product
#rational-result
A (72)
B (84)
C (96)
D \(\sqrt{175}\)
Explanation opens after your attempt
Step 1
Concept
\(\sqrt{63}\times\sqrt{112}=\sqrt{7056}\).
Step 2
Why this answer is correct
\(\sqrt{7056}=84\), so the result is rational.
Step 3
Exam Tip
In multiplication, multiply the inside numbers and check for a perfect square. चरण 1: \(\sqrt{63}\times\sqrt{112}=\sqrt{7056}\)। चरण 2: \(\sqrt{7056}=84\), इसलिए परिणाम परिमेय है। चरण 3: गुणन में अंदर की संख्याओं को गुणा करके पूर्ण वर्ग जांचें।
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कौन-सा विकल्प दो अपरिमेय संख्याओं का ऐसा अंतर दिखाता है जो परिमेय है?
Which option shows a difference of two irrational numbers that is rational?
#real-numbers
#irrational-difference
#rational-result
A \(\sqrt{17}-\sqrt{17}\)
B \(\sqrt{8}-\sqrt{3}\)
C \(\sqrt{10}-2\)
D \(\sqrt{15}-\sqrt{5}\)
Explanation opens after your attempt
Correct Answer
A. \(\sqrt{17}-\sqrt{17}\)
Step 1
Concept
\(\sqrt{17}\) and \(\sqrt{17}\) are both irrational.
Step 2
Why this answer is correct
Their difference is (0), which is rational.
Step 3
Exam Tip
The difference of equal irrational terms can be rational. चरण 1: \(\sqrt{17}\) और \(\sqrt{17}\) दोनों अपरिमेय हैं। चरण 2: उनका अंतर (0) है, जो परिमेय है। चरण 3: समान अपरिमेय पदों का अंतर परिमेय हो सकता है।
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