किस विकल्प में दो अलग-अलग अपरिमेय संख्याओं का गुणनफल परिमेय है?
In which option is the product of two different irrational numbers rational?
#irrational-product
#counterexample
#rational-result
A \(\sqrt{2}\) और \(3\sqrt{2}\) / \(\sqrt{2}\) and \(3\sqrt{2}\)
B \(\sqrt{2}\) और \(\sqrt{3}\) / \(\sqrt{2}\) and \(\sqrt{3}\)
C \(\sqrt{5}\) और \(\sqrt{7}\) / \(\sqrt{5}\) and \(\sqrt{7}\)
D \(\sqrt{3}\) और \(2\sqrt{5}\) / \(\sqrt{3}\) and \(2\sqrt{5}\)
Explanation opens after your attempt
Correct Answer
A. \(\sqrt{2}\) और \(3\sqrt{2}\) / \(\sqrt{2}\) and \(3\sqrt{2}\)
Step 1
Concept
\(\sqrt{2}\cdot3\sqrt{2}=6\), which is rational. In exams remember counterexamples for products of irrational numbers.
Step 2
Why this answer is correct
The correct answer is A. \(\sqrt{2}\) और \(3\sqrt{2}\) / \(\sqrt{2}\) and \(3\sqrt{2}\). \(\sqrt{2}\cdot3\sqrt{2}=6\), which is rational. In exams remember counterexamples for products of irrational numbers.
Step 3
Exam Tip
\(\sqrt{2}\cdot3\sqrt{2}=6\), जो परिमेय है। परीक्षा में अपरिमेय संख्याओं के गुणनफल के लिए प्रतिउदाहरण याद रखें।
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कौन सा विकल्प (\sqrt{2}\times\(\sqrt{18}-\sqrt{8}\)) का मान है?
Which option is the value of (\sqrt{2}\times\(\sqrt{18}-\sqrt{8}\))?
#surds
#multiplication
#rational-result
A (2)
B (4)
C \(\sqrt{10}\)
D \(2\sqrt{2}\)
Explanation opens after your attempt
Step 1
Concept
\(\sqrt{18}=3\sqrt{2}\) and \(\sqrt{8}=2\sqrt{2}\), so the bracket is \(\sqrt{2}\). The product is (2).
Step 2
Why this answer is correct
The correct answer is A. (2). \(\sqrt{18}=3\sqrt{2}\) and \(\sqrt{8}=2\sqrt{2}\), so the bracket is \(\sqrt{2}\). The product is (2).
Step 3
Exam Tip
\(\sqrt{18}=3\sqrt{2}\) और \(\sqrt{8}=2\sqrt{2}\), इसलिए कोष्ठक \(\sqrt{2}\) है। गुणनफल (2) है।
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कौन सा विकल्प \(\frac{\sqrt{3}}{\sqrt{12}}\) का मान है?
Which option is the value of \(\frac{\sqrt{3}}{\sqrt{12}}\)?
#division
#square-root
#rational-result
A \(\frac{1}{2}\)
B (2)
C \(\frac{1}{4}\)
D \(\sqrt{9}\)
Explanation opens after your attempt
Correct Answer
A. \(\frac{1}{2}\)
Step 1
Concept
\(\frac{\sqrt{3}}{\sqrt{12}}=\sqrt{\frac{3}{12}}=\sqrt{\frac{1}{4}}=\frac{1}{2}\). Simplify the ratio inside the roots.
Step 2
Why this answer is correct
The correct answer is A. \(\frac{1}{2}\). \(\frac{\sqrt{3}}{\sqrt{12}}=\sqrt{\frac{3}{12}}=\sqrt{\frac{1}{4}}=\frac{1}{2}\). Simplify the ratio inside the roots.
Step 3
Exam Tip
\(\frac{\sqrt{3}}{\sqrt{12}}=\sqrt{\frac{3}{12}}=\sqrt{\frac{1}{4}}=\frac{1}{2}\) है। जड़ों के भाग में अनुपात सरल करें।
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यदि \(a=\sqrt{7}+\sqrt{2}\) और \(b=\sqrt{7}-\sqrt{2}\) हैं तो (ab) का मान क्या है?
If \(a=\sqrt{7}+\sqrt{2}\) and \(b=\sqrt{7}-\sqrt{2}\), what is the value of (ab)?
#conjugate
#product
#rational-result
A (5)
B (9)
C \(\sqrt{14}\)
D \(7+2\sqrt{2}\)
Explanation opens after your attempt
Step 1
Concept
In conjugate multiplication, (ab=7-2=5). The difference of squares formula gives the answer quickly.
Step 2
Why this answer is correct
The correct answer is A. (5). In conjugate multiplication, (ab=7-2=5). The difference of squares formula gives the answer quickly.
Step 3
Exam Tip
संयुग्मी गुणन में (ab=7-2=5) होता है। अंतर वर्ग सूत्र जल्दी उत्तर देता है।
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यदि \(z=\sqrt[3]{9}\) है तो \(z^3\) किस प्रकार की संख्या है?
If \(z=\sqrt[3]{9}\), what type of number is \(z^3\)?
#cube-root
#powers
#rational-result
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
Cubing gives \(z^3=9\). Even if (z) is irrational, its cube here is rational.
Step 2
Why this answer is correct
The correct answer is A. परिमेय संख्या / Rational number. Cubing gives \(z^3=9\). Even if (z) is irrational, its cube here is rational.
Step 3
Exam Tip
घन करने पर \(z^3=9\) मिलता है। भले (z) अपरिमेय हो, उसका घन यहाँ परिमेय है।
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कौन सा विकल्प \(\sqrt[3]{216}+\sqrt[3]{125}\) का मान है?
Which option is the value of \(\sqrt[3]{216}+\sqrt[3]{125}\)?
#cube-root
#perfect-cube
#rational-result
A (11)
B (341)
C \(\sqrt[3]{341}\)
D (30)
Explanation opens after your attempt
Step 1
Concept
\(\sqrt[3]{216}=6\) and \(\sqrt[3]{125}=5\). So the sum is (11).
Step 2
Why this answer is correct
The correct answer is A. (11). \(\sqrt[3]{216}=6\) and \(\sqrt[3]{125}=5\). So the sum is (11).
Step 3
Exam Tip
\(\sqrt[3]{216}=6\) और \(\sqrt[3]{125}=5\) है। इसलिए योग (11) है।
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कौन सा विकल्प \(\frac{\sqrt{98}-\sqrt{18}}{\sqrt{2}}\) का मान है?
Which option is the value of \(\frac{\sqrt{98}-\sqrt{18}}{\sqrt{2}}\)?
#surds
#division
#rational-result
A (4)
B \(2\sqrt{2}\)
C (8)
D \(\sqrt{80}\)
Explanation opens after your attempt
Step 1
Concept
\(\sqrt{98}=7\sqrt{2}\) and \(\sqrt{18}=3\sqrt{2}\). The numerator is \(4\sqrt{2}\), and division gives (4).
Step 2
Why this answer is correct
The correct answer is A. (4). \(\sqrt{98}=7\sqrt{2}\) and \(\sqrt{18}=3\sqrt{2}\). The numerator is \(4\sqrt{2}\), and division gives (4).
Step 3
Exam Tip
\(\sqrt{98}=7\sqrt{2}\) और \(\sqrt{18}=3\sqrt{2}\) है। अंश \(4\sqrt{2}\) है और भाग देने पर (4) मिलता है।
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कौन सा विकल्प \(4\sqrt{3}+3\sqrt{12}-2\sqrt{75}\) का मान है?
Which option is the value of \(4\sqrt{3}+3\sqrt{12}-2\sqrt{75}\)?
#surds
#simplification
#rational-result
A (0)
B \(6\sqrt{3}\)
C \(10\sqrt{3}\)
D \(2\sqrt{3}\)
Explanation opens after your attempt
Step 1
Concept
\(\sqrt{12}=2\sqrt{3}\) and \(\sqrt{75}=5\sqrt{3}\). So \(4\sqrt{3}+6\sqrt{3}-10\sqrt{3}=0\).
Step 2
Why this answer is correct
The correct answer is A. (0). \(\sqrt{12}=2\sqrt{3}\) and \(\sqrt{75}=5\sqrt{3}\). So \(4\sqrt{3}+6\sqrt{3}-10\sqrt{3}=0\).
Step 3
Exam Tip
\(\sqrt{12}=2\sqrt{3}\) और \(\sqrt{75}=5\sqrt{3}\) है। इसलिए \(4\sqrt{3}+6\sqrt{3}-10\sqrt{3}=0\) है।
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कौन सा विकल्प \(\frac{\sqrt{27}+\sqrt{12}}{\sqrt{3}}\) का मान है?
Which option is the value of \(\frac{\sqrt{27}+\sqrt{12}}{\sqrt{3}}\)?
#surds
#division
#rational-result
A (5)
B \(5\sqrt{3}\)
C \(\sqrt{39}\)
D \(3+\sqrt{12}\)
Explanation opens after your attempt
Step 1
Concept
\(\sqrt{27}=3\sqrt{3}\) and \(\sqrt{12}=2\sqrt{3}\), so the numerator is \(5\sqrt{3}\). Dividing gives (5).
Step 2
Why this answer is correct
The correct answer is A. (5). \(\sqrt{27}=3\sqrt{3}\) and \(\sqrt{12}=2\sqrt{3}\), so the numerator is \(5\sqrt{3}\). Dividing gives (5).
Step 3
Exam Tip
\(\sqrt{27}=3\sqrt{3}\) और \(\sqrt{12}=2\sqrt{3}\), इसलिए अंश \(5\sqrt{3}\) है। भाग देने पर (5) मिलता है।
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कौन सा विकल्प (\(\sqrt{13}+\sqrt{12}\)\(\sqrt{13}-\sqrt{12}\)) का मान है?
Which option is the value of (\(\sqrt{13}+\sqrt{12}\)\(\sqrt{13}-\sqrt{12}\))?
#conjugate
#identity
#rational-result
A (1)
B (25)
C \(\sqrt{156}\)
D \(13+\sqrt{12}\)
Explanation opens after your attempt
Step 1
Concept
By difference of squares the value is (13-12=1). Product of conjugate pairs often gives a rational number.
Step 2
Why this answer is correct
The correct answer is A. (1). By difference of squares the value is (13-12=1). Product of conjugate pairs often gives a rational number.
Step 3
Exam Tip
अंतर वर्ग सूत्र से मान (13-12=1) है। संयुग्मी जोड़े का गुणन अक्सर परिमेय देता है।
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यदि \(a=\sqrt{8}+\sqrt{18}\) है तो (a) का वर्ग किस प्रकार की संख्या है?
If \(a=\sqrt{8}+\sqrt{18}\), what type of number is \(a^2\)?
#surds
#square
#rational-result
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
\(\sqrt{8}=2\sqrt{2}\) and \(\sqrt{18}=3\sqrt{2}\), so \(a=5\sqrt{2}\). Its square is (50), a rational number.
Step 2
Why this answer is correct
The correct answer is A. परिमेय संख्या / Rational number. \(\sqrt{8}=2\sqrt{2}\) and \(\sqrt{18}=3\sqrt{2}\), so \(a=5\sqrt{2}\). Its square is (50), a rational number.
Step 3
Exam Tip
\(\sqrt{8}=2\sqrt{2}\) और \(\sqrt{18}=3\sqrt{2}\), इसलिए \(a=5\sqrt{2}\)। इसका वर्ग (50) परिमेय है।
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कौन सा विकल्प \(2\sqrt{12}-3\sqrt{27}+\sqrt{75}\) का सरल रूप है?
Which option is the simplified form of \(2\sqrt{12}-3\sqrt{27}+\sqrt{75}\)?
#surds
#addition-subtraction
#rational-result
A (0)
B \(4\sqrt{3}\)
C \(2\sqrt{3}\)
D \(10\sqrt{3}\)
Explanation opens after your attempt
Step 1
Concept
It becomes \(4\sqrt{3}-9\sqrt{3}+5\sqrt{3}=0\). First convert all roots to like radical form.
Step 2
Why this answer is correct
The correct answer is A. (0). It becomes \(4\sqrt{3}-9\sqrt{3}+5\sqrt{3}=0\). First convert all roots to like radical form.
Step 3
Exam Tip
यह \(4\sqrt{3}-9\sqrt{3}+5\sqrt{3}=0\) बनता है। पहले सभी जड़ों को समान रूप में बदलें।
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यदि \(x=\sqrt{5}+\sqrt{2}\) है तो \(x^2-2\sqrt{10}\) किस प्रकार की संख्या है?
If \(x=\sqrt{5}+\sqrt{2}\), what type of number is \(x^2-2\sqrt{10}\)?
#surds
#expression
#rational-result
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
Here \(x^2=7+2\sqrt{10}\), so subtracting gives (7). In such questions expand the square first.
Step 2
Why this answer is correct
The correct answer is A. परिमेय संख्या / Rational number. Here \(x^2=7+2\sqrt{10}\), so subtracting gives (7). In such questions expand the square first.
Step 3
Exam Tip
\(x^2=7+2\sqrt{10}\) इसलिए घटाने पर (7) मिलता है। ऐसे प्रश्नों में पहले वर्ग विस्तार करें।
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कौन सा विकल्प (\(\sqrt{15}+\sqrt{6}\)\(\sqrt{15}-\sqrt{6}\)) का मान है?
Which option is the value of (\(\sqrt{15}+\sqrt{6}\)\(\sqrt{15}-\sqrt{6}\))?
#conjugate
#identity
#rational-result
A (9)
B (21)
C \(\sqrt{90}\)
D \(15+6\sqrt{6}\)
Explanation opens after your attempt
Step 1
Concept
This is the difference of squares formula and the value is (15-6=9). In conjugate multiplication the irrational part cancels.
Step 2
Why this answer is correct
The correct answer is A. (9). This is the difference of squares formula and the value is (15-6=9). In conjugate multiplication the irrational part cancels.
Step 3
Exam Tip
यह अंतर वर्ग सूत्र है और मान (15-6=9) मिलता है। संयुग्मी गुणन में अपरिमेय भाग हट जाता है।
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कौन सा विकल्प (\(\sqrt{10}+\sqrt{5}\)\(\sqrt{10}-\sqrt{5}\)) का मान है?
Which option is the value of (\(\sqrt{10}+\sqrt{5}\)\(\sqrt{10}-\sqrt{5}\))?
#conjugate
#identity
#rational-result
A (5)
B (15)
C \(\sqrt{50}\)
D \(10+\sqrt{5}\)
Explanation opens after your attempt
Step 1
Concept
This is the difference of squares formula. The value is (10-5=5).
Step 2
Why this answer is correct
The correct answer is A. (5). This is the difference of squares formula. The value is (10-5=5).
Step 3
Exam Tip
यह अंतर वर्ग सूत्र है। मान (10-5=5) होगा।
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कौन सा विकल्प \(5\sqrt{11}-\sqrt{275}\) का मान है?
Which option is the value of \(5\sqrt{11}-\sqrt{275}\)?
#surds
#subtraction
#rational-result
A (0)
B \(10\sqrt{11}\)
C \(5\sqrt{264}\)
D \(\sqrt{11}\)
Explanation opens after your attempt
Step 1
Concept
\(\sqrt{275}=\sqrt{25\times11}=5\sqrt{11}\). Therefore the difference is (0).
Step 2
Why this answer is correct
The correct answer is A. (0). \(\sqrt{275}=\sqrt{25\times11}=5\sqrt{11}\). Therefore the difference is (0).
Step 3
Exam Tip
\(\sqrt{275}=\sqrt{25\times11}=5\sqrt{11}\) है। इसलिए अंतर (0) है।
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कौन सा विकल्प \(2+\sqrt{5}\) और \(2-\sqrt{5}\) के गुणनफल का मान है?
Which option is the value of the product of \(2+\sqrt{5}\) and \(2-\sqrt{5}\)?
#conjugate
#surds
#rational-result
A (-1)
B (1)
C \(4+\sqrt{5}\)
D \(4-\sqrt{5}\)
Explanation opens after your attempt
Step 1
Concept
(\(2+\sqrt{5}\)\(2-\sqrt{5}\)=4-5=-1). In conjugate multiplication the irrational part cancels.
Step 2
Why this answer is correct
The correct answer is A. (-1). (\(2+\sqrt{5}\)\(2-\sqrt{5}\)=4-5=-1). In conjugate multiplication the irrational part cancels.
Step 3
Exam Tip
(\(2+\sqrt{5}\)\(2-\sqrt{5}\)=4-5=-1) है। संयुग्मी गुणन में अपरिमेय भाग हट जाता है।
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कौन सा विकल्प \(3\sqrt{6}\times2\sqrt{6}\) का मान है?
Which option is the value of \(3\sqrt{6}\times2\sqrt{6}\)?
#surds
#multiplication
#rational-result
A (36)
B \(6\sqrt{6}\)
C \(36\sqrt{6}\)
D (12)
Explanation opens after your attempt
Step 1
Concept
\(3\sqrt{6}\times2\sqrt{6}=6\times6=36\). Multiplying same roots can give a rational result.
Step 2
Why this answer is correct
The correct answer is A. (36). \(3\sqrt{6}\times2\sqrt{6}=6\times6=36\). Multiplying same roots can give a rational result.
Step 3
Exam Tip
\(3\sqrt{6}\times2\sqrt{6}=6\times6=36\) है। समान जड़ का गुणन परिमेय परिणाम दे सकता है।
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कौन सा विकल्प \(\frac{\sqrt{147}}{\sqrt{3}}\) का मान है?
Which option is the value of \(\frac{\sqrt{147}}{\sqrt{3}}\)?
#division
#square-root
#rational-result
A (7)
B \(\sqrt{144}\)
C (49)
D \(7\sqrt{3}\)
Explanation opens after your attempt
Step 1
Concept
\(\frac{\sqrt{147}}{\sqrt{3}}=\sqrt{49}=7\). In division of roots simplify the quotient inside.
Step 2
Why this answer is correct
The correct answer is A. (7). \(\frac{\sqrt{147}}{\sqrt{3}}=\sqrt{49}=7\). In division of roots simplify the quotient inside.
Step 3
Exam Tip
\(\frac{\sqrt{147}}{\sqrt{3}}=\sqrt{49}=7\) है। जड़ों के भाग में अंदर का भागफल सरल करें।
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कौन सा विकल्प (\(\sqrt{5}+\sqrt{2}\)\(\sqrt{5}-\sqrt{2}\)) का मान है?
Which option is the value of (\(\sqrt{5}+\sqrt{2}\)\(\sqrt{5}-\sqrt{2}\))?
#conjugate
#surds
#rational-result
A (3)
B (7)
C \(\sqrt{10}\)
D \(5+2\sqrt{2}\)
Explanation opens after your attempt
Step 1
Concept
This is ((a+b)(a-b)=a-2 -b-2 ). The value is (5-2=3).
Step 2
Why this answer is correct
The correct answer is A. (3). This is ((a+b)(a-b)=a-2 -b-2 ). The value is (5-2=3).
Step 3
Exam Tip
यह ((a+b)(a-b)=a-2 -b-2 ) है। मान (5-2=3) मिलेगा।
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कौन सा विकल्प \(\sqrt{18}\times\sqrt{50}\) का मान है?
Which option is the value of \(\sqrt{18}\times\sqrt{50}\)?
#multiplication
#irrational-numbers
#rational-result
A (30)
B \(\sqrt{68}\)
C \(15\sqrt{2}\)
D \(50\sqrt{18}\)
Explanation opens after your attempt
Step 1
Concept
\(\sqrt{18}\times\sqrt{50}=\sqrt{900}=30\). The product of two irrational numbers can be rational.
Step 2
Why this answer is correct
The correct answer is A. (30). \(\sqrt{18}\times\sqrt{50}=\sqrt{900}=30\). The product of two irrational numbers can be rational.
Step 3
Exam Tip
\(\sqrt{18}\times\sqrt{50}=\sqrt{900}=30\) है। दो अपरिमेय संख्याओं का गुणनफल परिमेय हो सकता है।
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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
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 (\(4+\sqrt{7}\)\(4-\sqrt{7}\)) का मान है?
Which option is the value of (\(4+\sqrt{7}\)\(4-\sqrt{7}\))?
#conjugate
#surds
#rational-result
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 \(4\sqrt{7}-\sqrt{112}\) का मान है?
Which option is the value of \(4\sqrt{7}-\sqrt{112}\)?
#surds
#subtraction
#rational-result
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 \(1+\sqrt{7}\) 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
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 \(2\sqrt{5}\times3\sqrt{5}\) का मान है?
Which option is the value of \(2\sqrt{5}\times3\sqrt{5}\)?
#surds
#multiplication
#rational-result
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 \(\frac{\sqrt{80}}{\sqrt{5}}\) का मान है?
Which option is the value of \(\frac{\sqrt{80}}{\sqrt{5}}\)?
#division
#square-root
#rational-result
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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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
#surds
#rational-result
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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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
#rational-result
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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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
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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