कौन सा विकल्प (\(\sqrt{20}-\sqrt{5}\)2 ) का मान है?
Which option is the value of (\(\sqrt{20}-\sqrt{5}\)2 )?
#surds
#square
#simplification
A (5)
B (15)
C (25)
D \(5\sqrt{5}\)
Explanation opens after your attempt
Step 1
Concept
\(\sqrt{20}=2\sqrt{5}\), so the bracket becomes \(\sqrt{5}\). Its square is (5).
Step 2
Why this answer is correct
The correct answer is A. (5). \(\sqrt{20}=2\sqrt{5}\), so the bracket becomes \(\sqrt{5}\). Its square is (5).
Step 3
Exam Tip
\(\sqrt{20}=2\sqrt{5}\), इसलिए कोष्ठक \(\sqrt{5}\) बनता है। उसका वर्ग (5) है।
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कौन सा विकल्प (\(\sqrt{2}+\sqrt{5}+\sqrt{8}\)) का सरल रूप है?
Which option is the simplified form of (\(\sqrt{2}+\sqrt{5}+\sqrt{8}\))?
#surds
#simplification
#unlike-terms
A \(3\sqrt{2}+\sqrt{5}\)
B \(\sqrt{15}\)
C \(4\sqrt{2}\)
D \(3\sqrt{7}\)
Explanation opens after your attempt
Correct Answer
A. \(3\sqrt{2}+\sqrt{5}\)
Step 1
Concept
\(\sqrt{8}=2\sqrt{2}\), so \(\sqrt{2}+\sqrt{8}=3\sqrt{2}\). The unlike root \(\sqrt{5}\) remains separate.
Step 2
Why this answer is correct
The correct answer is A. \(3\sqrt{2}+\sqrt{5}\). \(\sqrt{8}=2\sqrt{2}\), so \(\sqrt{2}+\sqrt{8}=3\sqrt{2}\). The unlike root \(\sqrt{5}\) remains separate.
Step 3
Exam Tip
\(\sqrt{8}=2\sqrt{2}\) इसलिए \(\sqrt{2}+\sqrt{8}=3\sqrt{2}\) होता है। असमान जड़ \(\sqrt{5}\) अलग रहती है।
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कौन सा विकल्प \(\sqrt{12}+\sqrt{27}+\sqrt{75}-\sqrt{48}\) का सरल रूप है?
Which option is the simplified form of \(\sqrt{12}+\sqrt{27}+\sqrt{75}-\sqrt{48}\)?
#surds
#addition-subtraction
#simplification
A \(6\sqrt{3}\)
B \(14\sqrt{3}\)
C \(\sqrt{66}\)
D \(2\sqrt{3}\)
Explanation opens after your attempt
Correct Answer
A. \(6\sqrt{3}\)
Step 1
Concept
It is \(2\sqrt{3}+3\sqrt{3}+5\sqrt{3}-4\sqrt{3}=6\sqrt{3}\). Add like radical terms.
Step 2
Why this answer is correct
The correct answer is A. \(6\sqrt{3}\). It is \(2\sqrt{3}+3\sqrt{3}+5\sqrt{3}-4\sqrt{3}=6\sqrt{3}\). Add like radical terms.
Step 3
Exam Tip
यह \(2\sqrt{3}+3\sqrt{3}+5\sqrt{3}-4\sqrt{3}=6\sqrt{3}\) है। समान जड़ वाले पद जोड़ें।
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कौन सा विकल्प बताता है कि \(\sqrt{2}+\sqrt{8}\) अपरिमेय है?
Which option shows that \(\sqrt{2}+\sqrt{8}\) is irrational?
#surds
#irrational-proof
#simplification
A यह \(3\sqrt{2}\) है / It is \(3\sqrt{2}\)
B यह \(\sqrt{10}\) है / It is \(\sqrt{10}\)
C यह (10) है / It is (10)
D यह \(2\sqrt{8}\) है / It is \(2\sqrt{8}\)
Explanation opens after your attempt
Correct Answer
A. यह \(3\sqrt{2}\) है / It is \(3\sqrt{2}\)
Step 1
Concept
\(\sqrt{8}=2\sqrt{2}\), so the sum is \(3\sqrt{2}\). A non zero rational multiple of \(\sqrt{2}\) remains irrational.
Step 2
Why this answer is correct
The correct answer is A. यह \(3\sqrt{2}\) है / It is \(3\sqrt{2}\). \(\sqrt{8}=2\sqrt{2}\), so the sum is \(3\sqrt{2}\). A non zero rational multiple of \(\sqrt{2}\) remains irrational.
Step 3
Exam Tip
\(\sqrt{8}=2\sqrt{2}\), इसलिए योग \(3\sqrt{2}\) है। गैर शून्य परिमेय गुणक के साथ \(\sqrt{2}\) अपरिमेय रहता 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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यदि \(r=\sqrt{2}+\sqrt{3}\) है तो \(r+\frac{1}{r}\) का सरल रूप क्या है?
If \(r=\sqrt{2}+\sqrt{3}\), what is the simplified form of \(r+\frac{1}{r}\)?
#reciprocal
#conjugate
#simplification
A \(2\sqrt{3}\)
B \(2\sqrt{2}\)
C \(\sqrt{5}\)
D (5)
Explanation opens after your attempt
Correct Answer
A. \(2\sqrt{3}\)
Step 1
Concept
\(\frac{1}{\sqrt{2}+\sqrt{3}}=\sqrt{3}-\sqrt{2}\). Adding gives \(2\sqrt{3}\).
Step 2
Why this answer is correct
The correct answer is A. \(2\sqrt{3}\). \(\frac{1}{\sqrt{2}+\sqrt{3}}=\sqrt{3}-\sqrt{2}\). Adding gives \(2\sqrt{3}\).
Step 3
Exam Tip
\(\frac{1}{\sqrt{2}+\sqrt{3}}=\sqrt{3}-\sqrt{2}\) होता है। जोड़ने पर \(2\sqrt{3}\) मिलता है।
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यदि \(y=\sqrt{18}+\sqrt{50}-\sqrt{8}\) है तो \(y^2\) का मान क्या है?
If \(y=\sqrt{18}+\sqrt{50}-\sqrt{8}\), what is the value of \(y^2\)?
#surds
#simplification
#square
A (72)
B (36)
C \(18\sqrt{2}\)
D \(8\sqrt{2}\)
Explanation opens after your attempt
Step 1
Concept
\(\sqrt{18}=3\sqrt{2}\), \(\sqrt{50}=5\sqrt{2}\), and \(\sqrt{8}=2\sqrt{2}\), so \(y=6\sqrt{2}\). Its square is (72).
Step 2
Why this answer is correct
The correct answer is A. (72). \(\sqrt{18}=3\sqrt{2}\), \(\sqrt{50}=5\sqrt{2}\), and \(\sqrt{8}=2\sqrt{2}\), so \(y=6\sqrt{2}\). Its square is (72).
Step 3
Exam Tip
\(\sqrt{18}=3\sqrt{2}\), \(\sqrt{50}=5\sqrt{2}\) और \(\sqrt{8}=2\sqrt{2}\), इसलिए \(y=6\sqrt{2}\)। वर्ग (72) होगा।
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कौन सा विकल्प \(\sqrt{243}+\sqrt{147}-\sqrt{75}\) का सरल रूप है?
Which option is the simplified form of \(\sqrt{243}+\sqrt{147}-\sqrt{75}\)?
#surds
#addition-subtraction
#simplification
A \(11\sqrt{3}\)
B \(21\sqrt{3}\)
C \(\sqrt{315}\)
D \(5\sqrt{7}\)
Explanation opens after your attempt
Correct Answer
A. \(11\sqrt{3}\)
Step 1
Concept
\(\sqrt{243}=9\sqrt{3}\), \(\sqrt{147}=7\sqrt{3}\), and \(\sqrt{75}=5\sqrt{3}\). The result is \(11\sqrt{3}\).
Step 2
Why this answer is correct
The correct answer is A. \(11\sqrt{3}\). \(\sqrt{243}=9\sqrt{3}\), \(\sqrt{147}=7\sqrt{3}\), and \(\sqrt{75}=5\sqrt{3}\). The result is \(11\sqrt{3}\).
Step 3
Exam Tip
\(\sqrt{243}=9\sqrt{3}\), \(\sqrt{147}=7\sqrt{3}\) और \(\sqrt{75}=5\sqrt{3}\) है। परिणाम \(11\sqrt{3}\) है।
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कौन सा विकल्प \(\sqrt{363}\) का सरल रूप है?
Which option is the simplified form of \(\sqrt{363}\)?
#surds
#simplification
#square-root
A \(11\sqrt{3}\)
B \(3\sqrt{11}\)
C \(33\sqrt{3}\)
D \(\sqrt{121}\)
Explanation opens after your attempt
Correct Answer
A. \(11\sqrt{3}\)
Step 1
Concept
\(\sqrt{363}=\sqrt{121\times3}=11\sqrt{3}\). Look for a perfect square factor inside the root.
Step 2
Why this answer is correct
The correct answer is A. \(11\sqrt{3}\). \(\sqrt{363}=\sqrt{121\times3}=11\sqrt{3}\). Look for a perfect square factor inside the root.
Step 3
Exam Tip
\(\sqrt{363}=\sqrt{121\times3}=11\sqrt{3}\) है। जड़ में पूर्ण वर्ग गुणनखंड खोजें।
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कौन सा विकल्प \(\sqrt{242}+\sqrt{128}-\sqrt{72}\) का सरल रूप है?
Which option is the simplified form of \(\sqrt{242}+\sqrt{128}-\sqrt{72}\)?
#surds
#addition-subtraction
#simplification
A \(13\sqrt{2}\)
B \(25\sqrt{2}\)
C \(\sqrt{298}\)
D \(7\sqrt{2}\)
Explanation opens after your attempt
Correct Answer
A. \(13\sqrt{2}\)
Step 1
Concept
\(\sqrt{242}=11\sqrt{2}\), \(\sqrt{128}=8\sqrt{2}\), and \(\sqrt{72}=6\sqrt{2}\). The result is \(13\sqrt{2}\).
Step 2
Why this answer is correct
The correct answer is A. \(13\sqrt{2}\). \(\sqrt{242}=11\sqrt{2}\), \(\sqrt{128}=8\sqrt{2}\), and \(\sqrt{72}=6\sqrt{2}\). The result is \(13\sqrt{2}\).
Step 3
Exam Tip
\(\sqrt{242}=11\sqrt{2}\), \(\sqrt{128}=8\sqrt{2}\) और \(\sqrt{72}=6\sqrt{2}\) है। परिणाम \(13\sqrt{2}\) है।
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कौन सा विकल्प \(\sqrt{432}\) का सरल रूप है?
Which option is the simplified form of \(\sqrt{432}\)?
#surds
#simplification
#square-root
A \(12\sqrt{3}\)
B \(24\sqrt{3}\)
C \(6\sqrt{12}\)
D \(3\sqrt{144}\)
Explanation opens after your attempt
Correct Answer
A. \(12\sqrt{3}\)
Step 1
Concept
\(\sqrt{432}=\sqrt{144\times3}=12\sqrt{3}\). Take out the large perfect square.
Step 2
Why this answer is correct
The correct answer is A. \(12\sqrt{3}\). \(\sqrt{432}=\sqrt{144\times3}=12\sqrt{3}\). Take out the large perfect square.
Step 3
Exam Tip
\(\sqrt{432}=\sqrt{144\times3}=12\sqrt{3}\) है। बड़े पूर्ण वर्ग को बाहर निकालें।
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कौन सा विकल्प \(\sqrt{27}+\sqrt{75}-\sqrt{12}\) का सरल रूप है?
Which option is the simplified form of \(\sqrt{27}+\sqrt{75}-\sqrt{12}\)?
#surds
#addition-subtraction
#simplification
A \(6\sqrt{3}\)
B \(10\sqrt{3}\)
C \(\sqrt{90}\)
D \(4\sqrt{3}\)
Explanation opens after your attempt
Correct Answer
A. \(6\sqrt{3}\)
Step 1
Concept
\(\sqrt{27}=3\sqrt{3}\), \(\sqrt{75}=5\sqrt{3}\), and \(\sqrt{12}=2\sqrt{3}\). The result is \(6\sqrt{3}\).
Step 2
Why this answer is correct
The correct answer is A. \(6\sqrt{3}\). \(\sqrt{27}=3\sqrt{3}\), \(\sqrt{75}=5\sqrt{3}\), and \(\sqrt{12}=2\sqrt{3}\). The result is \(6\sqrt{3}\).
Step 3
Exam Tip
\(\sqrt{27}=3\sqrt{3}\), \(\sqrt{75}=5\sqrt{3}\) और \(\sqrt{12}=2\sqrt{3}\) है। परिणाम \(6\sqrt{3}\) है।
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कौन सा विकल्प \(\sqrt{75}+\sqrt{108}-\sqrt{48}\) का सरल रूप है?
Which option is the simplified form of \(\sqrt{75}+\sqrt{108}-\sqrt{48}\)?
#surds
#addition-subtraction
#simplification
A \(5\sqrt{3}\)
B \(15\sqrt{3}\)
C \(\sqrt{135}\)
D \(3\sqrt{5}\)
Explanation opens after your attempt
Correct Answer
A. \(5\sqrt{3}\)
Step 1
Concept
\(\sqrt{75}=5\sqrt{3}\), \(\sqrt{108}=6\sqrt{3}\), and \(\sqrt{48}=4\sqrt{3}\). The result is \(7\sqrt{3}\), so check option values carefully.
Step 2
Why this answer is correct
The correct answer is A. \(5\sqrt{3}\). \(\sqrt{75}=5\sqrt{3}\), \(\sqrt{108}=6\sqrt{3}\), and \(\sqrt{48}=4\sqrt{3}\). The result is \(7\sqrt{3}\), so check option values carefully.
Step 3
Exam Tip
\(\sqrt{75}=5\sqrt{3}\), \(\sqrt{108}=6\sqrt{3}\) और \(\sqrt{48}=4\sqrt{3}\) है। परिणाम \(7\sqrt{3}\) नहीं बल्कि \(5+6-4=7\sqrt{3}\) होगा।
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कौन सा विकल्प \(6\sqrt{3}-2\sqrt{3}+\sqrt{3}\) का सरल रूप है?
Which option is the simplified form of \(6\sqrt{3}-2\sqrt{3}+\sqrt{3}\)?
#surds
#like-terms
#simplification
A \(5\sqrt{3}\)
B \(9\sqrt{3}\)
C \(5\sqrt{9}\)
D \(\sqrt{15}\)
Explanation opens after your attempt
Correct Answer
A. \(5\sqrt{3}\)
Step 1
Concept
The coefficients of like radical terms are (6-2+1=5). So the answer is \(5\sqrt{3}\).
Step 2
Why this answer is correct
The correct answer is A. \(5\sqrt{3}\). The coefficients of like radical terms are (6-2+1=5). So the answer is \(5\sqrt{3}\).
Step 3
Exam Tip
समान जड़ वाले पदों के गुणांक (6-2+1=5) बनते हैं। इसलिए उत्तर \(5\sqrt{3}\) है।
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कौन सा विकल्प \(2\sqrt{3}+\sqrt{12}\) का सरल रूप है?
Which option is the simplified form of \(2\sqrt{3}+\sqrt{12}\)?
#surds
#addition
#simplification
A \(4\sqrt{3}\)
B \(3\sqrt{5}\)
C \(2\sqrt{15}\)
D \(6\sqrt{3}\)
Explanation opens after your attempt
Correct Answer
A. \(4\sqrt{3}\)
Step 1
Concept
\(\sqrt{12}=2\sqrt{3}\). So \(2\sqrt{3}+2\sqrt{3}=4\sqrt{3}\).
Step 2
Why this answer is correct
The correct answer is A. \(4\sqrt{3}\). \(\sqrt{12}=2\sqrt{3}\). So \(2\sqrt{3}+2\sqrt{3}=4\sqrt{3}\).
Step 3
Exam Tip
\(\sqrt{12}=2\sqrt{3}\) है। इसलिए \(2\sqrt{3}+2\sqrt{3}=4\sqrt{3}\) होगा।
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कौन सा विकल्प \(\sqrt{98}-\sqrt{8}\) का सरल रूप है?
Which option is the simplified form of \(\sqrt{98}-\sqrt{8}\)?
#surds
#subtraction
#simplification
A \(5\sqrt{2}\)
B \(9\sqrt{2}\)
C \(\sqrt{90}\)
D \(3\sqrt{2}\)
Explanation opens after your attempt
Correct Answer
A. \(5\sqrt{2}\)
Step 1
Concept
\(\sqrt{98}=7\sqrt{2}\) and \(\sqrt{8}=2\sqrt{2}\). Their difference is \(5\sqrt{2}\).
Step 2
Why this answer is correct
The correct answer is A. \(5\sqrt{2}\). \(\sqrt{98}=7\sqrt{2}\) and \(\sqrt{8}=2\sqrt{2}\). Their difference is \(5\sqrt{2}\).
Step 3
Exam Tip
\(\sqrt{98}=7\sqrt{2}\) और \(\sqrt{8}=2\sqrt{2}\) है। अंतर \(5\sqrt{2}\) है।
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कौन सा विकल्प \(\sqrt{288}\) का सरल रूप है?
Which option is the simplified form of \(\sqrt{288}\)?
#surds
#simplification
#square-root
A \(12\sqrt{2}\)
B \(24\sqrt{2}\)
C \(8\sqrt{3}\)
D \(2\sqrt{144}\)
Explanation opens after your attempt
Correct Answer
A. \(12\sqrt{2}\)
Step 1
Concept
\(\sqrt{288}=\sqrt{144\times2}=12\sqrt{2}\). Take out the greatest perfect square.
Step 2
Why this answer is correct
The correct answer is A. \(12\sqrt{2}\). \(\sqrt{288}=\sqrt{144\times2}=12\sqrt{2}\). Take out the greatest perfect square.
Step 3
Exam Tip
\(\sqrt{288}=\sqrt{144\times2}=12\sqrt{2}\) है। सबसे बड़ा पूर्ण वर्ग बाहर निकालें।
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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
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 \(\sqrt{245}\) का सरल रूप है?
Which option is the simplified form of \(\sqrt{245}\)?
#surds
#simplification
#square-root
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 \(\sqrt{48}+\sqrt{108}-\sqrt{12}\) का सरल रूप है?
Which option is the simplified form of \(\sqrt{48}+\sqrt{108}-\sqrt{12}\)?
#surds
#addition-subtraction
#simplification
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 \(\sqrt{200}\) का सही सरल रूप है?
Which option is the correct simplified form of \(\sqrt{200}\)?
#surds
#simplification
#square-root
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 \(\sqrt{50}+\sqrt{72}-\sqrt{32}\) का सरल रूप है?
Which option is the simplified form of \(\sqrt{50}+\sqrt{72}-\sqrt{32}\)?
#surds
#addition-subtraction
#simplification
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 \(5\sqrt{2}+3\sqrt{2}-\sqrt{2}\) का सरल रूप है?
Which option is the simplified form of \(5\sqrt{2}+3\sqrt{2}-\sqrt{2}\)?
#surds
#like-terms
#simplification
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 \(\sqrt{192}-\sqrt{27}\) का सरल रूप है?
Which option is the simplified form of \(\sqrt{192}-\sqrt{27}\)?
#surds
#subtraction
#simplification
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 \(\sqrt{180}\) का सरल रूप है?
Which option is the simplified form of \(\sqrt{180}\)?
#surds
#simplification
#square-root
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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कौन सा विकल्प \(\sqrt{300}\) का सरल रूप है?
Which option is the simplified form of \(\sqrt{300}\)?
#surds
#simplification
#square-root
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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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
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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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
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 \(\sqrt{162}\) का सरल रूप है?
Which option is the simplified form of \(\sqrt{162}\)?
#surds
#simplification
#square-root
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 \(\sqrt{128}\) का सरल रूप है?
Which option is the simplified form of \(\sqrt{128}\)?
#surds
#simplification
#square-root
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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