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 (\(\sqrt{6}+\sqrt{2}\)2 ) का सही विस्तार है?
Which option is the correct expansion of (\(\sqrt{6}+\sqrt{2}\)2 )?
#surds
#identity
#expansion
A \(8+4\sqrt{3}\)
B \(8+2\sqrt{3}\)
C \(4+4\sqrt{3}\)
D \(6+2\sqrt{2}\)
Explanation opens after your attempt
Correct Answer
A. \(8+4\sqrt{3}\)
Step 1
Concept
(\(\sqrt{6}+\sqrt{2}\)2 =6+2+2\sqrt{12}=8+4\sqrt{3}). Apply the (2ab) term correctly.
Step 2
Why this answer is correct
The correct answer is A. \(8+4\sqrt{3}\). (\(\sqrt{6}+\sqrt{2}\)2 =6+2+2\sqrt{12}=8+4\sqrt{3}). Apply the (2ab) term correctly.
Step 3
Exam Tip
(\(\sqrt{6}+\sqrt{2}\)2 =6+2+2\sqrt{12}=8+4\sqrt{3}) है। वर्ग सूत्र में (2ab) पद सही लगाएँ।
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यदि \(x=2+\sqrt{10}\) और \(y=2-\sqrt{10}\) हैं तो (x-y) का सरल रूप क्या है?
If \(x=2+\sqrt{10}\) and \(y=2-\sqrt{10}\), what is the simplified form of (x-y)?
#surds
#subtraction
#expression
A \(2\sqrt{10}\)
B (4)
C (0)
D (10)
Explanation opens after your attempt
Correct Answer
A. \(2\sqrt{10}\)
Step 1
Concept
On subtracting, the (2) terms cancel and (\sqrt{10}-\(-\sqrt{10}\)=2\sqrt{10}). Watch the signs carefully.
Step 2
Why this answer is correct
The correct answer is A. \(2\sqrt{10}\). On subtracting, the (2) terms cancel and (\sqrt{10}-\(-\sqrt{10}\)=2\sqrt{10}). Watch the signs carefully.
Step 3
Exam Tip
घटाने पर (2) पद कटते हैं और (\sqrt{10}-\(-\sqrt{10}\)=2\sqrt{10}) मिलता है। चिह्नों का ध्यान रखें।
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कौन सा विकल्प \(\sqrt{72}+\sqrt{128}-\sqrt{50}\) 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 (\(4+\sqrt{7}\)\(4-\sqrt{7}\)) 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 \(\sqrt{245}\) 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 \(4\sqrt{7}-\sqrt{112}\) 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 (\(\sqrt{5}-\sqrt{2}\)2 ) का सही विस्तार है?
Which option is the correct expansion of (\(\sqrt{5}-\sqrt{2}\)2 )?
#surds
#identity
#expansion
A \(7-2\sqrt{10}\)
B \(3-2\sqrt{10}\)
C \(7-\sqrt{10}\)
D \(5-2\sqrt{2}\)
Explanation opens after your attempt
Correct Answer
A. \(7-2\sqrt{10}\)
Step 1
Concept
(\(\sqrt{5}-\sqrt{2}\)2 =5+2-2\sqrt{10}). Apply the (2ab) term carefully in the square formula.
Step 2
Why this answer is correct
The correct answer is A. \(7-2\sqrt{10}\). (\(\sqrt{5}-\sqrt{2}\)2 =5+2-2\sqrt{10}). Apply the (2ab) term carefully in the square formula.
Step 3
Exam Tip
(\(\sqrt{5}-\sqrt{2}\)2 =5+2-2\sqrt{10}) है। वर्ग सूत्र में (2ab) पद ध्यान से लगाएँ।
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कौन सा विकल्प \(2+\sqrt{3}\) और \(2-\sqrt{3}\) के योग और गुणनफल को सही बताता है?
Which option correctly gives the sum and product of \(2+\sqrt{3}\) and \(2-\sqrt{3}\)?
#conjugate
#sum-product
#surds
A योग (4), गुणनफल (1) / Sum (4), product (1)
B योग (0), गुणनफल (4) / Sum (0), product (4)
C योग \(2\sqrt{3}\), गुणनफल (7) / Sum \(2\sqrt{3}\), product (7)
D योग (4), गुणनफल (7) / Sum (4), product (7)
Explanation opens after your attempt
Correct Answer
A. योग (4), गुणनफल (1) / Sum (4), product (1)
Step 1
Concept
The radical terms cancel in the sum and the product is (4-3=1). This method is quick for conjugates.
Step 2
Why this answer is correct
The correct answer is A. योग (4), गुणनफल (1) / Sum (4), product (1). The radical terms cancel in the sum and the product is (4-3=1). This method is quick for conjugates.
Step 3
Exam Tip
योग में जड़ वाले पद कटते हैं और गुणनफल (4-3=1) है। संयुग्मी संख्याओं में यह तरीका तेज है।
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कौन सा विकल्प \(\sqrt{48}+\sqrt{108}-\sqrt{12}\) 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 \(1+\sqrt{7}\) 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 \(\sqrt{200}\) 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 \(2\sqrt{5}\times3\sqrt{5}\) 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 (\sqrt{3}\(4+\sqrt{3}\)) का मान है?
Which option is the value of (\sqrt{3}\(4+\sqrt{3}\))?
#surds
#distribution
#expression
A \(3+4\sqrt{3}\)
B \(7\sqrt{3}\)
C \(12+\sqrt{3}\)
D \(4+3\sqrt{3}\)
Explanation opens after your attempt
Correct Answer
A. \(3+4\sqrt{3}\)
Step 1
Concept
Distributing gives \(4\sqrt{3}+3\). Keep rational and irrational terms separate.
Step 2
Why this answer is correct
The correct answer is A. \(3+4\sqrt{3}\). Distributing gives \(4\sqrt{3}+3\). Keep rational and irrational terms separate.
Step 3
Exam Tip
वितरण करने पर \(4\sqrt{3}+3\) मिलता है। परिमेय और अपरिमेय पद अलग रखें।
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कौन सा विकल्प (\(3+\sqrt{2}\)2 ) का सही विस्तार है?
Which option is the correct expansion of (\(3+\sqrt{2}\)2 )?
#surds
#identity
#expansion
A \(11+6\sqrt{2}\)
B \(9+3\sqrt{2}\)
C \(11+3\sqrt{2}\)
D \(7+6\sqrt{2}\)
Explanation opens after your attempt
Correct Answer
A. \(11+6\sqrt{2}\)
Step 1
Concept
(\(3+\sqrt{2}\)2 =9+6\sqrt{2}+2=11+6\sqrt{2}). Do not miss the middle term in the square formula.
Step 2
Why this answer is correct
The correct answer is A. \(11+6\sqrt{2}\). (\(3+\sqrt{2}\)2 =9+6\sqrt{2}+2=11+6\sqrt{2}). Do not miss the middle term in the square formula.
Step 3
Exam Tip
(\(3+\sqrt{2}\)2 =9+6\sqrt{2}+2=11+6\sqrt{2}) है। वर्ग सूत्र में बीच का पद न छोड़ें।
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कौन सा विकल्प (\(\sqrt{11}+2\)\(\sqrt{11}-2\)) का मान है?
Which option is the value of (\(\sqrt{11}+2\)\(\sqrt{11}-2\))?
#identity
#conjugate
#surds
A (7)
B (13)
C \(\sqrt{11}\)
D \(11+2\sqrt{11}\)
Explanation opens after your attempt
Step 1
Concept
This is ((a+b)(a-b)=a-2 -b-2 ). The value is (11-4=7).
Step 2
Why this answer is correct
The correct answer is A. (7). This is ((a+b)(a-b)=a-2 -b-2 ). The value is (11-4=7).
Step 3
Exam Tip
यह ((a+b)(a-b)=a-2 -b-2 ) है। मान (11-4=7) होगा।
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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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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 \(\sqrt{125}+\sqrt{45}\) का सरल रूप है?
Which option is the simplified form of \(\sqrt{125}+\sqrt{45}\)?
#surds
#addition
#like-terms
A \(8\sqrt{5}\)
B \(10\sqrt{5}\)
C \(\sqrt{170}\)
D \(6\sqrt{10}\)
Explanation opens after your attempt
Correct Answer
A. \(8\sqrt{5}\)
Step 1
Concept
\(\sqrt{125}=5\sqrt{5}\) and \(\sqrt{45}=3\sqrt{5}\). Adding like terms gives \(8\sqrt{5}\).
Step 2
Why this answer is correct
The correct answer is A. \(8\sqrt{5}\). \(\sqrt{125}=5\sqrt{5}\) and \(\sqrt{45}=3\sqrt{5}\). Adding like terms gives \(8\sqrt{5}\).
Step 3
Exam Tip
\(\sqrt{125}=5\sqrt{5}\) और \(\sqrt{45}=3\sqrt{5}\) है। समान पद जोड़ने पर \(8\sqrt{5}\) मिलता है।
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कौन सा विकल्प \(\sqrt{180}\) 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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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
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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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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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 \(4\sqrt{3}-\sqrt{27}\) का मान है?
Which option is the value of \(4\sqrt{3}-\sqrt{27}\)?
#surds
#subtraction
#like-terms
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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