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 \(p=2+\sqrt{3}\) है तो \(\frac{1}{p}\) किसके बराबर है?
If \(p=2+\sqrt{3}\), what is \(\frac{1}{p}\) equal to?
#reciprocal
#conjugate
#surds
A \(2-\sqrt{3}\)
B \(2+\sqrt{3}\)
C \(\sqrt{3}-2\)
D \(\frac{2-\sqrt{3}}{7}\)
Explanation opens after your attempt
Correct Answer
A. \(2-\sqrt{3}\)
Step 1
Concept
Since (\(2+\sqrt{3}\)\(2-\sqrt{3}\)=1), the reciprocal is \(2-\sqrt{3}\). Recognizing conjugates is a fast method.
Step 2
Why this answer is correct
The correct answer is A. \(2-\sqrt{3}\). Since (\(2+\sqrt{3}\)\(2-\sqrt{3}\)=1), the reciprocal is \(2-\sqrt{3}\). Recognizing conjugates is a fast method.
Step 3
Exam Tip
क्योंकि (\(2+\sqrt{3}\)\(2-\sqrt{3}\)=1), इसलिए व्युत्क्रम \(2-\sqrt{3}\) है। संयुग्मी को पहचानना तेज तरीका है।
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कौन सा विकल्प \(\frac{2}{\sqrt{7}-\sqrt{3}}\) का सरल रूप है?
Which option is the simplified form of \(\frac{2}{\sqrt{7}-\sqrt{3}}\)?
#rationalisation
#surds
#division
A \(\frac{\sqrt{7}+\sqrt{3}}{2}\)
B \(\sqrt{7}+\sqrt{3}\)
C \(\frac{\sqrt{7}-\sqrt{3}}{2}\)
D \(2\sqrt{7}-2\sqrt{3}\)
Explanation opens after your attempt
Correct Answer
A. \(\frac{\sqrt{7}+\sqrt{3}}{2}\)
Step 1
Concept
Multiplying by the conjugate makes the denominator (7-3=4). Hence we get (\frac{2\(\sqrt{7}+\sqrt{3}\)}{4}).
Step 2
Why this answer is correct
The correct answer is A. \(\frac{\sqrt{7}+\sqrt{3}}{2}\). Multiplying by the conjugate makes the denominator (7-3=4). Hence we get (\frac{2\(\sqrt{7}+\sqrt{3}\)}{4}).
Step 3
Exam Tip
संयुग्मी से गुणा करने पर हर (7-3=4) बनता है। इसलिए (\frac{2\(\sqrt{7}+\sqrt{3}\)}{4}) मिलता है।
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कौन सा विकल्प \(\frac{1}{3+\sqrt{5}}\) का परिमेय हर वाला रूप है?
Which option is the rationalized form of \(\frac{1}{3+\sqrt{5}}\)?
#rationalisation
#conjugate
#surds
A \(\frac{3-\sqrt{5}}{4}\)
B \(\frac{3+\sqrt{5}}{4}\)
C \(\frac{3-\sqrt{5}}{14}\)
D \(\frac{1}{4}\)
Explanation opens after your attempt
Correct Answer
A. \(\frac{3-\sqrt{5}}{4}\)
Step 1
Concept
The conjugate of the denominator is \(3-\sqrt{5}\) and the denominator becomes (9-5=4). Multiply by the conjugate to rationalize.
Step 2
Why this answer is correct
The correct answer is A. \(\frac{3-\sqrt{5}}{4}\). The conjugate of the denominator is \(3-\sqrt{5}\) and the denominator becomes (9-5=4). Multiply by the conjugate to rationalize.
Step 3
Exam Tip
हर का संयुग्मी \(3-\sqrt{5}\) है और हर (9-5=4) बनता है। परिमेयकरण में संयुग्मी से गुणा करें।
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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 (\(\sqrt{11}+\sqrt{5}\)2 -\(\sqrt{11}-\sqrt{5}\)2 ) का मान है?
Which option is the value of (\(\sqrt{11}+\sqrt{5}\)2 -\(\sqrt{11}-\sqrt{5}\)2 )?
#identity
#surds
#expansion
A \(4\sqrt{55}\)
B (16)
C \(2\sqrt{55}\)
D (55)
Explanation opens after your attempt
Correct Answer
A. \(4\sqrt{55}\)
Step 1
Concept
By identity the difference is (4ab), where \(a=\sqrt{11}\) and \(b=\sqrt{5}\). So the answer is \(4\sqrt{55}\).
Step 2
Why this answer is correct
The correct answer is A. \(4\sqrt{55}\). By identity the difference is (4ab), where \(a=\sqrt{11}\) and \(b=\sqrt{5}\). So the answer is \(4\sqrt{55}\).
Step 3
Exam Tip
सूत्र से अंतर (4ab) होता है जहाँ \(a=\sqrt{11}\) और \(b=\sqrt{5}\) हैं। इसलिए उत्तर \(4\sqrt{55}\) है।
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यदि \(a=3+\sqrt{7}\) और \(b=3-\sqrt{7}\) हैं तो \(a^2+b^2\) का मान क्या है?
If \(a=3+\sqrt{7}\) and \(b=3-\sqrt{7}\), what is the value of \(a^2+b^2\)?
#conjugate
#surds
#square-sum
A (32)
B (18)
C \(14\sqrt{7}\)
D \(16\sqrt{7}\)
Explanation opens after your attempt
Step 1
Concept
On adding the two squares the radical terms cancel and the result is (32). Identify cancelling terms in conjugates.
Step 2
Why this answer is correct
The correct answer is A. (32). On adding the two squares the radical terms cancel and the result is (32). Identify cancelling terms in conjugates.
Step 3
Exam Tip
दोनों वर्ग जोड़ने पर जड़ वाले पद कट जाते हैं और (32) मिलता है। संयुग्मी संख्याओं में कटने वाले पद पहचानें।
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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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यदि \(p=7+\sqrt{11}\) और \(q=7-\sqrt{11}\) हैं तो (pq) का मान क्या है?
If \(p=7+\sqrt{11}\) and \(q=7-\sqrt{11}\), what is the value of (pq)?
#conjugate
#surds
#product
A (38)
B (60)
C \(14\sqrt{11}\)
D \(49+\sqrt{11}\)
Explanation opens after your attempt
Step 1
Concept
Conjugate multiplication gives (pq=72 -\(\sqrt{11}\)2 =49-11=38). Use \(a^2-b^2\) in such questions.
Step 2
Why this answer is correct
The correct answer is A. (38). Conjugate multiplication gives (pq=72 -\(\sqrt{11}\)2 =49-11=38). Use \(a^2-b^2\) in such questions.
Step 3
Exam Tip
संयुग्मी गुणन से (pq=72 -\(\sqrt{11}\)2 =49-11=38) मिलता है। ऐसे प्रश्नों में \(a^2-b^2\) लगाएँ।
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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 \(\sqrt{3}+\sqrt{27}+\sqrt{75}\) का सरल रूप है?
Which option is the simplified form of \(\sqrt{3}+\sqrt{27}+\sqrt{75}\)?
#surds
#addition
#like-terms
A \(9\sqrt{3}\)
B \(6\sqrt{3}\)
C \(\sqrt{105}\)
D \(15\sqrt{3}\)
Explanation opens after your attempt
Correct Answer
A. \(9\sqrt{3}\)
Step 1
Concept
\(\sqrt{27}=3\sqrt{3}\) and \(\sqrt{75}=5\sqrt{3}\). The total is \(9\sqrt{3}\).
Step 2
Why this answer is correct
The correct answer is A. \(9\sqrt{3}\). \(\sqrt{27}=3\sqrt{3}\) and \(\sqrt{75}=5\sqrt{3}\). The total is \(9\sqrt{3}\).
Step 3
Exam Tip
\(\sqrt{27}=3\sqrt{3}\) और \(\sqrt{75}=5\sqrt{3}\) है। कुल \(9\sqrt{3}\) मिलता है।
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कौन सा विकल्प (\(2\sqrt{3}+1\)2 ) का सही विस्तार है?
Which option is the correct expansion of (\(2\sqrt{3}+1\)2 )?
#surds
#identity
#expansion
A \(13+4\sqrt{3}\)
B \(12+2\sqrt{3}\)
C \(7+4\sqrt{3}\)
D \(13+\sqrt{3}\)
Explanation opens after your attempt
Correct Answer
A. \(13+4\sqrt{3}\)
Step 1
Concept
(\(2\sqrt{3}+1\)2 =12+4\sqrt{3}+1=13+4\sqrt{3}). Always include the middle term (2ab).
Step 2
Why this answer is correct
The correct answer is A. \(13+4\sqrt{3}\). (\(2\sqrt{3}+1\)2 =12+4\sqrt{3}+1=13+4\sqrt{3}). Always include the middle term (2ab).
Step 3
Exam Tip
(\(2\sqrt{3}+1\)2 =12+4\sqrt{3}+1=13+4\sqrt{3}) है। बीच का पद (2ab) जरूर लगाएँ।
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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 \(5\sqrt{11}-\sqrt{275}\) 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 (\(\sqrt{7}-\sqrt{3}\)2 ) का सही विस्तार है?
Which option is the correct expansion of (\(\sqrt{7}-\sqrt{3}\)2 )?
#surds
#identity
#expansion
A \(10-2\sqrt{21}\)
B \(4-2\sqrt{21}\)
C \(10-\sqrt{21}\)
D \(7-2\sqrt{3}\)
Explanation opens after your attempt
Correct Answer
A. \(10-2\sqrt{21}\)
Step 1
Concept
(\(\sqrt{7}-\sqrt{3}\)2 =7+3-2\sqrt{21}). Apply the (2ab) term carefully in the square formula.
Step 2
Why this answer is correct
The correct answer is A. \(10-2\sqrt{21}\). (\(\sqrt{7}-\sqrt{3}\)2 =7+3-2\sqrt{21}). Apply the (2ab) term carefully in the square formula.
Step 3
Exam Tip
(\(\sqrt{7}-\sqrt{3}\)2 =7+3-2\sqrt{21}) है। वर्ग सूत्र में (2ab) पद सावधानी से लगाएँ।
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कौन सा विकल्प \(3+\sqrt{8}\) और \(3-\sqrt{8}\) के योग और गुणनफल को सही बताता है?
Which option correctly gives the sum and product of \(3+\sqrt{8}\) and \(3-\sqrt{8}\)?
#conjugate
#sum-product
#surds
A योग (6), गुणनफल (1) / Sum (6), product (1)
B योग (0), गुणनफल (9) / Sum (0), product (9)
C योग \(2\sqrt{8}\), गुणनफल (17) / Sum \(2\sqrt{8}\), product (17)
D योग (6), गुणनफल (17) / Sum (6), product (17)
Explanation opens after your attempt
Correct Answer
A. योग (6), गुणनफल (1) / Sum (6), product (1)
Step 1
Concept
The radical terms cancel in the sum and the product is (9-8=1). This method is quick for conjugates.
Step 2
Why this answer is correct
The correct answer is A. योग (6), गुणनफल (1) / Sum (6), product (1). The radical terms cancel in the sum and the product is (9-8=1). This method is quick for conjugates.
Step 3
Exam Tip
योग में जड़ वाले पद कटते हैं और गुणनफल (9-8=1) है। संयुग्मी संख्याओं में यह तरीका तेज 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 \(\sqrt{27}+\sqrt{75}-\sqrt{12}\) 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 \(3\sqrt{6}\times2\sqrt{6}\) 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 (\sqrt{2}\(5-\sqrt{2}\)) का मान है?
Which option is the value of (\sqrt{2}\(5-\sqrt{2}\))?
#surds
#distribution
#expression
A \(5\sqrt{2}-2\)
B \(3\sqrt{2}\)
C \(10-\sqrt{2}\)
D \(5-2\sqrt{2}\)
Explanation opens after your attempt
Correct Answer
A. \(5\sqrt{2}-2\)
Step 1
Concept
Distributing gives \(5\sqrt{2}-2\). Keep rational and irrational terms separate.
Step 2
Why this answer is correct
The correct answer is A. \(5\sqrt{2}-2\). Distributing gives \(5\sqrt{2}-2\). Keep rational and irrational terms separate.
Step 3
Exam Tip
वितरण करने पर \(5\sqrt{2}-2\) मिलता है। परिमेय और अपरिमेय पदों को अलग रखें।
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कौन सा विकल्प \(\frac{4}{\sqrt{2}}\) का सरल रूप है?
Which option is the simplified form of \(\frac{4}{\sqrt{2}}\)?
#rationalisation
#division
#surds
A \(2\sqrt{2}\)
B \(4\sqrt{2}\)
C \(\sqrt{2}\)
D (2)
Explanation opens after your attempt
Correct Answer
A. \(2\sqrt{2}\)
Step 1
Concept
\(\frac{4}{\sqrt{2}}=\frac{4\sqrt{2}}{2}=2\sqrt{2}\). Rationalise when a root is in the denominator.
Step 2
Why this answer is correct
The correct answer is A. \(2\sqrt{2}\). \(\frac{4}{\sqrt{2}}=\frac{4\sqrt{2}}{2}=2\sqrt{2}\). Rationalise when a root is in the denominator.
Step 3
Exam Tip
\(\frac{4}{\sqrt{2}}=\frac{4\sqrt{2}}{2}=2\sqrt{2}\) है। हर में जड़ हो तो परिमेयकरण करें।
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कौन सा विकल्प (\(\sqrt{3}+\sqrt{12}\)2 ) का मान है?
Which option is the value of (\(\sqrt{3}+\sqrt{12}\)2 )?
#surds
#square
#calculation
A (27)
B (15)
C \(9\sqrt{3}\)
D \(3+\sqrt{12}\)
Explanation opens after your attempt
Step 1
Concept
\(\sqrt{12}=2\sqrt{3}\), so the bracket becomes \(3\sqrt{3}\). Its square is (27).
Step 2
Why this answer is correct
The correct answer is A. (27). \(\sqrt{12}=2\sqrt{3}\), so the bracket becomes \(3\sqrt{3}\). Its square is (27).
Step 3
Exam Tip
\(\sqrt{12}=2\sqrt{3}\) इसलिए कोष्ठक \(3\sqrt{3}\) बनता है। उसका वर्ग (27) 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 (\(\sqrt{5}+\sqrt{2}\)\(\sqrt{5}-\sqrt{2}\)) 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 \(\sqrt{98}-\sqrt{8}\) 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 \(\sqrt{7}+\sqrt{63}\) का सरल रूप है?
Which option is the simplified form of \(\sqrt{7}+\sqrt{63}\)?
#surds
#addition
#like-terms
A \(4\sqrt{7}\)
B \(10\sqrt{7}\)
C \(\sqrt{70}\)
D \(3\sqrt{14}\)
Explanation opens after your attempt
Correct Answer
A. \(4\sqrt{7}\)
Step 1
Concept
\(\sqrt{63}=3\sqrt{7}\), so the sum is \(4\sqrt{7}\). Simplify roots first and then add like terms.
Step 2
Why this answer is correct
The correct answer is A. \(4\sqrt{7}\). \(\sqrt{63}=3\sqrt{7}\), so the sum is \(4\sqrt{7}\). Simplify roots first and then add like terms.
Step 3
Exam Tip
\(\sqrt{63}=3\sqrt{7}\) है इसलिए योग \(4\sqrt{7}\) है। पहले जड़ सरल करें फिर समान पद जोड़ें।
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