यदि \(x=4+\sqrt{6}\), तो (x-4) की प्रकृति क्या होगी?
If \(x=4+\sqrt{6}\), what will be the nature of (x-4)?
#irrational expression
#simplification
#class 10
A परिमेय / Rational
B अपरिमेय / Irrational
C पूर्णांक / Integer
D सांत दशमलव / Terminating decimal
Explanation opens after your attempt
Correct Answer
B. अपरिमेय / Irrational
Step 1
Concept
(x-4=\(4+\sqrt{6}\)-4) है। / (x-4=\(4+\sqrt{6}\)-4).
Step 2
Why this answer is correct
सरल करने पर \(x-4=\sqrt{6}\), और (6) पूर्ण वर्ग नहीं है, इसलिए \(\sqrt{6}\) अपरिमेय है। / On simplifying, \(x-4=\sqrt{6}\), and since (6) is not a perfect square, \(\sqrt{6}\) is irrational.
Step 3
Exam Tip
व्यंजक में परिमेय पद कट जाए तो बचे हुए मूल की प्रकृति देखें। / When rational terms cancel, check the nature of the remaining radical.
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यदि \(a=\sqrt{2}+\sqrt{8}\), तो (a) किस प्रकार की संख्या है?
If \(a=\sqrt{2}+\sqrt{8}\), what type of number is (a)?
#surds
#simplification
#irrational numbers
#class 10
A परिमेय / Rational
B अपरिमेय / Irrational
C पूर्णांक / Integer
D प्राकृतिक संख्या / Natural number
Explanation opens after your attempt
Correct Answer
B. अपरिमेय / Irrational
Step 1
Concept
\(\sqrt{8}=2\sqrt{2}\) होता है। / \(\sqrt{8}=2\sqrt{2}\).
Step 2
Why this answer is correct
इसलिए \(a=\sqrt{2}+2\sqrt{2}=3\sqrt{2}\), और \(\sqrt{2}\) अपरिमेय है। / So \(a=\sqrt{2}+2\sqrt{2}=3\sqrt{2}\), and \(\sqrt{2}\) is irrational.
Step 3
Exam Tip
समान मूल वाले पदों को पहले सरल करें। / Simplify like radical terms before deciding the type of number.
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\(\sqrt{242}+\sqrt{98}-\sqrt{32}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{242}+\sqrt{98}-\sqrt{32}\)?
#real-numbers
#radical-expression
#simplification
A \(14\sqrt{2}\)
B \(13\sqrt{2}\)
C \(12\sqrt{2}\)
D \(\sqrt{308}\)
Explanation opens after your attempt
Correct Answer
A. \(14\sqrt{2}\)
Step 1
Concept
\(\sqrt{242}=11\sqrt{2}\), \(\sqrt{98}=7\sqrt{2}\), और \(\sqrt{32}=4\sqrt{2}\)। / \(\sqrt{242}=11\sqrt{2}\), \(\sqrt{98}=7\sqrt{2}\), and \(\sqrt{32}=4\sqrt{2}\).
Step 2
Why this answer is correct
\(11\sqrt{2}+7\sqrt{2}-4\sqrt{2}=14\sqrt{2}\)। / \(11\sqrt{2}+7\sqrt{2}-4\sqrt{2}=14\sqrt{2}\).
Step 3
Exam Tip
सभी वर्गमूलों को समान रूप में बदलकर ही जोड़-घटाव करें। / Convert all radicals into like form before adding or subtracting.
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\(\sqrt{245}+\sqrt{180}-\sqrt{80}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{245}+\sqrt{180}-\sqrt{80}\)?
#real-numbers
#radical-expression
#simplification
A \(7\sqrt{5}\)
B \(8\sqrt{5}\)
C \(9\sqrt{5}\)
D \(10\sqrt{5}\)
Explanation opens after your attempt
Correct Answer
C. \(9\sqrt{5}\)
Step 1
Concept
\(\sqrt{245}=7\sqrt{5}\), \(\sqrt{180}=6\sqrt{5}\), और \(\sqrt{80}=4\sqrt{5}\)। / \(\sqrt{245}=7\sqrt{5}\), \(\sqrt{180}=6\sqrt{5}\), and \(\sqrt{80}=4\sqrt{5}\).
Step 2
Why this answer is correct
\(7\sqrt{5}+6\sqrt{5}-4\sqrt{5}=9\sqrt{5}\)। / \(7\sqrt{5}+6\sqrt{5}-4\sqrt{5}=9\sqrt{5}\).
Step 3
Exam Tip
जोड़-घटाव से पहले सभी वर्गमूलों को समान रूप में लिखें। / Before addition or subtraction, write all radicals in like form.
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\(\frac{9}{\sqrt{9}}\) का सरल रूप क्या है?
What is the simplified form of \(\frac{9}{\sqrt{9}}\)?
#real-numbers
#simplification
#perfect-square
A (1)
B (3)
C \(\sqrt{9}\)
D \(9\sqrt{9}\)
Explanation opens after your attempt
Step 1
Concept
पहले \(\sqrt{9}=3\) लिखें। / First write \(\sqrt{9}=3\).
Step 2
Why this answer is correct
\(\frac{9}{\sqrt{9}}=\frac{9}{3}=3\)। / \(\frac{9}{\sqrt{9}}=\frac{9}{3}=3\).
Step 3
Exam Tip
हर बार परिमेयकरण जरूरी नहीं, पूर्ण वर्ग का वर्गमूल सीधे निकालें। / Rationalisation is not always needed; first evaluate square roots of perfect squares.
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\(\sqrt{28}+\sqrt{63}+\sqrt{175}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{28}+\sqrt{63}+\sqrt{175}\)?
#real-numbers
#radical-addition
#simplification
A \(12\sqrt{7}\)
B \(10\sqrt{7}\)
C \(14\sqrt{7}\)
D \(15\sqrt{7}\)
Explanation opens after your attempt
Correct Answer
B. \(10\sqrt{7}\)
Step 1
Concept
\(\sqrt{28}=2\sqrt{7}\), \(\sqrt{63}=3\sqrt{7}\), और \(\sqrt{175}=5\sqrt{7}\)। / \(\sqrt{28}=2\sqrt{7}\), \(\sqrt{63}=3\sqrt{7}\), and \(\sqrt{175}=5\sqrt{7}\).
Step 2
Why this answer is correct
योग \(2\sqrt{7}+3\sqrt{7}+5\sqrt{7}=10\sqrt{7}\) है। / The sum is \(2\sqrt{7}+3\sqrt{7}+5\sqrt{7}=10\sqrt{7}\).
Step 3
Exam Tip
समान वर्गमूल बनने पर केवल गुणांक जोड़ें। / Once radicals become like terms, add only the coefficients.
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\(\sqrt{147}-\sqrt{75}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{147}-\sqrt{75}\)?
#real-numbers
#radical-subtraction
#simplification
A \(2\sqrt{3}\)
B \(4\sqrt{3}\)
C \(6\sqrt{3}\)
D \(\sqrt{72}\)
Explanation opens after your attempt
Correct Answer
A. \(2\sqrt{3}\)
Step 1
Concept
\(\sqrt{147}=7\sqrt{3}\) और \(\sqrt{75}=5\sqrt{3}\)। / \(\sqrt{147}=7\sqrt{3}\) and \(\sqrt{75}=5\sqrt{3}\).
Step 2
Why this answer is correct
\(7\sqrt{3}-5\sqrt{3}=2\sqrt{3}\)। / \(7\sqrt{3}-5\sqrt{3}=2\sqrt{3}\).
Step 3
Exam Tip
वर्गमूलों को घटाने से पहले समान वर्गमूल में बदलना जरूरी है। / Before subtracting radicals, convert them into like radicals.
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\(\sqrt{128}+\sqrt{72}-\sqrt{50}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{128}+\sqrt{72}-\sqrt{50}\)?
#real-numbers
#radical-expression
#simplification
A \(9\sqrt{2}\)
B \(7\sqrt{2}\)
C \(11\sqrt{2}\)
D \(\sqrt{150}\)
Explanation opens after your attempt
Correct Answer
A. \(9\sqrt{2}\)
Step 1
Concept
\(\sqrt{128}=8\sqrt{2}\), \(\sqrt{72}=6\sqrt{2}\), और \(\sqrt{50}=5\sqrt{2}\)। / \(\sqrt{128}=8\sqrt{2}\), \(\sqrt{72}=6\sqrt{2}\), and \(\sqrt{50}=5\sqrt{2}\).
Step 2
Why this answer is correct
\(8\sqrt{2}+6\sqrt{2}-5\sqrt{2}=9\sqrt{2}\)। / \(8\sqrt{2}+6\sqrt{2}-5\sqrt{2}=9\sqrt{2}\).
Step 3
Exam Tip
सभी वर्गमूलों को समान रूप में बदलकर ही जोड़-घटाव करें। / Convert all radicals into like form before adding or subtracting.
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\(\sqrt{75}+\sqrt{300}-\sqrt{48}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{75}+\sqrt{300}-\sqrt{48}\)?
#real-numbers
#radical-expression
#simplification
A \(9\sqrt{3}\)
B \(11\sqrt{3}\)
C \(7\sqrt{3}\)
D \(\sqrt{327}\)
Explanation opens after your attempt
Correct Answer
B. \(11\sqrt{3}\)
Step 1
Concept
\(\sqrt{75}=5\sqrt{3}\), \(\sqrt{300}=10\sqrt{3}\), और \(\sqrt{48}=4\sqrt{3}\)। / \(\sqrt{75}=5\sqrt{3}\), \(\sqrt{300}=10\sqrt{3}\), and \(\sqrt{48}=4\sqrt{3}\).
Step 2
Why this answer is correct
\(5\sqrt{3}+10\sqrt{3}-4\sqrt{3}=11\sqrt{3}\)। / \(5\sqrt{3}+10\sqrt{3}-4\sqrt{3}=11\sqrt{3}\).
Step 3
Exam Tip
जोड़ और घटाव से पहले सभी वर्गमूलों को सरल करें। / Simplify all radicals before addition and subtraction.
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\(\frac{7}{\sqrt{7}}\) का सरल रूप क्या है?
What is the simplified form of \(\frac{7}{\sqrt{7}}\)?
#real-numbers
#rationalisation
#simplification
A \(\sqrt{7}\)
B \(7\sqrt{7}\)
C \(\frac{1}{\sqrt{7}}\)
D (49)
Explanation opens after your attempt
Correct Answer
A. \(\sqrt{7}\)
Step 1
Concept
हर से वर्गमूल हटाने के लिए ऊपर और नीचे \(\sqrt{7}\) से गुणा करें। / Multiply numerator and denominator by \(\sqrt{7}\) to remove the root from the denominator.
Step 2
Why this answer is correct
\(\frac{7}{\sqrt{7}}=\frac{7\sqrt{7}}{7}=\sqrt{7}\)। / \(\frac{7}{\sqrt{7}}=\frac{7\sqrt{7}}{7}=\sqrt{7}\).
Step 3
Exam Tip
हर में वर्गमूल हो तो परिमेयकरण मदद करता है। / Rationalisation helps when the denominator contains a square root.
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\(\sqrt{20}+\sqrt{45}+\sqrt{125}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{20}+\sqrt{45}+\sqrt{125}\)?
#real-numbers
#radical-addition
#simplification
A \(10\sqrt{5}\)
B \(12\sqrt{5}\)
C \(8\sqrt{5}\)
D \(15\sqrt{5}\)
Explanation opens after your attempt
Correct Answer
A. \(10\sqrt{5}\)
Step 1
Concept
\(\sqrt{20}=2\sqrt{5}\), \(\sqrt{45}=3\sqrt{5}\), और \(\sqrt{125}=5\sqrt{5}\)। / \(\sqrt{20}=2\sqrt{5}\), \(\sqrt{45}=3\sqrt{5}\), and \(\sqrt{125}=5\sqrt{5}\).
Step 2
Why this answer is correct
योग \(2\sqrt{5}+3\sqrt{5}+5\sqrt{5}=10\sqrt{5}\) है। / The sum is \(2\sqrt{5}+3\sqrt{5}+5\sqrt{5}=10\sqrt{5}\).
Step 3
Exam Tip
समान वर्गमूल बनने पर केवल गुणांक जोड़ें। / Once radicals are like terms, add only the coefficients.
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\(\sqrt{98}-\sqrt{32}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{98}-\sqrt{32}\)?
#real-numbers
#radical-subtraction
#simplification
A \(3\sqrt{2}\)
B \(7\sqrt{2}\)
C \(11\sqrt{2}\)
D \(\sqrt{66}\)
Explanation opens after your attempt
Correct Answer
A. \(3\sqrt{2}\)
Step 1
Concept
\(\sqrt{98}=7\sqrt{2}\) और \(\sqrt{32}=4\sqrt{2}\)। / \(\sqrt{98}=7\sqrt{2}\) and \(\sqrt{32}=4\sqrt{2}\).
Step 2
Why this answer is correct
\(7\sqrt{2}-4\sqrt{2}=3\sqrt{2}\)। / \(7\sqrt{2}-4\sqrt{2}=3\sqrt{2}\).
Step 3
Exam Tip
वर्गमूलों को घटाने से पहले समान वर्गमूल में बदलें। / Convert radicals into like radicals before subtracting.
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\(\sqrt{98}+\sqrt{50}-\sqrt{18}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{98}+\sqrt{50}-\sqrt{18}\)?
#real-numbers
#radical-expression
#simplification
A \(9\sqrt{2}\)
B \(5\sqrt{2}\)
C \(15\sqrt{2}\)
D \(\sqrt{130}\)
Explanation opens after your attempt
Correct Answer
A. \(9\sqrt{2}\)
Step 1
Concept
\(\sqrt{98}=7\sqrt{2}\), \(\sqrt{50}=5\sqrt{2}\), और \(\sqrt{18}=3\sqrt{2}\)। / \(\sqrt{98}=7\sqrt{2}\), \(\sqrt{50}=5\sqrt{2}\), and \(\sqrt{18}=3\sqrt{2}\).
Step 2
Why this answer is correct
\(7\sqrt{2}+5\sqrt{2}-3\sqrt{2}=9\sqrt{2}\)। / \(7\sqrt{2}+5\sqrt{2}-3\sqrt{2}=9\sqrt{2}\).
Step 3
Exam Tip
सभी पदों को समान वर्गमूल में बदलने के बाद ही जोड़-घटाव करें। / Add or subtract only after converting all terms to like radicals.
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\(\sqrt{45}+\sqrt{80}-\sqrt{20}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{45}+\sqrt{80}-\sqrt{20}\)?
#real-numbers
#radical-expression
#simplification
A \(5\sqrt{5}\)
B \(3\sqrt{5}\)
C \(7\sqrt{5}\)
D \(\sqrt{105}\)
Explanation opens after your attempt
Correct Answer
A. \(5\sqrt{5}\)
Step 1
Concept
\(\sqrt{45}=3\sqrt{5}\), \(\sqrt{80}=4\sqrt{5}\), और \(\sqrt{20}=2\sqrt{5}\)। / \(\sqrt{45}=3\sqrt{5}\), \(\sqrt{80}=4\sqrt{5}\), and \(\sqrt{20}=2\sqrt{5}\).
Step 2
Why this answer is correct
\(3\sqrt{5}+4\sqrt{5}-2\sqrt{5}=5\sqrt{5}\)। / \(3\sqrt{5}+4\sqrt{5}-2\sqrt{5}=5\sqrt{5}\).
Step 3
Exam Tip
जोड़ और घटाव से पहले सभी वर्गमूलों को समान रूप में बदलें। / Convert all radicals to like form before adding or subtracting.
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\(\frac{5}{\sqrt{5}}\) का सरल रूप क्या है?
What is the simplified form of \(\frac{5}{\sqrt{5}}\)?
#real-numbers
#rationalisation
#simplification
A \(\sqrt{5}\)
B \(5\sqrt{5}\)
C \(\frac{1}{\sqrt{5}}\)
D (25)
Explanation opens after your attempt
Correct Answer
A. \(\sqrt{5}\)
Step 1
Concept
हर को सरल करने के लिए ऊपर और नीचे \(\sqrt{5}\) से गुणा करें। / To simplify the denominator, multiply top and bottom by \(\sqrt{5}\).
Step 2
Why this answer is correct
\(\frac{5}{\sqrt{5}}=\frac{5\sqrt{5}}{5}=\sqrt{5}\)। / \(\frac{5}{\sqrt{5}}=\frac{5\sqrt{5}}{5}=\sqrt{5}\).
Step 3
Exam Tip
हर में वर्गमूल हो तो परिमेयकरण उपयोगी होता है। / Rationalising is useful when a square root appears in the denominator.
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\(\sqrt{12}+\sqrt{27}+\sqrt{75}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{12}+\sqrt{27}+\sqrt{75}\)?
#real-numbers
#radical-addition
#simplification
A \(10\sqrt{3}\)
B \(9\sqrt{3}\)
C \(6\sqrt{3}\)
D \(15\sqrt{3}\)
Explanation opens after your attempt
Correct Answer
A. \(10\sqrt{3}\)
Step 1
Concept
\(\sqrt{12}=2\sqrt{3}\), \(\sqrt{27}=3\sqrt{3}\), और \(\sqrt{75}=5\sqrt{3}\)। / \(\sqrt{12}=2\sqrt{3}\), \(\sqrt{27}=3\sqrt{3}\), and \(\sqrt{75}=5\sqrt{3}\).
Step 2
Why this answer is correct
जोड़ने पर \(2\sqrt{3}+3\sqrt{3}+5\sqrt{3}=10\sqrt{3}\)। / Adding gives \(2\sqrt{3}+3\sqrt{3}+5\sqrt{3}=10\sqrt{3}\).
Step 3
Exam Tip
समान वर्गमूल बनने पर केवल गुणांक जोड़ें। / Once radicals are like terms, add only the coefficients.
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\(\sqrt{72}-\sqrt{18}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{72}-\sqrt{18}\)?
#real-numbers
#radical-subtraction
#simplification
A \(3\sqrt{2}\)
B \(6\sqrt{2}\)
C \(\sqrt{54}\)
D \(9\sqrt{2}\)
Explanation opens after your attempt
Correct Answer
A. \(3\sqrt{2}\)
Step 1
Concept
\(\sqrt{72}=6\sqrt{2}\) और \(\sqrt{18}=3\sqrt{2}\)। / \(\sqrt{72}=6\sqrt{2}\) and \(\sqrt{18}=3\sqrt{2}\).
Step 2
Why this answer is correct
\(6\sqrt{2}-3\sqrt{2}=3\sqrt{2}\)। / \(6\sqrt{2}-3\sqrt{2}=3\sqrt{2}\).
Step 3
Exam Tip
घटाने से पहले दोनों वर्गमूलों को सरल करना जरूरी है। / Simplify both square roots before subtracting.
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कौन-सा विकल्प \(\sqrt{216}\) का सरल रूप है?
Which option is the simplified form of \(\sqrt{216}\)?
#real-numbers
#sqrt216
#simplification
A \(6\sqrt{6}\)
B \(9\sqrt{6}\)
C \(12\sqrt{3}\)
D \(36\sqrt{6}\)
Explanation opens after your attempt
Correct Answer
A. \(6\sqrt{6}\)
Step 1
Concept
\(216=36 \times 6\) है। / \(216=36 \times 6\).
Step 2
Why this answer is correct
\(\sqrt{216}=\sqrt{36 \times 6}=6\sqrt{6}\)। / \(\sqrt{216}=\sqrt{36 \times 6}=6\sqrt{6}\).
Step 3
Exam Tip
अंदर बचे (6) में कोई पूर्ण वर्ग गुणनखंड नहीं है, इसलिए रूप सरल है। / The remaining (6) has no perfect square factor, so the form is simplified.
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\(\sqrt{243}\) को सरल कीजिए।
Simplify \(\sqrt{243}\).
#real-numbers
#sqrt243
#simplification
A \(3\sqrt{27}\)
B \(9\sqrt{3}\)
C \(27\sqrt{3}\)
D \(81\sqrt{3}\)
Explanation opens after your attempt
Correct Answer
B. \(9\sqrt{3}\)
Step 1
Concept
\(243=81 \times 3\) लिखें। / Write \(243=81 \times 3\).
Step 2
Why this answer is correct
\(\sqrt{243}=\sqrt{81 \times 3}=9\sqrt{3}\)। / \(\sqrt{243}=\sqrt{81 \times 3}=9\sqrt{3}\).
Step 3
Exam Tip
बड़ा पूर्ण वर्ग चुनने से उत्तर एक ही चरण में सरल हो जाता है। / Choosing a larger perfect square simplifies the answer in one step.
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\(\sqrt{135}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{135}\)?
#real-numbers
#sqrt135
#simplification
A \(5\sqrt{27}\)
B \(3\sqrt{15}\)
C \(9\sqrt{15}\)
D \(15\sqrt{3}\)
Explanation opens after your attempt
Correct Answer
B. \(3\sqrt{15}\)
Step 1
Concept
\(135=9 \times 15\) लिखें। / Write \(135=9 \times 15\).
Step 2
Why this answer is correct
\(\sqrt{135}=\sqrt{9 \times 15}=3\sqrt{15}\)। / \(\sqrt{135}=\sqrt{9 \times 15}=3\sqrt{15}\).
Step 3
Exam Tip
अंदर बची संख्या में पूर्ण वर्ग गुणनखंड न हो, तब रूप सरल माना जाता है। / The form is simplified when the remaining number inside has no perfect square factor.
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\(\sqrt{288}\) का सरल रूप कौन-सा है?
Which is the simplified form of \(\sqrt{288}\)?
#real-numbers
#sqrt288
#simplification
A \(12\sqrt{2}\)
B \(24\sqrt{2}\)
C \(8\sqrt{6}\)
D \(144\sqrt{2}\)
Explanation opens after your attempt
Correct Answer
A. \(12\sqrt{2}\)
Step 1
Concept
\(288=144 \times 2\) है। / \(288=144 \times 2\).
Step 2
Why this answer is correct
\(\sqrt{288}=\sqrt{144 \times 2}=12\sqrt{2}\)। / \(\sqrt{288}=\sqrt{144 \times 2}=12\sqrt{2}\).
Step 3
Exam Tip
बड़े पूर्ण वर्ग का उपयोग करने से उत्तर सीधे सरल रूप में मिलता है। / Using a large perfect square gives the simplified form directly.
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\(\sqrt{32}+\sqrt{128}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{32}+\sqrt{128}\)?
#real-numbers
#radical-addition
#simplification
A \(12\sqrt{2}\)
B \(16\sqrt{2}\)
C \(8\sqrt{2}\)
D \(\sqrt{160}\)
Explanation opens after your attempt
Correct Answer
A. \(12\sqrt{2}\)
Step 1
Concept
\(\sqrt{32}=4\sqrt{2}\) और \(\sqrt{128}=8\sqrt{2}\)। / \(\sqrt{32}=4\sqrt{2}\) and \(\sqrt{128}=8\sqrt{2}\).
Step 2
Why this answer is correct
\(4\sqrt{2}+8\sqrt{2}=12\sqrt{2}\)। / \(4\sqrt{2}+8\sqrt{2}=12\sqrt{2}\).
Step 3
Exam Tip
समान वर्गमूल बनने पर ही उन्हें जोड़ा जा सकता है। / Radicals can be added only when they become like radicals.
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\(\sqrt{175}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{175}\)?
#real-numbers
#sqrt175
#simplification
A \(25\sqrt{7}\)
B \(7\sqrt{5}\)
C \(5\sqrt{7}\)
D (35)
Explanation opens after your attempt
Correct Answer
C. \(5\sqrt{7}\)
Step 1
Concept
\(175=25 \times 7\) लिखें। / Write \(175=25 \times 7\).
Step 2
Why this answer is correct
\(\sqrt{175}=\sqrt{25 \times 7}=5\sqrt{7}\)। / \(\sqrt{175}=\sqrt{25 \times 7}=5\sqrt{7}\).
Step 3
Exam Tip
पूर्ण वर्ग गुणनखंड को बाहर और बाकी संख्या को अंदर रखें। / Take the perfect square factor outside and keep the remaining number inside.
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कौन-सा विकल्प \(\sqrt{24}\) का सरल रूप है?
Which option is the simplified form of \(\sqrt{24}\)?
#real-numbers
#sqrt24
#simplification
A \(2\sqrt{6}\)
B \(4\sqrt{6}\)
C \(6\sqrt{2}\)
D \(12\sqrt{2}\)
Explanation opens after your attempt
Correct Answer
A. \(2\sqrt{6}\)
Step 1
Concept
\(24=4 \times 6\) है। / \(24=4 \times 6\).
Step 2
Why this answer is correct
\(\sqrt{24}=\sqrt{4 \times 6}=2\sqrt{6}\)। / \(\sqrt{24}=\sqrt{4 \times 6}=2\sqrt{6}\).
Step 3
Exam Tip
यदि अंदर (6) बचे तो वह आगे सरल नहीं होगा क्योंकि (6) में पूर्ण वर्ग गुणनखंड नहीं है। / If (6) remains inside, it cannot be simplified further because it has no perfect square factor.
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\(\sqrt{147}\) को सरल कीजिए।
Simplify \(\sqrt{147}\).
#real-numbers
#sqrt147
#simplification
A \(7\sqrt{3}\)
B \(3\sqrt{7}\)
C \(21\sqrt{3}\)
D \(49\sqrt{3}\)
Explanation opens after your attempt
Correct Answer
A. \(7\sqrt{3}\)
Step 1
Concept
\(147=49 \times 3\) लिखें। / Write \(147=49 \times 3\).
Step 2
Why this answer is correct
\(\sqrt{147}=\sqrt{49 \times 3}=7\sqrt{3}\)। / \(\sqrt{147}=\sqrt{49 \times 3}=7\sqrt{3}\).
Step 3
Exam Tip
पूर्ण वर्ग (49) को पहचानना यहां मुख्य कदम है। / Recognising the perfect square (49) is the main step here.
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\(\sqrt{90}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{90}\)?
#real-numbers
#sqrt90
#simplification
A \(3\sqrt{10}\)
B \(9\sqrt{10}\)
C \(10\sqrt{9}\)
D \(5\sqrt{6}\)
Explanation opens after your attempt
Correct Answer
A. \(3\sqrt{10}\)
Step 1
Concept
\(90=9 \times 10\) लिखें। / Write \(90=9 \times 10\).
Step 2
Why this answer is correct
\(\sqrt{90}=\sqrt{9 \times 10}=3\sqrt{10}\)। / \(\sqrt{90}=\sqrt{9 \times 10}=3\sqrt{10}\).
Step 3
Exam Tip
पूर्ण वर्ग को बाहर निकालकर शेष भाग अंदर रखें। / Take the perfect square outside and keep the remaining part inside.
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\(\sqrt{200}\) का सरल रूप कौन-सा है?
Which is the simplified form of \(\sqrt{200}\)?
#real-numbers
#sqrt200
#simplification
A \(10\sqrt{2}\)
B \(20\sqrt{5}\)
C \(2\sqrt{100}\)
D \(100\sqrt{2}\)
Explanation opens after your attempt
Correct Answer
A. \(10\sqrt{2}\)
Step 1
Concept
\(200=100 \times 2\) है। / \(200=100 \times 2\).
Step 2
Why this answer is correct
\(\sqrt{200}=\sqrt{100 \times 2}=10\sqrt{2}\)। / \(\sqrt{200}=\sqrt{100 \times 2}=10\sqrt{2}\).
Step 3
Exam Tip
बड़े पूर्ण वर्ग (100) को पहचानने से उत्तर जल्दी मिलता है। / Recognising a large perfect square like (100) gives the answer quickly.
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\(\sqrt{8}+\sqrt{18}\) का सरल रूप क्या होगा?
What is the simplified form of \(\sqrt{8}+\sqrt{18}\)?
#real-numbers
#radical-addition
#simplification
A \(5\sqrt{2}\)
B \(2\sqrt{26}\)
C \(\sqrt{26}\)
D \(10\sqrt{2}\)
Explanation opens after your attempt
Correct Answer
A. \(5\sqrt{2}\)
Step 1
Concept
\(\sqrt{8}=2\sqrt{2}\) और \(\sqrt{18}=3\sqrt{2}\)। / \(\sqrt{8}=2\sqrt{2}\) and \(\sqrt{18}=3\sqrt{2}\).
Step 2
Why this answer is correct
\(2\sqrt{2}+3\sqrt{2}=5\sqrt{2}\)। / \(2\sqrt{2}+3\sqrt{2}=5\sqrt{2}\).
Step 3
Exam Tip
समान वर्गमूल बनने पर ही उन्हें जोड़ा जा सकता है। / Radicals can be added only after they become like radicals.
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\(\sqrt{125}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{125}\)?
#real-numbers
#square-root
#simplification
A \(5\sqrt{5}\)
B \(25\sqrt{5}\)
C \(3\sqrt{5}\)
D \(5\sqrt{25}\)
Explanation opens after your attempt
Correct Answer
A. \(5\sqrt{5}\)
Step 1
Concept
\(125=25 \times 5\) लिखें। / Write \(125=25 \times 5\).
Step 2
Why this answer is correct
\(\sqrt{125}=\sqrt{25 \times 5}=5\sqrt{5}\)। / \(\sqrt{125}=\sqrt{25 \times 5}=5\sqrt{5}\).
Step 3
Exam Tip
पूर्ण वर्ग (25) को बाहर (5) के रूप में निकालें। / Take the perfect square (25) outside as (5).
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\(\sqrt{98}\) का सरल रूप क्या होगा?
What will be the simplified form of \(\sqrt{98}\)?
#real-numbers
#sqrt98
#simplification
A \(7\sqrt{2}\)
B \(2\sqrt{7}\)
C \(14\sqrt{2}\)
D \(49\sqrt{2}\)
Explanation opens after your attempt
Correct Answer
A. \(7\sqrt{2}\)
Step 1
Concept
\(98=49 \times 2\) है। / \(98=49 \times 2\).
Step 2
Why this answer is correct
\(\sqrt{98}=\sqrt{49 \times 2}=7\sqrt{2}\)। / \(\sqrt{98}=\sqrt{49 \times 2}=7\sqrt{2}\).
Step 3
Exam Tip
बड़े पूर्ण वर्ग जैसे (49) को पहचानना सरलीकरण में मदद करता है। / Recognising larger perfect squares like (49) helps in simplification.
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