यदि \(A=14+6\sqrt{5}\), तो \(\sqrt{A}\) का सरल रूप क्या है?
If \(A=14+6\sqrt{5}\), what is the simplified form of \(\sqrt{A}\)?
#surds
#square_root
#identity
A \(3+\sqrt{5}\)
B \(\sqrt{10}+2\)
C \(\sqrt{9}+\sqrt{5}\)
D \(2+\sqrt{5}\)
Explanation opens after your attempt
Correct Answer
A. \(3+\sqrt{5}\)
Step 1
Concept
Because (\(3+\sqrt{5}\)^{2}=9+5+6\sqrt{5}=14+6\sqrt{5}), \(\sqrt{A}=3+\sqrt{5}\). In exams, identify perfect-square surd forms.
Step 2
Why this answer is correct
The correct answer is A. \(3+\sqrt{5}\). Because (\(3+\sqrt{5}\)^{2}=9+5+6\sqrt{5}=14+6\sqrt{5}), \(\sqrt{A}=3+\sqrt{5}\). In exams, identify perfect-square surd forms.
Step 3
Exam Tip
क्योंकि (\(3+\sqrt{5}\)^{2}=9+5+6\sqrt{5}=14+6\sqrt{5}), इसलिए \(\sqrt{A}=3+\sqrt{5}\)। परीक्षा में पूर्ण वर्ग करणी पहचानें।
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यदि \(A=9+4\sqrt{5}\), तो \(\sqrt{A}\) का सरल रूप क्या है?
If \(A=9+4\sqrt{5}\), what is the simplified form of \(\sqrt{A}\)?
#surds
#square_root
#identity
A \(2+\sqrt{5}\)
B \(\sqrt{5}+4\)
C \(3+\sqrt{5}\)
D \(1+2\sqrt{5}\)
Explanation opens after your attempt
Correct Answer
A. \(2+\sqrt{5}\)
Step 1
Concept
Because (\(2+\sqrt{5}\)^{2}=4+5+4\sqrt{5}=9+4\sqrt{5}), \(\sqrt{A}=2+\sqrt{5}\). In exams, recognize a perfect-square surd form.
Step 2
Why this answer is correct
The correct answer is A. \(2+\sqrt{5}\). Because (\(2+\sqrt{5}\)^{2}=4+5+4\sqrt{5}=9+4\sqrt{5}), \(\sqrt{A}=2+\sqrt{5}\). In exams, recognize a perfect-square surd form.
Step 3
Exam Tip
क्योंकि (\(2+\sqrt{5}\)^{2}=4+5+4\sqrt{5}=9+4\sqrt{5}), इसलिए \(\sqrt{A}=2+\sqrt{5}\)। परीक्षा में पूर्ण वर्ग करणी को पहचानें।
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(\left\(81x^{4}\right\)^{\frac{1}{2}}) का सरल रूप क्या है, जहाँ \(x\ge0\)?
What is the simplified form of (\left\(81x^{4}\right\)^{\frac{1}{2}}), where \(x\ge0\)?
#fractional_exponents
#square_root
#polynomials
A \(9x^{2}\)
B (9x)
C \(81x^{2}\)
D \(3x^{2}\)
Explanation opens after your attempt
Correct Answer
A. \(9x^{2}\)
Step 1
Concept
(\left\(81x^{4}\right\)^{\frac{1}{2}}=\sqrt{81x^{4}}=9x^{2}). In exams, the exponent becomes half under a square root.
Step 2
Why this answer is correct
The correct answer is A. \(9x^{2}\). (\left\(81x^{4}\right\)^{\frac{1}{2}}=\sqrt{81x^{4}}=9x^{2}). In exams, the exponent becomes half under a square root.
Step 3
Exam Tip
(\left\(81x^{4}\right\)^{\frac{1}{2}}=\sqrt{81x^{4}}=9x^{2})। परीक्षा में वर्गमूल में घात आधी हो जाती है।
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यदि \(A=7+4\sqrt{3}\), तो \(\sqrt{A}\) का सही सरल रूप क्या है?
If \(A=7+4\sqrt{3}\), what is the correct simplified form of \(\sqrt{A}\)?
#surds
#square_root
#identity
A \(2+\sqrt{3}\)
B \(3+\sqrt{2}\)
C \(\sqrt{7}+2\sqrt{3}\)
D \(4+\sqrt{3}\)
Explanation opens after your attempt
Correct Answer
A. \(2+\sqrt{3}\)
Step 1
Concept
Since (\(2+\sqrt{3}\)^{2}=4+3+4\sqrt{3}=7+4\sqrt{3}), \(\sqrt{A}=2+\sqrt{3}\). In exams, recognize the form ((a+b)^{2}).
Step 2
Why this answer is correct
The correct answer is A. \(2+\sqrt{3}\). Since (\(2+\sqrt{3}\)^{2}=4+3+4\sqrt{3}=7+4\sqrt{3}), \(\sqrt{A}=2+\sqrt{3}\). In exams, recognize the form ((a+b)^{2}).
Step 3
Exam Tip
(\(2+\sqrt{3}\)^{2}=4+3+4\sqrt{3}=7+4\sqrt{3}), इसलिए \(\sqrt{A}=2+\sqrt{3}\)। परीक्षा में रूप ((a+b)^{2}) पहचानें।
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एक संख्या के वर्ग में (17) घटाने पर (127) मिलता है। धनात्मक संख्या क्या है?
When (17) is subtracted from the square of a number, the result is (127). What is the positive number?
#quadratic-equations
#word-problems
#square-root
A (12)
B (10)
C (14)
D (8)
Explanation opens after your attempt
Step 1
Concept
Let the number be (x), so \(x^2-17=127\). This gives \(x^2=144\), so the positive number is (12).
Step 2
Why this answer is correct
The correct answer is A. (12). Let the number be (x), so \(x^2-17=127\). This gives \(x^2=144\), so the positive number is (12).
Step 3
Exam Tip
मान लें संख्या (x) है, तो \(x^2-17=127\)। इससे \(x^2=144\), इसलिए धनात्मक संख्या (12) है।
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एक संख्या के वर्ग में (11) घटाने पर (85) मिलता है। धनात्मक संख्या क्या है?
When (11) is subtracted from the square of a number, the result is (85). What is the positive number?
#quadratic-equations
#word-problems
#square-root
A \(4\sqrt{6}\)
B \(6\sqrt{4}\)
C (9)
D (12)
Explanation opens after your attempt
Correct Answer
A. \(4\sqrt{6}\)
Step 1
Concept
Let the number be (x), so \(x^2-11=85\). This gives \(x^2=96\), so the positive number is \(4\sqrt{6}\).
Step 2
Why this answer is correct
The correct answer is A. \(4\sqrt{6}\). Let the number be (x), so \(x^2-11=85\). This gives \(x^2=96\), so the positive number is \(4\sqrt{6}\).
Step 3
Exam Tip
मान लें संख्या (x) है, तो \(x^2-11=85\)। इससे \(x^2=96\), इसलिए धनात्मक संख्या \(4\sqrt{6}\) है।
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समीकरण \(x^2=121\) के मूल कौन से हैं?
What are the roots of \(x^2=121\)?
#roots
#square_root
#plus_minus
A (11) और (-11) / (11) and (-11)
B केवल (11) / Only (11)
C (22) और (-22) / (22) and (-22)
D (0) और (121) / (0) and (121)
Explanation opens after your attempt
Correct Answer
A. (11) और (-11) / (11) and (-11)
Step 1
Concept
From \(x^2=121\), we get \(x=\pm11\). Take both signs while finding square roots.
Step 2
Why this answer is correct
The correct answer is A. (11) और (-11) / (11) and (-11). From \(x^2=121\), we get \(x=\pm11\). Take both signs while finding square roots.
Step 3
Exam Tip
\(x^2=121\) से \(x=\pm11\) मिलता है। वर्गमूल लेते समय दोनों चिन्ह लें।
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समीकरण \(5x^2-45=0\) के मूल कौन से हैं?
What are the roots of \(5x^2-45=0\)?
#roots
#square_root
#plus_minus
A (3) और (-3) / (3) and (-3)
B (9) और (-9) / (9) and (-9)
C (0) और (3) / (0) and (3)
D केवल (3) / Only (3)
Explanation opens after your attempt
Correct Answer
A. (3) और (-3) / (3) and (-3)
Step 1
Concept
From \(5x^2-45=0\), we get \(x^2=9\). Therefore \(x=\pm3\).
Step 2
Why this answer is correct
The correct answer is A. (3) और (-3) / (3) and (-3). From \(5x^2-45=0\), we get \(x^2=9\). Therefore \(x=\pm3\).
Step 3
Exam Tip
\(5x^2-45=0\) से \(x^2=9\) मिलता है। इसलिए \(x=\pm3\) है।
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समीकरण \(x^2=49\) के मूल कौन से हैं?
What are the roots of \(x^2=49\)?
#roots
#square_root
#plus_minus
A (7) और (-7) / (7) and (-7)
B केवल (7) / Only (7)
C (14) और (-14) / (14) and (-14)
D (0) और (49) / (0) and (49)
Explanation opens after your attempt
Correct Answer
A. (7) और (-7) / (7) and (-7)
Step 1
Concept
From \(x^2=49\), we get \(x=\pm7\). Take both signs while finding square roots.
Step 2
Why this answer is correct
The correct answer is A. (7) और (-7) / (7) and (-7). From \(x^2=49\), we get \(x=\pm7\). Take both signs while finding square roots.
Step 3
Exam Tip
\(x^2=49\) से \(x=\pm7\) मिलता है। वर्गमूल लेते समय दोनों चिन्ह लें।
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समीकरण \(3x^2-27=0\) के मूल कौन से हैं?
What are the roots of \(3x^2-27=0\)?
#roots
#square_root
#plus_minus
A (3) और (-3) / (3) and (-3)
B (9) और (-9) / (9) and (-9)
C (0) और (3) / (0) and (3)
D केवल (3) / Only (3)
Explanation opens after your attempt
Correct Answer
A. (3) और (-3) / (3) and (-3)
Step 1
Concept
From \(3x^2-27=0\), we get \(x^2=9\). Therefore \(x=\pm3\).
Step 2
Why this answer is correct
The correct answer is A. (3) और (-3) / (3) and (-3). From \(3x^2-27=0\), we get \(x^2=9\). Therefore \(x=\pm3\).
Step 3
Exam Tip
\(3x^2-27=0\) से \(x^2=9\) मिलता है। इसलिए \(x=\pm3\) है।
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समीकरण \(x^2=16\) के मूल कौन से हैं?
What are the roots of \(x^2=16\)?
#roots
#square_root
#plus_minus
A (4) और (-4) / (4) and (-4)
B केवल (4) / Only (4)
C (8) और (-8) / (8) and (-8)
D (0) और (16) / (0) and (16)
Explanation opens after your attempt
Correct Answer
A. (4) और (-4) / (4) and (-4)
Step 1
Concept
From \(x^2=16\) we get \(x=\pm4\). In a square equation check both positive and negative roots.
Step 2
Why this answer is correct
The correct answer is A. (4) और (-4) / (4) and (-4). From \(x^2=16\) we get \(x=\pm4\). In a square equation check both positive and negative roots.
Step 3
Exam Tip
\(x^2=16\) से \(x=\pm4\) मिलता है। वर्ग समीकरण में धनात्मक और ऋणात्मक दोनों मूल देखें।
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समीकरण \(2x^2-8=0\) के मूल कौन से हैं?
What are the roots of \(2x^2-8=0\)?
#roots
#square_root
#plus_minus
A (2) और (-2) / (2) and (-2)
B (4) और (-4) / (4) and (-4)
C (0) और (2) / (0) and (2)
D केवल (2) / Only (2)
Explanation opens after your attempt
Correct Answer
A. (2) और (-2) / (2) and (-2)
Step 1
Concept
From \(2x^2-8=0\) we get \(x^2=4\) so \(x=\pm 2\). Take both signs while finding square roots.
Step 2
Why this answer is correct
The correct answer is A. (2) और (-2) / (2) and (-2). From \(2x^2-8=0\) we get \(x^2=4\) so \(x=\pm 2\). Take both signs while finding square roots.
Step 3
Exam Tip
\(2x^2-8=0\) से \(x^2=4\) मिलता है इसलिए \(x=\pm 2\)। वर्गमूल लेते समय दोनों चिन्ह लें।
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कौन सा विकल्प \(\sqrt{a^2}=a\) हमेशा सही नहीं होने का कारण बताता है?
Which option explains why \(\sqrt{a^2}=a\) is not always true?
#absolute-value
#square-root
#real-numbers
A यदि (a<0), तो \(\sqrt{a^2}=|a|\) होता है / If (a<0), then \(\sqrt{a^2}=|a|\)
B यदि (a>0), तो \(\sqrt{a^2}=0\) होता है / If (a>0), then \(\sqrt{a^2}=0\)
C यदि (a=1), तो \(\sqrt{a^2}\) अपरिमेय होता है / If (a=1), then \(\sqrt{a^2}\) is irrational
D यदि \(a\ne0\), तो \(\sqrt{a^2}\) वास्तविक नहीं होता / If \(a\ne0\), then \(\sqrt{a^2}\) is not real
Explanation opens after your attempt
Correct Answer
A. यदि (a<0), तो \(\sqrt{a^2}=|a|\) होता है / If (a<0), then \(\sqrt{a^2}=|a|\)
Step 1
Concept
The principal square root is non-negative so \(\sqrt{a^2}=|a|\). In exams be careful when (a) is negative.
Step 2
Why this answer is correct
The correct answer is A. यदि (a<0), तो \(\sqrt{a^2}=|a|\) होता है / If (a<0), then \(\sqrt{a^2}=|a|\). The principal square root is non-negative so \(\sqrt{a^2}=|a|\). In exams be careful when (a) is negative.
Step 3
Exam Tip
मुख्य वर्गमूल अऋणात्मक होता है इसलिए \(\sqrt{a^2}=|a|\) है। परीक्षा में ऋणात्मक (a) के लिए सावधान रहें।
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\(\sqrt{a^2}\) के बारे में सही कथन कौन सा है, जहां (a) वास्तविक संख्या है?
Which statement is correct about \(\sqrt{a^2}\), where (a) is a real number?
#real-numbers
#square-root
#absolute-value
A \(\sqrt{a^2}=|a|\)
B \(\sqrt{a^2}=a\) हमेशा / \(\sqrt{a^2}=a\) always
C \(\sqrt{a^2}=-a\) हमेशा / \(\sqrt{a^2}=-a\) always
D \(\sqrt{a^2}\) वास्तविक नहीं है / \(\sqrt{a^2}\) is not real
Explanation opens after your attempt
Correct Answer
A. \(\sqrt{a^2}=|a|\)
Step 1
Concept
The principal square root is always non-negative, so \(\sqrt{a^2}=|a|\). In exams do not forget the possibility of negative (a).
Step 2
Why this answer is correct
The correct answer is A. \(\sqrt{a^2}=|a|\). The principal square root is always non-negative, so \(\sqrt{a^2}=|a|\). In exams do not forget the possibility of negative (a).
Step 3
Exam Tip
मुख्य वर्गमूल हमेशा अऋणात्मक होता है, इसलिए \(\sqrt{a^2}=|a|\) है। परीक्षा में (a) ऋणात्मक होने की संभावना न भूलें।
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किस विकल्प में वास्तविक संख्या नहीं है?
Which option is not a real number?
#real-numbers
#classification
#square-root
A \(\sqrt{-9}\)
B \(\sqrt{0}\)
C \(-\sqrt{9}\)
D \(\sqrt{\frac{9}{16}}\)
Explanation opens after your attempt
Correct Answer
A. \(\sqrt{-9}\)
Step 1
Concept
\(\sqrt{-9}\) is not a real number, while the others are real. In exams do not take the square root of a negative number in the real number system.
Step 2
Why this answer is correct
The correct answer is A. \(\sqrt{-9}\). \(\sqrt{-9}\) is not a real number, while the others are real. In exams do not take the square root of a negative number in the real number system.
Step 3
Exam Tip
\(\sqrt{-9}\) वास्तविक संख्या नहीं है, जबकि बाकी सभी वास्तविक हैं। परीक्षा में ऋणात्मक संख्या का वर्गमूल वास्तविक संख्या पद्धति में नहीं लेते।
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यदि \(x=\sqrt{3}\) है, तो \(x^2-3\) का मान क्या है?
If \(x=\sqrt{3}\), what is the value of \(x^2-3\)?
#substitution
#square root
#polynomial value
A \(\sqrt{3}\)
B (0)
C \(3\sqrt{3}\)
D (6)
Explanation opens after your attempt
Step 1
Concept
Since (\(\sqrt{3}\)2 =3), \(x^2-3=0\). In exams the square of a square root gives the radicand.
Step 2
Why this answer is correct
The correct answer is B. (0). Since (\(\sqrt{3}\)2 =3), \(x^2-3=0\). In exams the square of a square root gives the radicand.
Step 3
Exam Tip
क्योंकि (\(\sqrt{3}\)2 =3), इसलिए \(x^2-3=0\) है। परीक्षा में वर्गमूल का वर्ग मूलांक देता 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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कौन सा विकल्प \(\sqrt{48}\), \(\sqrt{75}\), \(\sqrt{108}\) का आरोही क्रम है?
Which option is the ascending order of \(\sqrt{48}\), \(\sqrt{75}\), \(\sqrt{108}\)?
#comparison
#square-root
#order
A \(\sqrt{48}<\sqrt{75}<\sqrt{108}\)
B \(\sqrt{108}<\sqrt{75}<\sqrt{48}\)
C \(\sqrt{75}<\sqrt{48}<\sqrt{108}\)
D \(\sqrt{48}<\sqrt{108}<\sqrt{75}\)
Explanation opens after your attempt
Correct Answer
A. \(\sqrt{48}<\sqrt{75}<\sqrt{108}\)
Step 1
Concept
For positive numbers a larger value inside the root gives a larger square root. Here (48<75<108).
Step 2
Why this answer is correct
The correct answer is A. \(\sqrt{48}<\sqrt{75}<\sqrt{108}\). For positive numbers a larger value inside the root gives a larger square root. Here (48<75<108).
Step 3
Exam Tip
धनात्मक संख्याओं में जड़ के अंदर बड़ी संख्या हो तो वर्गमूल भी बड़ा होता है। (48<75<108) 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 \(\sqrt{432}\) 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 \(\frac{\sqrt{147}}{\sqrt{3}}\) 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 \(\sqrt{130}\) और \(\sqrt{145}\) की तुलना सही करता है?
Which option correctly compares \(\sqrt{130}\) and \(\sqrt{145}\)?
#comparison
#square-root
#number-line
A \(\sqrt{145}>\sqrt{130}\)
B \(\sqrt{145}<\sqrt{130}\)
C \(\sqrt{145}=\sqrt{130}\)
D तुलना संभव नहीं / Comparison is not possible
Explanation opens after your attempt
Correct Answer
A. \(\sqrt{145}>\sqrt{130}\)
Step 1
Concept
For positive numbers a larger number inside the square root gives a larger root. Here (145>130).
Step 2
Why this answer is correct
The correct answer is A. \(\sqrt{145}>\sqrt{130}\). For positive numbers a larger number inside the square root gives a larger root. Here (145>130).
Step 3
Exam Tip
धनात्मक संख्याओं में अंदर की संख्या बड़ी हो तो वर्गमूल भी बड़ा होता है। (145>130) है।
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कौन सा विकल्प \(\sqrt{11}\) के निकटतम दो पूर्णांकों को सही बताता है?
Which option correctly gives the two nearest integers between which \(\sqrt{11}\) lies?
#estimation
#square-root
#number-line
A (3) और (4) / (3) and (4)
B (2) और (3) / (2) and (3)
C (4) और (5) / (4) and (5)
D (10) और (11) / (10) and (11)
Explanation opens after your attempt
Correct Answer
A. (3) और (4) / (3) and (4)
Step 1
Concept
Since (9<11<16), \(3<\sqrt{11}<4\). Estimate using squares.
Step 2
Why this answer is correct
The correct answer is A. (3) और (4) / (3) and (4). Since (9<11<16), \(3<\sqrt{11}<4\). Estimate using squares.
Step 3
Exam Tip
क्योंकि (9<11<16) इसलिए \(3<\sqrt{11}<4\)। वर्गों की मदद से अनुमान लगाएँ।
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यदि \(x=\sqrt{23}\) है तो \(x^2+2x\) किस प्रकार की संख्या है?
If \(x=\sqrt{23}\), what type of number is \(x^2+2x\)?
#expression
#irrational-number
#square-root
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
\(x^2+2x=23+2\sqrt{23}\). The sum of a rational and an irrational number is irrational.
Step 2
Why this answer is correct
The correct answer is A. अपरिमेय संख्या / Irrational number. \(x^2+2x=23+2\sqrt{23}\). The sum of a rational and an irrational number is irrational.
Step 3
Exam Tip
\(x^2+2x=23+2\sqrt{23}\) है। परिमेय और अपरिमेय का योग अपरिमेय होता 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 \(\sqrt{245}\) 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 \(\sqrt{200}\) 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 \(\frac{\sqrt{80}}{\sqrt{5}}\) 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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कौन सा विकल्प \(\sqrt{90}\) और \(\sqrt{99}\) की तुलना सही करता है?
Which option correctly compares \(\sqrt{90}\) and \(\sqrt{99}\)?
#comparison
#square-root
#number-line
A \(\sqrt{99}>\sqrt{90}\)
B \(\sqrt{99}<\sqrt{90}\)
C \(\sqrt{99}=\sqrt{90}\)
D तुलना संभव नहीं / Comparison is not possible
Explanation opens after your attempt
Correct Answer
A. \(\sqrt{99}>\sqrt{90}\)
Step 1
Concept
For positive numbers a larger number inside the square root gives a larger value. Here (99>90).
Step 2
Why this answer is correct
The correct answer is A. \(\sqrt{99}>\sqrt{90}\). For positive numbers a larger number inside the square root gives a larger value. Here (99>90).
Step 3
Exam Tip
धनात्मक संख्याओं में अंदर की संख्या बड़ी हो तो वर्गमूल भी बड़ा होता है। (99>90) है।
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कौन सा विकल्प \(\sqrt{7}\) के निकटतम दो पूर्णांकों को सही बताता है?
Which option correctly gives the two nearest integers between which \(\sqrt{7}\) lies?
#estimation
#square-root
#number-line
A (2) और (3) / (2) and (3)
B (1) और (2) / (1) and (2)
C (3) और (4) / (3) and (4)
D (7) और (8) / (7) and (8)
Explanation opens after your attempt
Correct Answer
A. (2) और (3) / (2) and (3)
Step 1
Concept
Since (4<7<9), \(2<\sqrt{7}<3\). Locate roots using squares.
Step 2
Why this answer is correct
The correct answer is A. (2) और (3) / (2) and (3). Since (4<7<9), \(2<\sqrt{7}<3\). Locate roots using squares.
Step 3
Exam Tip
क्योंकि (4<7<9) इसलिए \(2<\sqrt{7}<3\)। जड़ की स्थिति वर्गों से पहचानें।
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