Level 3 • 50/50 questions • 35 seconds per question.
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What is the simplified surd form of \( \sqrt{320} \)?
A. \(8\sqrt{5}\)
\(320=64\times5\) इसलिए \( \sqrt{320}=8\sqrt{5} \)। सबसे बड़ा पूर्ण वर्ग गुणनखंड निकालें। / Since \(320=64\times5\), \( \sqrt{320}=8\sqrt{5} \). Take out the largest perfect-square factor.
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What is obtained by simplifying \( \sqrt{363} \)?
B. \(11\sqrt{3}\)
\(363=121\times3\) इसलिए \( \sqrt{363}=11\sqrt{3} \)। करणी में पूर्ण वर्ग को बाहर निकालें। / Since \(363=121\times3\), \( \sqrt{363}=11\sqrt{3} \). Take the perfect square out of the radical.
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Which is the simplified form of \( \sqrt{432} \)?
C. \(12\sqrt{3}\)
\(432=144\times3\) इसलिए \( \sqrt{432}=12\sqrt{3} \)। पहले सबसे बड़ा पूर्ण वर्ग खोजें। / Since \(432=144\times3\), \( \sqrt{432}=12\sqrt{3} \). First find the largest perfect square.
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What is the simplified form of \(3\sqrt{28}+2\sqrt{63}\)?
B. \(12\sqrt{7}\)
\(3\sqrt{28}=6\sqrt{7}\) और \(2\sqrt{63}=6\sqrt{7}\) है। इसलिए योग \(12\sqrt{7}\) है। / \(3\sqrt{28}=6\sqrt{7}\) and \(2\sqrt{63}=6\sqrt{7}\). So the sum is \(12\sqrt{7}\).
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What is the simplified form of \(6\sqrt{32}-4\sqrt{18}\)?
A. \(12\sqrt{2}\)
\(6\sqrt{32}=24\sqrt{2}\) और \(4\sqrt{18}=12\sqrt{2}\) है। अंतर \(12\sqrt{2}\) मिलता है। / \(6\sqrt{32}=24\sqrt{2}\) and \(4\sqrt{18}=12\sqrt{2}\). The difference is \(12\sqrt{2}\).
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What is the value of ( \sqrt{7}\(4+\sqrt{7}\) )?
B. \(4\sqrt{7}+7\)
वितरण नियम से \( \sqrt{7}\times4+\sqrt{7}\times\sqrt{7}=4\sqrt{7}+7 \)। समान वर्गमूल का गुणन अंदर की संख्या देता है। / By distributive law, \( \sqrt{7}\times4+\sqrt{7}\times\sqrt{7}=4\sqrt{7}+7 \). Multiplying the same square root gives the radicand.
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What is the expansion of ( \(5+\sqrt{2}\)2 )?
C. \(27+10\sqrt{2}\)
( (a+b)2 ) का प्रयोग करें। यहाँ \(25+10\sqrt{2}+2=27+10\sqrt{2}\) मिलता है। / Use ( (a+b)2 ). Here \(25+10\sqrt{2}+2=27+10\sqrt{2}\).
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What is the simplified form of ( \(7-\sqrt{3}\)2 )?
A. \(52-14\sqrt{3}\)
( (a-b)2=a-2-2ab+b-2 ) से \(49-14\sqrt{3}+3=52-14\sqrt{3}\) मिलता है। संकेतों पर ध्यान दें। / Using ( (a-b)2=a-2-2ab+b-2 ), we get \(49-14\sqrt{3}+3=52-14\sqrt{3}\). Watch the signs carefully.
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What is the value of ( \(6+\sqrt{23}\)\(6-\sqrt{23}\) )?
B. (13)
यह संयुग्मी गुणन है। (62-\(\sqrt{23}\)2=36-23=13) होगा। / This is conjugate multiplication. (62-\(\sqrt{23}\)2=36-23=13).
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What is the value of ( \(4+\sqrt{29}\)\(4-\sqrt{29}\) )?
B. ( -13 )
संयुग्मी गुणन से (42-\(\sqrt{29}\)2=16-29=-13) मिलता है। मध्य पद कट जाते हैं। / Conjugate multiplication gives (42-\(\sqrt{29}\)2=16-29=-13). The middle terms cancel.
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What is the rationalised form of \( \frac{8}{\sqrt{11}} \)?
A. \( \frac{8\sqrt{11}}{11} \)
अंश और हर को \( \sqrt{11} \) से गुणा करें। इससे हर (11) हो जाता है। / Multiply numerator and denominator by \( \sqrt{11} \). This makes the denominator (11).
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What is the rationalised form of \( \frac{9}{4\sqrt{5}} \)?
A. \( \frac{9\sqrt{5}}{20} \)
अंश और हर को \( \sqrt{5} \) से गुणा करने पर \( \frac{9\sqrt{5}}{20} \) मिलता है। हर से करणी हटनी चाहिए। / Multiplying numerator and denominator by \( \sqrt{5} \) gives \( \frac{9\sqrt{5}}{20} \). The radical should be removed from the denominator.
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What is the rationalised form of \( \frac{1}{\sqrt{13}+\sqrt{12}} \)?
A. \( \sqrt{13}-2\sqrt{3} \)
हर \( \sqrt{13}+2\sqrt{3} \) है और संयुग्मी \( \sqrt{13}-2\sqrt{3} \) होगा। हर (13-12=1) बनता है। / The denominator is \( \sqrt{13}+2\sqrt{3} \) and its conjugate is \( \sqrt{13}-2\sqrt{3} \). The denominator becomes (13-12=1).
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What is the rationalised form of \( \frac{1}{\sqrt{17}-\sqrt{8}} \)?
A. \( \frac{\sqrt{17}+\sqrt{8}}{9} \)
संयुग्मी \( \sqrt{17}+\sqrt{8} \) से गुणा करें। हर (17-8=9) मिलेगा। / Multiply by the conjugate \( \sqrt{17}+\sqrt{8} \). The denominator becomes (17-8=9).
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What is the simplified form of \( \sqrt{128}+\sqrt{200}-\sqrt{72} \)?
A. \(12\sqrt{2}\)
\( \sqrt{128}=8\sqrt{2} \), \( \sqrt{200}=10\sqrt{2} \), और \( \sqrt{72}=6\sqrt{2} \)। इसलिए परिणाम \(12\sqrt{2}\) है। / \( \sqrt{128}=8\sqrt{2} \), \( \sqrt{200}=10\sqrt{2} \), and \( \sqrt{72}=6\sqrt{2} \). So the result is \(12\sqrt{2}\).
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What is the simplified form of \(3\sqrt{54}+2\sqrt{150}\)?
B. \(19\sqrt{6}\)
\(3\sqrt{54}=9\sqrt{6}\) और \(2\sqrt{150}=10\sqrt{6}\) है। योग \(19\sqrt{6}\) होगा। / \(3\sqrt{54}=9\sqrt{6}\) and \(2\sqrt{150}=10\sqrt{6}\). The sum is \(19\sqrt{6}\).
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What is the simplified form of \( \sqrt{200}+3\sqrt{72} \)?
A. \(28\sqrt{2}\)
\( \sqrt{200}=10\sqrt{2} \) और \(3\sqrt{72}=18\sqrt{2}\) है। योग \(28\sqrt{2}\) है। / \( \sqrt{200}=10\sqrt{2} \) and \(3\sqrt{72}=18\sqrt{2}\). The sum is \(28\sqrt{2}\).
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What is the simplified form of \(7\sqrt{27}-2\sqrt{108}\)?
A. \(9\sqrt{3}\)
\(7\sqrt{27}=21\sqrt{3}\) और \(2\sqrt{108}=12\sqrt{3}\) है। अंतर \(9\sqrt{3}\) मिलता है। / \(7\sqrt{27}=21\sqrt{3}\) and \(2\sqrt{108}=12\sqrt{3}\). The difference is \(9\sqrt{3}\).
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What is the value of \( \sqrt{45}\times\sqrt{80} \)?
A. (60)
\( \sqrt{45}\times\sqrt{80}=\sqrt{3600}=60 \)। करणी गुणन में अंदर की संख्याएँ गुणा करें। / \( \sqrt{45}\times\sqrt{80}=\sqrt{3600}=60 \). In radical multiplication, multiply the radicands.
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What is the value of \( \sqrt{242}\div\sqrt{2} \)?
B. (11)
\( \frac{\sqrt{242}}{\sqrt{2}}=\sqrt{121}=11 \)। वर्गमूल के भाग में अंदर की संख्याओं का भाग लें। / \( \frac{\sqrt{242}}{\sqrt{2}}=\sqrt{121}=11 \). In division of square roots, divide the radicands.
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What is the value of \( \frac{\sqrt{392}}{\sqrt{2}}+\sqrt{25} \)?
A. (19)
\( \frac{\sqrt{392}}{\sqrt{2}}=\sqrt{196}=14 \) और \( \sqrt{25}=5 \)। कुल मान (19) है। / \( \frac{\sqrt{392}}{\sqrt{2}}=\sqrt{196}=14 \) and \( \sqrt{25}=5 \). The total value is (19).
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What is the value of \( \sqrt{3.24}+\sqrt{0.49} \)?
A. (2.5)
\( \sqrt{3.24}=1.8 \) और \( \sqrt{0.49}=0.7 \) है। योग (2.5) होगा। / \( \sqrt{3.24}=1.8 \) and \( \sqrt{0.49}=0.7 \). The sum is (2.5).
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What is the value of \( \sqrt{6.25}-\sqrt{0.64} \)?
A. (1.7)
\( \sqrt{6.25}=2.5 \) और \( \sqrt{0.64}=0.8 \) है। अंतर (1.7) है। / \( \sqrt{6.25}=2.5 \) and \( \sqrt{0.64}=0.8 \). The difference is (1.7).
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What is the value of \( \sqrt{\frac{25}{49}}+\sqrt{\frac{16}{81}} \)?
A. \( \frac{73}{63} \)
पहला पद \( \frac{5}{7} \) और दूसरा \( \frac{4}{9} \) है। योग \( \frac{45}{63}+\frac{28}{63}=\frac{73}{63} \) है। / The first term is \( \frac{5}{7} \) and the second is \( \frac{4}{9} \). The sum is \( \frac{45}{63}+\frac{28}{63}=\frac{73}{63} \).
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What is the value of \( \sqrt{\frac{100}{169}}-\sqrt{\frac{9}{64}} \)?
A. \( \frac{41}{104} \)
\( \sqrt{\frac{100}{169}}=\frac{10}{13} \) और \( \sqrt{\frac{9}{64}}=\frac{3}{8} \) है। अंतर \( \frac{80}{104}-\frac{39}{104}=\frac{41}{104} \) है। / \( \sqrt{\frac{100}{169}}=\frac{10}{13} \) and \( \sqrt{\frac{9}{64}}=\frac{3}{8} \). The difference is \( \frac{80}{104}-\frac{39}{104}=\frac{41}{104} \).
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Which option is an irrational number between (6) and (7)?
B. \( \sqrt{43} \)
\(6^2<43<7^2\) इसलिए \( \sqrt{43} \) (6) और (7) के बीच है। (43) पूर्ण वर्ग नहीं है इसलिए यह अपरिमेय है। / Since \(6^2<43<7^2\), \( \sqrt{43} \) lies between (6) and (7). Since (43) is not a perfect square, it is irrational.
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Which is greater between \( \sqrt{63} \) and (8)?
B. (8)
\( \sqrt{63}<\sqrt{64}=8 \) है। इसलिए (8) बड़ा है।
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Between which two integers does \( \sqrt{101} \) lie?
C. (10) और (11)(10) and (11)
\(10^2=100\) और \(11^2=121\) है इसलिए \( \sqrt{101} \) (10) और (11) के बीच है। निकट पूर्ण वर्गों की तुलना करें। / \(10^2=100\) and \(11^2=121\), so \( \sqrt{101} \) lies between (10) and (11). Compare nearby perfect squares.
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Between which two integers will \( \sqrt{130} \) lie?
C. (11) और (12)(11) and (12)
\(11^2=121\) और \(12^2=144\) है इसलिए \( \sqrt{130} \) (11) और (12) के बीच है। सीमा वर्ग करके जाँचें। / \(11^2=121\) and \(12^2=144\), so \( \sqrt{130} \) lies between (11) and (12). Check the range by squaring.
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Which is greater between \( -\sqrt{65} \) and ( -8.1 )?
B. ( -8.1 )
\( \sqrt{65}\approx8.06 \) इसलिए \( -\sqrt{65}\approx-8.06 \)। ( -8.06 ) ( -8.1 ) से बड़ा होता है। / \( \sqrt{65}\approx8.06 \), so \( -\sqrt{65}\approx-8.06 \). ( -8.06 ) is greater than ( -8.1 ).
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If (0.3030030003...) has no fixed repetition, what type of number is it?
B. अपरिमेय वास्तविक संख्याIrrational real number
असमाप्त और अनावर्ती दशमलव अपरिमेय होता है। आवर्ती और अनावर्ती में अंतर पहचानें। / A non-terminating and non-repeating decimal is irrational. Identify the difference between repeating and non-repeating.
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What type of real number is (4.616161...)?
B. परिमेय वास्तविक संख्याRational real number
(61) बार-बार आ रहा है इसलिए दशमलव आवर्ती है। आवर्ती दशमलव परिमेय होते हैं। / The block (61) repeats, so the decimal is repeating. Repeating decimals are rational.
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If (0.090090009...) has no regular repetition, what is it?
C. अपरिमेय वास्तविक संख्याIrrational real number
नियमित आवृत्ति न होने पर असमाप्त दशमलव अपरिमेय होता है। केवल स्थिर आवर्ती दशमलव परिमेय होते हैं। / A non-terminating decimal without regular repetition is irrational. Only fixed repeating decimals are rational.
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What is the correct statement about the decimal form of \( \frac{11}{17} \)?
B. यह असमाप्त आवर्ती दशमलव हैIt is non-terminating repeating
हर (17) में (2) या (5) के अलावा गुणनखंड है। इसलिए दशमलव असमाप्त आवर्ती होगा। / The denominator (17) has factors other than (2) or (5). Therefore the decimal will be non-terminating repeating.
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What is the correct statement about the decimal form of \( \frac{33}{160} \)?
A. यह समाप्त दशमलव हैIt is terminating
\(160=2^5\times5\) है इसलिए हर में केवल (2) और (5) हैं। ऐसा भिन्न समाप्त दशमलव देता है। / \(160=2^5\times5\), so the denominator has only (2) and (5). Such a fraction gives a terminating decimal.
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What is the correct statement about the decimal form of \( \frac{7}{66} \)?
B. यह असमाप्त आवर्ती दशमलव हैIt is non-terminating repeating decimal
\(66=2\times3\times11\) में (3) और (11) हैं। इसलिए दशमलव समाप्त नहीं होगा लेकिन आवर्ती होगा। / \(66=2\times3\times11\) has (3) and (11). So the decimal will not terminate but will repeat.
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What type will \( \frac{41}{500} \) be in decimal form?
A. समाप्त दशमलवTerminating decimal
\(500=2^2\times5^3\) है इसलिए हर में केवल (2) और (5) हैं। ऐसा भिन्न समाप्त दशमलव देता है। / \(500=2^2\times5^3\), so the denominator has only (2) and (5). Such a fraction gives a terminating decimal.
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What will be the decimal expansion of \( \frac{37}{54} \)?
B. असमाप्त आवर्तीNon-terminating repeating
\(54=2\times3^3\) में (3) भी है। इसलिए यह असमाप्त आवर्ती दशमलव होगा। / \(54=2\times3^3\) also has (3). Therefore it will be a non-terminating repeating decimal.
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What is \( \sqrt{10}+\sqrt{40} \) equal to?
A. \(3\sqrt{10}\)
\( \sqrt{40}=2\sqrt{10} \) है। इसलिए \( \sqrt{10}+2\sqrt{10}=3\sqrt{10} \)। / \( \sqrt{40}=2\sqrt{10} \). Therefore \( \sqrt{10}+2\sqrt{10}=3\sqrt{10} \).
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What type of number is \( \sqrt{18}\times\sqrt{50} \)?
A. परिमेय वास्तविक संख्याRational real number
\( \sqrt{18}\times\sqrt{50}=\sqrt{900}=30 \) है। इसलिए परिणाम परिमेय वास्तविक संख्या है। / \( \sqrt{18}\times\sqrt{50}=\sqrt{900}=30 \). Therefore the result is a rational real number.
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What type of number is \( \sqrt{5}\times\sqrt{45} \)?
B. परिमेय वास्तविक संख्याRational real number
\( \sqrt{5}\times\sqrt{45}=\sqrt{225}=15 \) है। इसलिए परिणाम परिमेय वास्तविक संख्या है। / \( \sqrt{5}\times\sqrt{45}=\sqrt{225}=15 \). Therefore the result is a rational real number.
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What is the product of \(4+\sqrt{21}\) and \(4-\sqrt{21}\)?
B. ( -5 )
संयुग्मी गुणन से (42-\(\sqrt{21}\)2=16-21=-5) मिलता है। अंतर के वर्ग का नियम लगाएँ। / Conjugate multiplication gives (42-\(\sqrt{21}\)2=16-21=-5). Use the difference of squares rule.
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What is the value of \( \frac{4+\sqrt{3}}{4-\sqrt{3}} \) after rationalising?
A. \( \frac{19+8\sqrt{3}}{13} \)
हर के संयुग्मी \(4+\sqrt{3}\) से गुणा करें। अंश (\(4+\sqrt{3}\)2=19+8\sqrt{3}) और हर (13) होगा। / Multiply by the conjugate \(4+\sqrt{3}\). The numerator is (\(4+\sqrt{3}\)2=19+8\sqrt{3}) and the denominator is (13).
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What will be the denominator after rationalising \( \frac{\sqrt{11}+3}{\sqrt{11}-3} \)?
A. (2)
हर के संयुग्मी \( \sqrt{11}+3 \) से गुणा करने पर हर (11-9=2) होगा। संयुग्मी विधि में अंतर के वर्ग का प्रयोग करें। / Multiplying by the conjugate \( \sqrt{11}+3 \) makes the denominator (11-9=2). Use difference of squares in the conjugate method.
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What is the value of \( |-\sqrt{100}+6| \)?
A. (4)
\( -\sqrt{100}+6=-10+6=-4 \) है और ( |-4|=4 )। निरपेक्ष मान दूरी देता है। / \( -\sqrt{100}+6=-10+6=-4 \) and ( |-4|=4 ). Absolute value gives distance.
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What is the value of \( |\sqrt{36}-\sqrt{121}| \)?
A. (5)
\( \sqrt{36}=6 \) और \( \sqrt{121}=11 \) है। ( |6-11|=5 ) होगा। / \( \sqrt{36}=6 \) and \( \sqrt{121}=11 \). So ( |6-11|=5 ).
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What is the value of ( \sqrt{( -12)2} )?
B. (12)
वास्तविक संख्याओं में \( \sqrt{a^2}=|a| \) होता है। इसलिए ( \sqrt{( -12)2}=12 )। / In real numbers, \( \sqrt{a^2}=|a| \). Therefore ( \sqrt{( -12)2}=12 ).
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If (x=-15), what is the value of \( \sqrt{x^2}-x \)?
C. (30)
\( \sqrt{x^2}=|x| \) होता है। (x=-15) होने पर (15-(-15)=30) मिलेगा। / \( \sqrt{x^2}=|x| \). When (x=-15), we get (15-(-15)=30).
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What is the rationalised form of \( \frac{1}{6+\sqrt{35}} \)?
A. \(6-\sqrt{35}\)
संयुग्मी \(6-\sqrt{35}\) से गुणा करने पर हर (36-35=1) बनता है। इसलिए परिमेय हर वाला रूप \(6-\sqrt{35}\) है। / Multiplying by the conjugate \(6-\sqrt{35}\) makes the denominator (36-35=1). So the rationalised form is \(6-\sqrt{35}\).
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What is the simplified form of \( \sqrt{500}-\sqrt{180}+\sqrt{45} \)?
A. \(7\sqrt{5}\)
\( \sqrt{500}=10\sqrt{5} \), \( \sqrt{180}=6\sqrt{5} \), और \( \sqrt{45}=3\sqrt{5} \)। इसलिए \(10\sqrt{5}-6\sqrt{5}+3\sqrt{5}=7\sqrt{5}\) है। / \( \sqrt{500}=10\sqrt{5} \), \( \sqrt{180}=6\sqrt{5} \), and \( \sqrt{45}=3\sqrt{5} \). Therefore \(10\sqrt{5}-6\sqrt{5}+3\sqrt{5}=7\sqrt{5}\).
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