Level 2 • 50/50 questions • 35 seconds per question.
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What is the simplified surd form of \( \sqrt{180} \)?
A. \(6\sqrt{5}\)
\(180=36\times5\) इसलिए \( \sqrt{180}=6\sqrt{5} \)। सबसे बड़ा पूर्ण वर्ग गुणनखंड चुनें। / Since \(180=36\times5\), \( \sqrt{180}=6\sqrt{5} \). Choose the largest perfect-square factor.
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What is obtained by simplifying \( \sqrt{245} \)?
B. \(7\sqrt{5}\)
\(245=49\times5\) इसलिए \( \sqrt{245}=7\sqrt{5} \)। करणी में पूर्ण वर्ग को बाहर निकालें। / Since \(245=49\times5\), \( \sqrt{245}=7\sqrt{5} \). Take the perfect square outside the radical.
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Which is the simplified form of \( \sqrt{288} \)?
C. \(12\sqrt{2}\)
\(288=144\times2\) इसलिए \( \sqrt{288}=12\sqrt{2} \)। पहले सबसे बड़ा पूर्ण वर्ग खोजें। / Since \(288=144\times2\), \( \sqrt{288}=12\sqrt{2} \). First find the largest perfect square.
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What is the simplified form of \(2\sqrt{45}+3\sqrt{20}\)?
A. \(12\sqrt{5}\)
\(2\sqrt{45}=6\sqrt{5}\) और \(3\sqrt{20}=6\sqrt{5}\) है। इसलिए योग \(12\sqrt{5}\) है। / \(2\sqrt{45}=6\sqrt{5}\) and \(3\sqrt{20}=6\sqrt{5}\). So the sum is \(12\sqrt{5}\).
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What is the simplified form of \(4\sqrt{27}-2\sqrt{75}\)?
A. \(2\sqrt{3}\)
\(4\sqrt{27}=12\sqrt{3}\) और \(2\sqrt{75}=10\sqrt{3}\) है। अंतर \(2\sqrt{3}\) मिलता है। / \(4\sqrt{27}=12\sqrt{3}\) and \(2\sqrt{75}=10\sqrt{3}\). The difference is \(2\sqrt{3}\).
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What is the value of ( \sqrt{5}\(3+\sqrt{5}\) )?
A. \(3\sqrt{5}+5\)
वितरण नियम से \( \sqrt{5}\times3+\sqrt{5}\times\sqrt{5}=3\sqrt{5}+5 \)। समान करणी गुणन में सावधानी रखें। / By distributive law, \( \sqrt{5}\times3+\sqrt{5}\times\sqrt{5}=3\sqrt{5}+5 \). Be careful in surd multiplication.
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What is the expansion of ( \(4+\sqrt{3}\)2 )?
A. \(19+8\sqrt{3}\)
( (a+b)2 ) का प्रयोग करें। यहाँ \(16+8\sqrt{3}+3=19+8\sqrt{3}\) मिलता है। / Use ( (a+b)2 ). Here \(16+8\sqrt{3}+3=19+8\sqrt{3}\).
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What is the simplified form of ( \(6-\sqrt{8}\)2 )?
B. \(44-24\sqrt{2}\)
( \(6-\sqrt{8}\)2=36-12\sqrt{8}+8 ) है। \( \sqrt{8}=2\sqrt{2} \) रखने पर \(44-24\sqrt{2}\) मिलता है। / ( \(6-\sqrt{8}\)2=36-12\sqrt{8}+8 ). Using \( \sqrt{8}=2\sqrt{2} \), it becomes \(44-24\sqrt{2}\).
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What is the value of ( \(5+\sqrt{17}\)\(5-\sqrt{17}\) )?
B. (8)
यह संयुग्मी गुणन है। (52-\(\sqrt{17}\)2=25-17=8) होगा। / This is conjugate multiplication. (52-\(\sqrt{17}\)2=25-17=8).
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What is the value of ( \(2+\sqrt{19}\)\(2-\sqrt{19}\) )?
B. ( -15 )
संयुग्मी गुणन से (22-\(\sqrt{19}\)2=4-19=-15) मिलता है। मध्य पद कट जाते हैं। / Conjugate multiplication gives (22-\(\sqrt{19}\)2=4-19=-15). The middle terms cancel.
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What is the rationalised form of \( \frac{6}{\sqrt{7}} \)?
A. \( \frac{6\sqrt{7}}{7} \)
अंश और हर को \( \sqrt{7} \) से गुणा करें। इससे हर (7) हो जाता है। / Multiply numerator and denominator by \( \sqrt{7} \). This makes the denominator (7).
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What is the rationalised form of \( \frac{5}{3\sqrt{2}} \)?
A. \( \frac{5\sqrt{2}}{6} \)
अंश और हर को \( \sqrt{2} \) से गुणा करने पर \( \frac{5\sqrt{2}}{6} \) मिलता है। हर से करणी हटनी चाहिए। / Multiplying numerator and denominator by \( \sqrt{2} \) gives \( \frac{5\sqrt{2}}{6} \). The radical should be removed from the denominator.
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What is the rationalised form of \( \frac{1}{\sqrt{10}+\sqrt{9}} \)?
A. \( \sqrt{10}-3 \)
हर \( \sqrt{10}+3 \) है और संयुग्मी \( \sqrt{10}-3 \) होगा। हर (10-9=1) बनता है। / The denominator is \( \sqrt{10}+3 \) and its conjugate is \( \sqrt{10}-3 \). The denominator becomes (10-9=1).
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What is the rationalised form of \( \frac{1}{\sqrt{11}-\sqrt{2}} \)?
A. \( \frac{\sqrt{11}+\sqrt{2}}{9} \)
संयुग्मी \( \sqrt{11}+\sqrt{2} \) से गुणा करें। हर (11-2=9) मिलेगा। / Multiply by the conjugate \( \sqrt{11}+\sqrt{2} \). The denominator becomes (11-2=9).
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What is the simplified form of \( \sqrt{98}+\sqrt{162}-\sqrt{50} \)?
A. \(11\sqrt{2}\)
\( \sqrt{98}=7\sqrt{2} \), \( \sqrt{162}=9\sqrt{2} \), और \( \sqrt{50}=5\sqrt{2} \)। इसलिए परिणाम \(11\sqrt{2}\) है। / \( \sqrt{98}=7\sqrt{2} \), \( \sqrt{162}=9\sqrt{2} \), and \( \sqrt{50}=5\sqrt{2} \). So the result is \(11\sqrt{2}\).
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What is the simplified form of \(2\sqrt{44}+3\sqrt{99}\)?
B. \(13\sqrt{11}\)
\(2\sqrt{44}=4\sqrt{11}\) और \(3\sqrt{99}=9\sqrt{11}\) है। योग \(13\sqrt{11}\) होगा। / \(2\sqrt{44}=4\sqrt{11}\) and \(3\sqrt{99}=9\sqrt{11}\). The sum is \(13\sqrt{11}\).
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What is the simplified form of \( \sqrt{112}+2\sqrt{175} \)?
B. \(14\sqrt{7}\)
\( \sqrt{112}=4\sqrt{7} \) और \(2\sqrt{175}=10\sqrt{7}\) है। योग \(14\sqrt{7}\) है। / \( \sqrt{112}=4\sqrt{7} \) and \(2\sqrt{175}=10\sqrt{7}\). The sum is \(14\sqrt{7}\).
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What is the simplified form of \(5\sqrt{48}-3\sqrt{75}\)?
A. \(5\sqrt{3}\)
\(5\sqrt{48}=20\sqrt{3}\) और \(3\sqrt{75}=15\sqrt{3}\) है। अंतर \(5\sqrt{3}\) मिलता है। / \(5\sqrt{48}=20\sqrt{3}\) and \(3\sqrt{75}=15\sqrt{3}\). The difference is \(5\sqrt{3}\).
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What is the value of \( \sqrt{32}\times\sqrt{50} \)?
A. (40)
\( \sqrt{32}\times\sqrt{50}=\sqrt{1600}=40 \)। करणी गुणन में अंदर की संख्याएँ गुणा करें। / \( \sqrt{32}\times\sqrt{50}=\sqrt{1600}=40 \). In radical multiplication, multiply the radicands.
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What is the value of \( \sqrt{180}\div\sqrt{20} \)?
B. (3)
\( \frac{\sqrt{180}}{\sqrt{20}}=\sqrt{9}=3 \)। वर्गमूल के भाग में अंदर की संख्याओं का भाग लें। / \( \frac{\sqrt{180}}{\sqrt{20}}=\sqrt{9}=3 \). In division of square roots, divide the radicands.
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What is the value of \( \frac{\sqrt{200}}{\sqrt{2}}+\sqrt{16} \)?
A. (14)
\( \frac{\sqrt{200}}{\sqrt{2}}=\sqrt{100}=10 \) और \( \sqrt{16}=4 \)। कुल मान (14) है। / \( \frac{\sqrt{200}}{\sqrt{2}}=\sqrt{100}=10 \) and \( \sqrt{16}=4 \). The total value is (14).
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What is the value of \( \sqrt{1.69}+\sqrt{0.09} \)?
A. (1.6)
\( \sqrt{1.69}=1.3 \) और \( \sqrt{0.09}=0.3 \) है। योग (1.6) होगा। / \( \sqrt{1.69}=1.3 \) and \( \sqrt{0.09}=0.3 \). The sum is (1.6).
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What is the value of \( \sqrt{4.84}-\sqrt{1.44} \)?
A. (1)
\( \sqrt{4.84}=2.2 \) और \( \sqrt{1.44}=1.2 \) है। अंतर (1) है। / \( \sqrt{4.84}=2.2 \) and \( \sqrt{1.44}=1.2 \). The difference is (1).
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What is the value of \( \sqrt{\frac{16}{25}}+\sqrt{\frac{9}{64}} \)?
A. \( \frac{47}{40} \)
पहला पद \( \frac{4}{5} \) और दूसरा \( \frac{3}{8} \) है। योग \( \frac{32}{40}+\frac{15}{40}=\frac{47}{40} \) है। / The first term is \( \frac{4}{5} \) and the second is \( \frac{3}{8} \). The sum is \( \frac{32}{40}+\frac{15}{40}=\frac{47}{40} \).
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What is the value of \( \sqrt{\frac{81}{121}}-\sqrt{\frac{4}{49}} \)?
B. \( \frac{41}{77} \)
\( \sqrt{\frac{81}{121}}=\frac{9}{11} \) और \( \sqrt{\frac{4}{49}}=\frac{2}{7} \) है। अंतर \( \frac{63}{77}-\frac{22}{77}=\frac{41}{77} \) है। / \( \sqrt{\frac{81}{121}}=\frac{9}{11} \) and \( \sqrt{\frac{4}{49}}=\frac{2}{7} \). The difference is \( \frac{63}{77}-\frac{22}{77}=\frac{41}{77} \).
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Which option is an irrational number between (5) and (6)?
B. \( \sqrt{31} \)
\(5^2<31<6^2\) इसलिए \( \sqrt{31} \) (5) और (6) के बीच है। (31) पूर्ण वर्ग नहीं है इसलिए यह अपरिमेय है। / Since \(5^2<31<6^2\), \( \sqrt{31} \) lies between (5) and (6). Since (31) is not a perfect square, it is irrational.
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Which is greater between \( \sqrt{45} \) and \( \frac{13}{2} \)?
A. \( \sqrt{45} \)
\( \sqrt{45}\approx6.70 \) और \( \frac{13}{2}=6.5 \) है। इसलिए \( \sqrt{45} \) बड़ा है। / \( \sqrt{45}\approx6.70 \) and \( \frac{13}{2}=6.5 \). Therefore \( \sqrt{45} \) is greater.
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Between which two integers does \( \sqrt{68} \) lie?
C. (8) और (9)(8) and (9)
\(8^2=64\) और \(9^2=81\) है इसलिए \( \sqrt{68} \) (8) और (9) के बीच है। निकट पूर्ण वर्गों की तुलना करें। / \(8^2=64\) and \(9^2=81\), so \( \sqrt{68} \) lies between (8) and (9). Compare nearby perfect squares.
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Between which two integers will \( \sqrt{86} \) lie?
C. (9) और (10)(9) and (10)
\(9^2=81\) और \(10^2=100\) है इसलिए \( \sqrt{86} \) (9) और (10) के बीच है। वर्ग करके सीमा जाँचें। / \(9^2=81\) and \(10^2=100\), so \( \sqrt{86} \) lies between (9) and (10). Check the range by squaring.
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Which is greater between \( -\sqrt{50} \) and ( -7.2 )?
A. \( -\sqrt{50} \)
\( \sqrt{50}\approx7.07 \) इसलिए \( -\sqrt{50}\approx-7.07 \)। यह ( -7.2 ) से बड़ी है क्योंकि यह शून्य के अधिक निकट है। / \( \sqrt{50}\approx7.07 \), so \( -\sqrt{50}\approx-7.07 \). It is greater than ( -7.2 ) because it is closer to zero.
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If (0.2020020002...) 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 (3.454545...)?
B. परिमेय वास्तविक संख्याRational real number
(45) बार-बार आ रहा है इसलिए दशमलव आवर्ती है। आवर्ती दशमलव परिमेय होते हैं। / The block (45) repeats, so the decimal is repeating. Repeating decimals are rational.
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If (0.070070007...) 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 \( \frac{8}{13} \)?
B. यह असमाप्त आवर्ती दशमलव हैIt is non-terminating repeating
हर (13) में (2) या (5) के अलावा गुणनखंड है। इसलिए दशमलव असमाप्त आवर्ती होगा। / The denominator (13) 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 \( \frac{21}{80} \)?
A. यह समाप्त दशमलव हैIt is terminating
\(80=2^4\times5\) है इसलिए हर में केवल (2) और (5) हैं। ऐसा भिन्न समाप्त दशमलव देता है। / \(80=2^4\times5\), 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 \( \frac{5}{42} \)?
B. यह असमाप्त आवर्ती दशमलव हैIt is non-terminating repeating decimal
\(42=2\times3\times7\) में (3) और (7) हैं। इसलिए दशमलव समाप्त नहीं होगा लेकिन आवर्ती होगा। / \(42=2\times3\times7\) has (3) and (7). So the decimal will not terminate but will repeat.
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What type will \( \frac{29}{200} \) be in decimal form?
A. समाप्त दशमलवTerminating decimal
\(200=2^3\times5^2\) है इसलिए हर में केवल (2) और (5) हैं। ऐसा भिन्न समाप्त दशमलव देता है। / \(200=2^3\times5^2\), 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 \( \frac{31}{45} \)?
B. असमाप्त आवर्तीNon-terminating repeating
\(45=3^2\times5\) में (3) भी है। इसलिए यह असमाप्त आवर्ती दशमलव होगा। / \(45=3^2\times5\) also has (3). Therefore it will be a non-terminating repeating decimal.
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What is \( \sqrt{6}+\sqrt{24} \) equal to?
A. \(3\sqrt{6}\)
\( \sqrt{24}=2\sqrt{6} \) है। इसलिए \( \sqrt{6}+2\sqrt{6}=3\sqrt{6} \)। / \( \sqrt{24}=2\sqrt{6} \). Therefore \( \sqrt{6}+2\sqrt{6}=3\sqrt{6} \).
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What type of number is \( \sqrt{12}\times\sqrt{75} \)?
A. परिमेय वास्तविक संख्याRational real number
\( \sqrt{12}\times\sqrt{75}=\sqrt{900}=30 \) है। इसलिए परिणाम परिमेय वास्तविक संख्या है। / \( \sqrt{12}\times\sqrt{75}=\sqrt{900}=30 \). Therefore the result is a rational real number.
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What type of number is \( \sqrt{3}\times\sqrt{21} \)?
B. अपरिमेय वास्तविक संख्याIrrational real number
\( \sqrt{3}\times\sqrt{21}=\sqrt{63}=3\sqrt{7} \) है। यह अपरिमेय वास्तविक संख्या है। / \( \sqrt{3}\times\sqrt{21}=\sqrt{63}=3\sqrt{7} \). This is an irrational real number.
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What is the product of \(3+\sqrt{14}\) and \(3-\sqrt{14}\)?
B. ( -5 )
संयुग्मी गुणन से (32-\(\sqrt{14}\)2=9-14=-5) मिलता है। अंतर के वर्ग का नियम लगाएँ। / Conjugate multiplication gives (32-\(\sqrt{14}\)2=9-14=-5). Use the difference of squares rule.
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What is the value of \( \frac{3+\sqrt{2}}{3-\sqrt{2}} \) after rationalising?
A. \( \frac{11+6\sqrt{2}}{7} \)
हर के संयुग्मी \(3+\sqrt{2}\) से गुणा करें। अंश (\(3+\sqrt{2}\)2=11+6\sqrt{2}) और हर (7) होगा। / Multiply by the conjugate \(3+\sqrt{2}\). The numerator is (\(3+\sqrt{2}\)2=11+6\sqrt{2}) and the denominator is (7).
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What will be the denominator after rationalising \( \frac{\sqrt{7}+2}{\sqrt{7}-2} \)?
A. (3)
हर के संयुग्मी \( \sqrt{7}+2 \) से गुणा करने पर हर (7-4=3) होगा। संयुग्मी विधि में अंतर के वर्ग का प्रयोग करें। / Multiplying by the conjugate \( \sqrt{7}+2 \) makes the denominator (7-4=3). Use difference of squares in the conjugate method.
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What is the value of \( |-\sqrt{64}+5| \)?
A. (3)
\( -\sqrt{64}+5=-8+5=-3 \) है और ( |-3|=3 )। निरपेक्ष मान दूरी देता है। / \( -\sqrt{64}+5=-8+5=-3 \) and ( |-3|=3 ). Absolute value gives distance.
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What is the value of \( |\sqrt{25}-\sqrt{100}| \)?
A. (5)
\( \sqrt{25}=5 \) और \( \sqrt{100}=10 \) है। ( |5-10|=5 ) होगा। / \( \sqrt{25}=5 \) and \( \sqrt{100}=10 \). So ( |5-10|=5 ).
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What is the value of ( \sqrt{( -9)2} )?
B. (9)
वास्तविक संख्याओं में \( \sqrt{a^2}=|a| \) होता है। इसलिए ( \sqrt{( -9)2}=9 )। / In real numbers, \( \sqrt{a^2}=|a| \). Therefore ( \sqrt{( -9)2}=9 ).
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If (x=-8), what is the value of \( \sqrt{x^2}+x \)?
A. (0)
\( \sqrt{x^2}=|x| \) होता है। (x=-8) होने पर (8+(-8)=0) मिलेगा। / \( \sqrt{x^2}=|x| \). When (x=-8), we get (8+(-8)=0).
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What is the rationalised form of \( \frac{1}{5+2\sqrt{6}} \)?
D. \(5-2\sqrt{6}\)
संयुग्मी \(5-2\sqrt{6}\) से गुणा करने पर हर (25-24=1) बनता है। इसलिए परिमेय हर वाला रूप \(5-2\sqrt{6}\) है। / Multiplying by the conjugate \(5-2\sqrt{6}\) makes the denominator (25-24=1). So the rationalised form is \(5-2\sqrt{6}\).
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What is the simplified form of \( \sqrt{242}-\sqrt{128} \)?
C. \(3\sqrt{2}\)
\( \sqrt{242}=11\sqrt{2} \) और \( \sqrt{128}=8\sqrt{2} \) है। इसलिए अंतर \(3\sqrt{2}\) मिलता है। / \( \sqrt{242}=11\sqrt{2} \) and \( \sqrt{128}=8\sqrt{2} \). Therefore the difference is \(3\sqrt{2}\).
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