Level 6 • 50/50 questions • 40 seconds per question.
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What type of real number is \( \sqrt{64} \)?
A. परिमेय वास्तविक संख्याRational real number
\( \sqrt{64}=8 \) है और (8) परिमेय संख्या है। पूर्ण वर्ग का वर्गमूल परिमेय होता है। / \( \sqrt{64}=8 \) and (8) is rational. The square root of a perfect square is rational.
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Which decimal is a rational real number?
B. (0.272727...)
(0.272727...) आवर्ती दशमलव है इसलिए परिमेय है। आवर्ती दशमलव को भिन्न में बदला जा सकता है। / (0.272727...) is repeating so it is rational. A repeating decimal can be converted into a fraction.
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Between which two integers does \( \sqrt{11} \) lie on the number line?
C. (3) और (4)(3) and (4)
\(3^2=9\) और \(4^2=16\) है इसलिए \( \sqrt{11} \) (3) और (4) के बीच है। वर्गों से वर्गमूल का स्थान पहचानें। / \(3^2=9\) and \(4^2=16\) so \( \sqrt{11} \) lies between (3) and (4). Use squares to locate square roots.
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What is the simplified surd form of \( \sqrt{98} \)?
A. \(7\sqrt{2}\)
\(98=49\times2\) इसलिए \( \sqrt{98}=7\sqrt{2} \)। सबसे बड़ा पूर्ण वर्ग गुणनखंड चुनें। / Since \(98=49\times2\), \( \sqrt{98}=7\sqrt{2} \). Choose the largest perfect-square factor.
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What is obtained by simplifying \( \sqrt{72} \)?
B. \(6\sqrt{2}\)
\(72=36\times2\) इसलिए \( \sqrt{72}=6\sqrt{2} \)। पूर्ण वर्ग को वर्गमूल से बाहर निकालें। / Since \(72=36\times2\), \( \sqrt{72}=6\sqrt{2} \). Take the perfect square outside the square root.
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Which is the simplified form of \( \sqrt{63} \)?
C. \(3\sqrt{7}\)
\(63=9\times7\) इसलिए \( \sqrt{63}=3\sqrt{7} \)। पूर्ण वर्ग गुणनखंड पहचानना जरूरी है। / Since \(63=9\times7\), \( \sqrt{63}=3\sqrt{7} \). Identifying perfect-square factors is important.
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What is the value of \( \sqrt{2}\times\sqrt{50} \)?
D. (10)
\( \sqrt{2}\times\sqrt{50}=\sqrt{100}=10 \)। गुणा में वर्गमूल के अंदर की संख्याएँ गुणा करें। / \( \sqrt{2}\times\sqrt{50}=\sqrt{100}=10 \). In multiplication, multiply the numbers inside square roots.
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What is the value of \( \sqrt{80}\div\sqrt{5} \)?
A. (4)
\( \frac{\sqrt{80}}{\sqrt{5}}=\sqrt{16}=4 \)। भाग करते समय वर्गमूल के अंदर का भाग लें। / \( \frac{\sqrt{80}}{\sqrt{5}}=\sqrt{16}=4 \). During division, divide the numbers inside square roots.
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What is the simplified form of \(4\sqrt{2}+5\sqrt{2}\)?
B. \(9\sqrt{2}\)
समान करणी पदों के गुणांक जोड़े जाते हैं। इसलिए \(4\sqrt{2}+5\sqrt{2}=9\sqrt{2}\)। / Coefficients of like surd terms are added. Thus \(4\sqrt{2}+5\sqrt{2}=9\sqrt{2}\).
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What is the simplified form of \(9\sqrt{7}-4\sqrt{7}\)?
C. \(5\sqrt{7}\)
समान करणी पदों में गुणांक घटते हैं। इसलिए \(9\sqrt{7}-4\sqrt{7}=5\sqrt{7}\)। / For like surd terms, subtract the coefficients. Hence \(9\sqrt{7}-4\sqrt{7}=5\sqrt{7}\).
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What is the simplified form of \( \sqrt{48}+\sqrt{27} \)?
B. \(7\sqrt{3}\)
\( \sqrt{48}=4\sqrt{3} \) और \( \sqrt{27}=3\sqrt{3} \) हैं। इसलिए योग \(7\sqrt{3}\) है। / \( \sqrt{48}=4\sqrt{3} \) and \( \sqrt{27}=3\sqrt{3} \). Therefore the sum is \(7\sqrt{3}\).
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What is the simplified form of \( \sqrt{75}-\sqrt{12} \)?
A. \(3\sqrt{3}\)
\( \sqrt{75}=5\sqrt{3} \) और \( \sqrt{12}=2\sqrt{3} \) हैं। अंतर \(3\sqrt{3}\) है। / \( \sqrt{75}=5\sqrt{3} \) and \( \sqrt{12}=2\sqrt{3} \). The difference is \(3\sqrt{3}\).
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What is the form of \( \frac{3}{\sqrt{2}} \) with rational denominator?
B. \( \frac{3\sqrt{2}}{2} \)
अंश और हर को \( \sqrt{2} \) से गुणा करें। इससे हर (2) हो जाता है। / Multiply numerator and denominator by \( \sqrt{2} \). This makes the denominator (2).
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What is obtained by rationalising the denominator of \( \frac{5}{\sqrt{7}} \)?
C. \( \frac{5\sqrt{7}}{7} \)
अंश और हर को \( \sqrt{7} \) से गुणा करने पर \( \frac{5\sqrt{7}}{7} \) मिलता है। हर को परिमेय करना परीक्षा में सामान्य प्रश्न है। / Multiplying numerator and denominator by \( \sqrt{7} \) gives \( \frac{5\sqrt{7}}{7} \). Rationalising the denominator is a common exam question.
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What is obtained by rationalising the denominator of \( \frac{1}{2+\sqrt{3}} \)?
D. \(2-\sqrt{3}\)
संयुग्मी \(2-\sqrt{3}\) से गुणा करें और हर (4-3=1) बनेगा। इसलिए उत्तर \(2-\sqrt{3}\) है। / Multiply by the conjugate \(2-\sqrt{3}\) and the denominator becomes (4-3=1). Hence the answer is \(2-\sqrt{3}\).
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What will come in the numerator after rationalising \( \frac{1}{3-\sqrt{5}} \)?
A. \(3+\sqrt{5}\)
हर के संयुग्मी \(3+\sqrt{5}\) से गुणा किया जाता है। इसलिए नए अंश में \(3+\sqrt{5}\) आएगा। / We multiply by the conjugate \(3+\sqrt{5}\). So the new numerator will contain \(3+\sqrt{5}\).
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What is the value of ( \(2+\sqrt{5}\)\(2-\sqrt{5}\) )?
B. ( -1 )
यह अंतर के वर्ग का रूप है (22-\(\sqrt{5}\)2=4-5=-1)। संयुग्मी गुणा में मध्य पद कट जाते हैं। / It is a difference of squares (22-\(\sqrt{5}\)2=4-5=-1). Middle terms cancel in conjugate multiplication.
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What is the value of ( \(3+\sqrt{2}\)\(3-\sqrt{2}\) )?
A. (7)
(32-\(\sqrt{2}\)2=9-2=7) होता है। संयुग्मी का गुणन अक्सर परिमेय उत्तर देता है। / (32-\(\sqrt{2}\)2=9-2=7). Multiplying conjugates often gives a rational answer.
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Which is greater between \( \sqrt{3} \) and \( \sqrt{12} \)?
C. \( \sqrt{12} \)
क्योंकि (12>3) है इसलिए \( \sqrt{12}>\sqrt{3} \)। धनात्मक संख्याओं में बड़ा आधार बड़ा वर्गमूल देता है। / Since (12>3), \( \sqrt{12}>\sqrt{3} \). For positive numbers, a larger radicand gives a larger square root.
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Which is smaller between \( \sqrt{35} \) and (6)?
B. \( \sqrt{35} \)
\( \sqrt{35}<\sqrt{36}=6 \) है। इसलिए \( \sqrt{35} \) छोटी है।
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Which is greater between \( -\sqrt{10} \) and ( -3 )?
C. ( -3 )
\( \sqrt{10}\approx3.16 \) इसलिए \( -\sqrt{10} \) ( -3 ) से छोटा है। शून्य के पास वाली ऋणात्मक संख्या बड़ी होती है। / \( \sqrt{10}\approx3.16 \), so \( -\sqrt{10} \) is less than ( -3 ). The negative number closer to zero is greater.
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What is the value of \( \sqrt{1.44} \)?
C. (1.2)
\(1.2^2=1.44\) इसलिए \( \sqrt{1.44}=1.2 \)। दशमलव वर्गमूल में स्थान मान ध्यान रखें। / \(1.2^2=1.44\), so \( \sqrt{1.44}=1.2 \). Be careful with place value in decimal square roots.
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What is the value of \( \sqrt{2.25} \)?
B. (1.5)
\(1.5^2=2.25\) इसलिए \( \sqrt{2.25}=1.5 \)। उत्तर को वर्ग करके जाँचें। / \(1.5^2=2.25\), so \( \sqrt{2.25}=1.5 \). Check the answer by squaring it.
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What is the value of \( \sqrt{\frac{25}{36}} \)?
C. \( \frac{5}{6} \)
अंश और हर के वर्गमूल अलग-अलग लें। \( \sqrt{\frac{25}{36}}=\frac{5}{6} \) है। / Take the square roots of numerator and denominator separately. \( \sqrt{\frac{25}{36}}=\frac{5}{6} \).
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What is \( \sqrt{\frac{121}{144}} \) equal to?
A. \( \frac{11}{12} \)
\( \sqrt{121}=11 \) और \( \sqrt{144}=12 \) है। इसलिए उत्तर \( \frac{11}{12} \) है। / \( \sqrt{121}=11 \) and \( \sqrt{144}=12 \). Therefore the answer is \( \frac{11}{12} \).
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What is obtained by converting (3.125) into a fraction?
B. \( \frac{25}{8} \)
\(3.125=\frac{3125}{1000}=\frac{25}{8} \)। समाप्त दशमलव को भिन्न बनाकर सरल करें। / \(3.125=\frac{3125}{1000}=\frac{25}{8} \). Convert the terminating decimal into a fraction and simplify.
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Which fraction is equal to (4.5)?
A. \( \frac{9}{2} \)
\(4.5=\frac{45}{10}=\frac{9}{2} \)। दशमलव को (10) की घात वाले हर में लिखें। / \(4.5=\frac{45}{10}=\frac{9}{2} \). Write the decimal with a denominator that is a power of (10).
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What is the decimal form of \( \frac{13}{20} \)?
C. (0.65)
\( \frac{13}{20}=\frac{65}{100}=0.65 \)। हर को (100) में बदलना आसान तरीका है। / \( \frac{13}{20}=\frac{65}{100}=0.65 \). Changing the denominator to (100) is an easy method.
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What is the decimal form of \( \frac{17}{25} \)?
B. (0.68)
\( \frac{17}{25}=\frac{68}{100}=0.68 \)। हर (25) को (100) बनाने के लिए (4) से गुणा करें। / \( \frac{17}{25}=\frac{68}{100}=0.68 \). Multiply denominator (25) by (4) to make (100).
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What type of number is \(0.\overline{45}\)?
C. परिमेय वास्तविक संख्याRational real number
\(0.\overline{45}\) आवर्ती दशमलव है इसलिए परिमेय है। हर परिमेय संख्या वास्तविक भी होती है। / \(0.\overline{45}\) is a repeating decimal, so it is rational. Every rational number is also real.
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If (3.14159...) is non-terminating and non-repeating, what type of number is it?
B. अपरिमेय वास्तविक संख्याIrrational real number
असमाप्त और अनावर्ती दशमलव अपरिमेय होता है। ऐसा दशमलव फिर भी वास्तविक संख्या हो सकता है। / A non-terminating and non-repeating decimal is irrational. Such a decimal can still be a real number.
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What type of number is ( \(4+\sqrt{6}\) )?
C. अपरिमेय वास्तविक संख्याIrrational real number
परिमेय (4) में अपरिमेय \( \sqrt{6} \) जोड़ने पर अपरिमेय संख्या मिलती है। यह वास्तविक संख्या भी है। / Adding irrational \( \sqrt{6} \) to rational (4) gives an irrational number. It is also a real number.
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What type of number is ( \(7-\sqrt{3}\) )?
A. अपरिमेय वास्तविक संख्याIrrational real number
परिमेय संख्या से अपरिमेय संख्या घटाने पर परिणाम अपरिमेय होता है। इसलिए \(7-\sqrt{3}\) अपरिमेय वास्तविक संख्या है। / Subtracting an irrational number from a rational number gives an irrational result. Thus \(7-\sqrt{3}\) is an irrational real number.
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What is the value of \( \sqrt{13}\times\sqrt{13} \)?
D. (13)
एक ही वर्गमूल को स्वयं से गुणा करने पर अंदर की संख्या मिलती है। इसलिए \( \sqrt{13}\times\sqrt{13}=13 \)। / Multiplying the same square root by itself gives the number inside. Therefore \( \sqrt{13}\times\sqrt{13}=13 \).
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What is the value of ( \(\sqrt{15}\)2 )?
A. (15)
किसी धनात्मक संख्या के वर्गमूल का वर्ग वही संख्या देता है। इसलिए ( \(\sqrt{15}\)2=15 )। / The square of the square root of a positive number gives the same number. Therefore ( \(\sqrt{15}\)2=15 ).
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What is the value of ( | -18 | )?
B. (18)
निरपेक्ष मान संख्या की (0) से दूरी बताता है। इसलिए ( | -18 |=18 )। / Absolute value shows the distance of a number from (0). Therefore ( | -18 |=18 ).
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What is the value of ( |6-14| )?
C. (8)
(6-14=-8) और ( |-8|=8 )। निरपेक्ष मान कभी ऋणात्मक नहीं होता। / (6-14=-8) and ( |-8|=8 ). Absolute value is never negative.
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Where is the real number ( -1.25 ) located on the number line?
D. ( -2 ) और ( -1 ) के बीचBetween ( -2 ) and ( -1 )
( -1.25 ) ( -2 ) से बड़ा और ( -1 ) से छोटा है। इसलिए यह ( -2 ) और ( -1 ) के बीच स्थित है। / ( -1.25 ) is greater than ( -2 ) and less than ( -1 ). So it lies between ( -2 ) and ( -1 ).
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Which is an irrational number between (3) and (4)?
B. \( \sqrt{10} \)
\(3^2<10<4^2\) इसलिए \( \sqrt{10} \) (3) और (4) के बीच है। (10) पूर्ण वर्ग नहीं है इसलिए यह अपरिमेय है। / Since \(3^2<10<4^2\), \( \sqrt{10} \) lies between (3) and (4). Since (10) is not a perfect square, it is irrational.
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Which is an irrational number between (4) and (5)?
C. \( \sqrt{22} \)
\(4^2<22<5^2\) इसलिए \( \sqrt{22} \) (4) और (5) के बीच है। (22) पूर्ण वर्ग नहीं है इसलिए यह अपरिमेय है। / Since \(4^2<22<5^2\), \( \sqrt{22} \) lies between (4) and (5). Since (22) is not a perfect square, it is irrational.
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How many irrational numbers are there between any two distinct real numbers?
D. अनंतInfinitely many
दो अलग-अलग वास्तविक संख्याओं के बीच अनंत अपरिमेय संख्याएँ होती हैं। यह वास्तविक संख्या रेखा की घनत्व विशेषता है। / There are infinitely many irrational numbers between two distinct real numbers. This is a density property of the real number line.
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How many real numbers are there between any two distinct real numbers?
A. अनंतInfinitely many
वास्तविक संख्या रेखा सतत होती है इसलिए दो अलग-अलग बिंदुओं के बीच अनंत वास्तविक संख्याएँ होती हैं। यह मूल गुण याद रखें। / The real number line is continuous, so infinitely many real numbers lie between two distinct points. Remember this basic property.
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What is the value of \( \sqrt{0}+\sqrt{100} \)?
B. (10)
\( \sqrt{0}=0 \) और \( \sqrt{100}=10 \) है। इसलिए योग (10) है। / \( \sqrt{0}=0 \) and \( \sqrt{100}=10 \). Therefore the sum is (10).
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What is the value of \( \sqrt{144}-\sqrt{25} \)?
B. (7)
\( \sqrt{144}=12 \) और \( \sqrt{25}=5 \) है। इसलिए अंतर (7) है। / \( \sqrt{144}=12 \) and \( \sqrt{25}=5 \). Therefore the difference is (7).
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What is the value of \( \sqrt{121}+\sqrt{169} \)?
B. (24)
\( \sqrt{121}=11 \) और \( \sqrt{169}=13 \) है। इसलिए योग (24) है। / \( \sqrt{121}=11 \) and \( \sqrt{169}=13 \). Therefore the sum is (24).
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What is the value of \( \sqrt{225}\div\sqrt{9} \)?
C. (5)
\( \sqrt{225}=15 \) और \( \sqrt{9}=3 \) है। \(15\div3=5\) होता है। / \( \sqrt{225}=15 \) and \( \sqrt{9}=3 \). \(15\div3=5\).
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What is the value of \(2\sqrt{3}\times3\sqrt{3}\)?
D. (18)
\(2\sqrt{3}\times3\sqrt{3}=6\times3=18\) होता है। गुणांक और करणी भाग अलग-अलग गुणा करें। / \(2\sqrt{3}\times3\sqrt{3}=6\times3=18\). Multiply coefficients and surd parts separately.
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What is the value of \( \sqrt{196} \)?
C. (14)
\(14^2=196\) इसलिए \( \sqrt{196}=14 \)। पूर्ण वर्गों को पहचानना परीक्षा में समय बचाता है। / Since \(14^2=196\), \( \sqrt{196}=14 \). Recognising perfect squares saves time in exams.
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What is the simplified surd form of \( \sqrt{108} \)?
A. \(6\sqrt{3}\)
\(108=36\times3\) इसलिए \( \sqrt{108}=6\sqrt{3} \)। सबसे बड़ा पूर्ण वर्ग गुणनखंड चुनें। / Since \(108=36\times3\), \( \sqrt{108}=6\sqrt{3} \). Choose the largest perfect-square factor.
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What is the simplified form of \( \sqrt{2}+\sqrt{18} \)?
B. \(4\sqrt{2}\)
\( \sqrt{18}=3\sqrt{2} \) इसलिए \( \sqrt{2}+3\sqrt{2}=4\sqrt{2} \)। पहले करणी को सरल करें फिर समान पद जोड़ें। / \( \sqrt{18}=3\sqrt{2} \), so \( \sqrt{2}+3\sqrt{2}=4\sqrt{2} \). First simplify the surd and then add like terms.
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