Level 19 • 13/50 questions • 25 seconds per question.
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Which option correctly compares \(\sqrt{18}\) and (4)?
C. \(\sqrt{18}>4\)
क्योंकि \(18>16=4^2\), इसलिए \(\sqrt{18}>4\)। तुलना के लिए दोनों ओर वर्ग करें। / Because \(18>16=4^2\), so \(\sqrt{18}>4\). Square both sides for comparison.
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Which interval should be identified before placing \(\sqrt{7}\) on the number line?
B. \(2<\sqrt{7}<3\)
क्योंकि \(2^2<7<3^2\) है। इसलिए \(\sqrt{7}\) (2) और (3) के बीच होगा। / Because \(2^2<7<3^2\). Therefore \(\sqrt{7}\) lies between (2) and (3).
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What is obtained after simplifying \(\sqrt{147}\)?
A. \(7\sqrt{3}\)
\(147=49\times3\), इसलिए \(\sqrt{147}=7\sqrt{3}\)। पूर्ण वर्ग को बाहर निकालें। / \(147=49\times3\), so \(\sqrt{147}=7\sqrt{3}\). Take the perfect square outside.
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Which number is greater than \(\sqrt{10}\) and less than \(\sqrt{17}\)?
B. (4)
\(\sqrt{10}\) (3) और (4) के बीच है, जबकि \(\sqrt{17}\) (4) और (5) के बीच है। इसलिए (4) बीच में है। / \(\sqrt{10}\) lies between (3) and (4), while \(\sqrt{17}\) lies between (4) and (5). Therefore (4) lies between them.
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If \(\sqrt{a}=9\), what is the value of (a)?
B. (81)
दोनों ओर वर्ग करने पर (a=81) मिलता है। वर्गमूल समीकरण में वर्ग करना उपयोगी है। / Squaring both sides gives (a=81). Squaring is useful in square root equations.
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What is the simplest form of \(\sqrt{200}\)?
A. \(10\sqrt{2}\)
\(200=100\times2\), इसलिए \(\sqrt{200}=10\sqrt{2}\)। सबसे बड़ा पूर्ण वर्ग निकालें। / \(200=100\times2\), so \(\sqrt{200}=10\sqrt{2}\). Take out the largest perfect square.
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When will \(\sqrt{a^2}\) be equal to (a)?
B. जब \(a\ge0\)When \(a\ge0\)
\(\sqrt{a^2}=|a|\) होता है। यह (a) के बराबर तभी है जब \(a\ge0\)। / \(\sqrt{a^2}=|a|\). It equals (a) only when \(a\ge0\).
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Which construction is correct for representing \(\sqrt{2}\) on the number line?
A. (1) और (1) भुजाओं वाला समकोण त्रिभुज बनाकर कर्ण लेनाMake a right triangle with sides (1) and (1), then take the hypotenuse
\(1^2+1^2=2\), इसलिए कर्ण \(\sqrt{2}\) होगा। संख्या रेखा पर वही कर्ण लंबाई स्थानांतरित करें। / \(1^2+1^2=2\), so the hypotenuse is \(\sqrt{2}\). Transfer that hypotenuse length to the number line.
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Which option is correct about \(\sqrt{64}\) and \(\sqrt{65}\)?
A. \(\sqrt{64}=8\) और \(\sqrt{65}\) (8) और (9) के बीच है\(\sqrt{64}=8\) and \(\sqrt{65}\) lies between (8) and (9)
\(64=8^2\) और \(8^2<65<9^2\) है। इसलिए पहला कथन सही है। / \(64=8^2\) and \(8^2<65<9^2\). Therefore the first statement is correct.
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Which number lies between (3) and (4)?
B. \(\sqrt{10}\)
\(3^2<10<4^2\), इसलिए \(\sqrt{10}\) (3) और (4) के बीच है। वर्गों की तुलना सबसे तेज तरीका है।
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Which whole number lies between \(\sqrt{11}\) and \(\sqrt{15}\)?
B. (3)
\(\sqrt{11}\) (3) और (4) के बीच है और \(\sqrt{15}\) भी (3) और (4) के बीच है। केवल (3) छोटा है, बीच में कोई पूर्ण संख्या नहीं आती। / \(\sqrt{11}\) and \(\sqrt{15}\) both lie between (3) and (4). No whole number lies strictly between them.
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Which statement is correct about comparing \(\sqrt{80}\) and (9)?
C. \(\sqrt{80}<9\)
क्योंकि \(80<81=9^2\), इसलिए \(\sqrt{80}<9\)। वर्गमूल तुलना में निकटतम पूर्ण वर्ग देखें। / Because \(80<81=9^2\), so \(\sqrt{80}<9\). In square root comparison, check the nearest perfect square.
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What is the value of \(\sqrt{0.0009}\)?
B. (0.03)
((0.03)2=0.0009), इसलिए \(\sqrt{0.0009}=0.03\)। दशमलव स्थानों को ध्यान से गिनें। / ((0.03)2=0.0009), so \(\sqrt{0.0009}=0.03\). Count decimal places carefully.
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