Last Updated on Mar 16, 2023
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Name: Square Roots and Cube Roots Question Answer: Mathematics Test
Subject: Mathematics / Numerical Aptitude
Topic: Square Roots and Cube Roots
Questions: 12 Objective Type Questions
Time Allowed: 30 Minutes
Language: English
Important for: Police Exam, SSC ( CGL, CHSL, GD etc), State PCS, UPSC CSE CSAT, Railway, IBPS Clerk, IBPS RRB, SBI Clerk, Engineering Entrance exam, CTET and State TET, समूह ग आदि |
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| Pos. | Name | Entered on | Points | Result |
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- Review
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Question 1 of 12
1. Question
1 points\(\left ( \frac{\sqrt{625}}{11}\times \frac{14}{\sqrt{25}}\times \frac{11}{\sqrt{196}} \right )\) is equal to:
Correct
Given Exp. = \(\frac{25}{11}\times\frac{14}{5}\times\frac{11}{14}= 5\)
Incorrect
Given Exp. = \(\frac{25}{11}\times\frac{14}{5}\times\frac{11}{14}= 5\)
Unattempted
Given Exp. = \(\frac{25}{11}\times\frac{14}{5}\times\frac{11}{14}= 5\)
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Question 2 of 12
2. Question
1 points\(\left ( \sqrt{\frac{225}{729} -\sqrt{\frac{25}{144}}}\right )\div \sqrt{\frac{16}{81}}\)= ?
Correct
Given Exp. \(\left ( \sqrt{\frac{225}{729} -\sqrt{\frac{25}{144}}}\right )\div \sqrt{\frac{16}{81}}= \left ( \frac{15}{27}-\frac{5}{12} \right ) + \frac{4}{9}= \left ( \frac{15}{108}\times\frac{9}{4} \right )=\frac{5}{16}\)
Incorrect
Given Exp. \(\left ( \sqrt{\frac{225}{729} -\sqrt{\frac{25}{144}}}\right )\div \sqrt{\frac{16}{81}}= \left ( \frac{15}{27}-\frac{5}{12} \right ) + \frac{4}{9}= \left ( \frac{15}{108}\times\frac{9}{4} \right )=\frac{5}{16}\)
Unattempted
Given Exp. \(\left ( \sqrt{\frac{225}{729} -\sqrt{\frac{25}{144}}}\right )\div \sqrt{\frac{16}{81}}= \left ( \frac{15}{27}-\frac{5}{12} \right ) + \frac{4}{9}= \left ( \frac{15}{108}\times\frac{9}{4} \right )=\frac{5}{16}\)
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Question 3 of 12
3. Question
1 pointsThe square root of\( \left ( 272^{2}-128^{8} \right )\) is:
Correct
\(\left ( 272^{2}-128^{8} \right )= \sqrt{(272 + 128)(272 – 128)}= \sqrt{400\times144} = \sqrt{57600} \)= 240
Incorrect
\(\left ( 272^{2}-128^{8} \right )= \sqrt{(272 + 128)(272 – 128)}= \sqrt{400\times144} = \sqrt{57600} \)= 240
Unattempted
\(\left ( 272^{2}-128^{8} \right )= \sqrt{(272 + 128)(272 – 128)}= \sqrt{400\times144} = \sqrt{57600} \)= 240
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Question 4 of 12
4. Question
1 pointsIf\( x\ast y = x + y + \sqrt{xy}\), the value of \(6\ast 24\) is:
Correct
\(6\ast 24 = 6+24 + \sqrt{6\times24}= 30+ \sqrt{144}= 30+ 12= 42\)
Incorrect
\(6\ast 24 = 6+24 + \sqrt{6\times24}= 30+ \sqrt{144}= 30+ 12= 42\)
Unattempted
\(6\ast 24 = 6+24 + \sqrt{6\times24}= 30+ \sqrt{144}= 30+ 12= 42\)
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Question 5 of 12
5. Question
1 pointsIf y = 5, than what is the value of \(10y\sqrt{y^{3}-y^{2}} \)=?
Correct
\(10y\sqrt{y^{3}-y^{2}}= 10\times5\sqrt{5^{3}-5^{2}}= 50\times\sqrt{125=25}= 50\times\sqrt{100}= 50\times10\) = 500
Incorrect
\(10y\sqrt{y^{3}-y^{2}}= 10\times5\sqrt{5^{3}-5^{2}}= 50\times\sqrt{125=25}= 50\times\sqrt{100}= 50\times10\) = 500
Unattempted
\(10y\sqrt{y^{3}-y^{2}}= 10\times5\sqrt{5^{3}-5^{2}}= 50\times\sqrt{125=25}= 50\times\sqrt{100}= 50\times10\) = 500
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Question 6 of 12
6. Question
1 pointsHow many two-digit number satisfy this property: The last digit (unit’s digit) of the square of the two-digit number is 8?
Correct
A number ending in 8 can never be a perfect square.
Incorrect
A number ending in 8 can never be a perfect square.
Unattempted
A number ending in 8 can never be a perfect square.
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Question 7 of 12
7. Question
1 pointsWhat is the square root of 0.16?
Correct
\(\sqrt{0.16}= \sqrt{\frac{16}{100}}= \frac{\sqrt{16}}{\sqrt{100}}=\frac{4}{10} = 0.4\)
Incorrect
\(\sqrt{0.16}= \sqrt{\frac{16}{100}}= \frac{\sqrt{16}}{\sqrt{100}}=\frac{4}{10} = 0.4\)
Unattempted
\(\sqrt{0.16}= \sqrt{\frac{16}{100}}= \frac{\sqrt{16}}{\sqrt{100}}=\frac{4}{10} = 0.4\)
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Question 8 of 12
8. Question
1 pointsThe value of \(\sqrt{0.01}+\sqrt{0.81}+ \sqrt{1.21}+ \sqrt{0.0009} \)is :
Correct
Given Exp. = \(\sqrt{\frac{1}{100}}+\sqrt{\frac{81}{100}}+\sqrt{\frac{121}{100}}+\sqrt{\frac{9}{10000}}= \frac{1}{10}+\frac{9}{10}+\frac{11}{10}+\frac{3}{100}\)
= 0.1 + 0.9 + 1.1 + 0.03 = 2.13Incorrect
Given Exp. = \(\sqrt{\frac{1}{100}}+\sqrt{\frac{81}{100}}+\sqrt{\frac{121}{100}}+\sqrt{\frac{9}{10000}}= \frac{1}{10}+\frac{9}{10}+\frac{11}{10}+\frac{3}{100}\)
= 0.1 + 0.9 + 1.1 + 0.03 = 2.13Unattempted
Given Exp. = \(\sqrt{\frac{1}{100}}+\sqrt{\frac{81}{100}}+\sqrt{\frac{121}{100}}+\sqrt{\frac{9}{10000}}= \frac{1}{10}+\frac{9}{10}+\frac{11}{10}+\frac{3}{100}\)
= 0.1 + 0.9 + 1.1 + 0.03 = 2.13 -
Question 9 of 12
9. Question
1 pointsIf \(\sqrt{18225}= 135,\) then the value of \(\left ( \sqrt{182.25}+\sqrt{1.8225}+\sqrt{0.018225}+\sqrt{0.00018225} \right ) is :\)
Correct
Given Exp. \(= \sqrt{\frac{18225}{10^{2}}}+ \sqrt{\frac{18225}{10^{4}}}+ \sqrt{\frac{18225}{10^{6}}}+ \sqrt{\frac{18225}{10^{8}}} = \frac{\sqrt{18225}}{10}+ \frac{\sqrt{18225}}{10^{2}}+\frac{\sqrt{18225}}{10^{3}}+ \frac{\sqrt{18225}}{10^{4}}= \frac{135}{10}+\frac{135}{100}+\frac{135}{1000}+ \frac{135}{10000} = 13.5+ 1.35+ 0.135 + 0.0135 = 14.9985.\)
Incorrect
Given Exp. \(= \sqrt{\frac{18225}{10^{2}}}+ \sqrt{\frac{18225}{10^{4}}}+ \sqrt{\frac{18225}{10^{6}}}+ \sqrt{\frac{18225}{10^{8}}} = \frac{\sqrt{18225}}{10}+ \frac{\sqrt{18225}}{10^{2}}+\frac{\sqrt{18225}}{10^{3}}+ \frac{\sqrt{18225}}{10^{4}}= \frac{135}{10}+\frac{135}{100}+\frac{135}{1000}+ \frac{135}{10000} = 13.5+ 1.35+ 0.135 + 0.0135 = 14.9985.\)
Unattempted
Given Exp. \(= \sqrt{\frac{18225}{10^{2}}}+ \sqrt{\frac{18225}{10^{4}}}+ \sqrt{\frac{18225}{10^{6}}}+ \sqrt{\frac{18225}{10^{8}}} = \frac{\sqrt{18225}}{10}+ \frac{\sqrt{18225}}{10^{2}}+\frac{\sqrt{18225}}{10^{3}}+ \frac{\sqrt{18225}}{10^{4}}= \frac{135}{10}+\frac{135}{100}+\frac{135}{1000}+ \frac{135}{10000} = 13.5+ 1.35+ 0.135 + 0.0135 = 14.9985.\)
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Question 10 of 12
10. Question
1 pointsThe value of \(\frac{\sqrt{80}-\sqrt{112}}{\sqrt{45}-\sqrt{63}} is:\)
Correct
\(\frac{\sqrt{80}-\sqrt{112}}{\sqrt{45}-\sqrt{63}}= \frac{\sqrt{16\times5}-\sqrt{16\times7}}{\sqrt{9\times5}-\sqrt{9\times7}}=\frac{4\sqrt{5}-4\sqrt{7}}{3\sqrt{5}-3\sqrt{7}} = \frac{4(\sqrt{}5)-\sqrt{7}}{3(\sqrt{5}-\sqrt{7})}=\frac{4}{3}= 1\frac{1}{3}\)
Incorrect
\(\frac{\sqrt{80}-\sqrt{112}}{\sqrt{45}-\sqrt{63}}= \frac{\sqrt{16\times5}-\sqrt{16\times7}}{\sqrt{9\times5}-\sqrt{9\times7}}=\frac{4\sqrt{5}-4\sqrt{7}}{3\sqrt{5}-3\sqrt{7}} = \frac{4(\sqrt{}5)-\sqrt{7}}{3(\sqrt{5}-\sqrt{7})}=\frac{4}{3}= 1\frac{1}{3}\)
Unattempted
\(\frac{\sqrt{80}-\sqrt{112}}{\sqrt{45}-\sqrt{63}}= \frac{\sqrt{16\times5}-\sqrt{16\times7}}{\sqrt{9\times5}-\sqrt{9\times7}}=\frac{4\sqrt{5}-4\sqrt{7}}{3\sqrt{5}-3\sqrt{7}} = \frac{4(\sqrt{}5)-\sqrt{7}}{3(\sqrt{5}-\sqrt{7})}=\frac{4}{3}= 1\frac{1}{3}\)
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Question 11 of 12
11. Question
1 pointsBy what least number 675 be multiplied to obtain a number which is a perfect cube?
Correct
\(675 = 5\times 5\times3\times3\times3\) To make it a perfect cube, It must be multiplied by 5.
Incorrect
\(675 = 5\times 5\times3\times3\times3\) To make it a perfect cube, It must be multiplied by 5.
Unattempted
\(675 = 5\times 5\times3\times3\times3\) To make it a perfect cube, It must be multiplied by 5.
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Question 12 of 12
12. Question
1 pointsWhat is the smallest number by which 3600 be divided to make it a perfect cube?
Correct
\(3600 = 2^{3}\times 5^{2}\times 3^{2}\times2\) To make it a perfect cube, it must be divided by \(5^{2}\times 3^{2}\times2\) i.e., 450.
Incorrect
\(3600 = 2^{3}\times 5^{2}\times 3^{2}\times2\) To make it a perfect cube, it must be divided by \(5^{2}\times 3^{2}\times2\) i.e., 450.
Unattempted
\(3600 = 2^{3}\times 5^{2}\times 3^{2}\times2\) To make it a perfect cube, it must be divided by \(5^{2}\times 3^{2}\times2\) i.e., 450.
