Square Root and Cube Root Questions Answers

Square Root and Cube Root Questions Answers (MCQ) listings with explanations are important for BANK PO, Clerk, IBPS, SBI-PO, RBI, MBA, MAT, CAT, IIFT, IGNOU, SSC CGL, CBI, CPO, CLAT, CTET, NDA, CDS, Specialist Officers and other competitive exams.

11) Evaluate \begin{aligned} \sqrt{248+\sqrt{64}} \end{aligned}

  • 1) 14
  • 2) 26
  • 3) 16
  • 4) 36
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Ans.   C
Explanation :
\begin{aligned} = \sqrt{248+\sqrt{64}} \end{aligned} \begin{aligned} = \sqrt{248+8} \end{aligned} \begin{aligned} = \sqrt{256} \end{aligned} \begin{aligned} = 16 \end{aligned}

12) Evaluate \begin{aligned} \sqrt{1\frac{9}{16}} \end{aligned}

  • 1) \begin{aligned} 1\frac{1}{6} \end{aligned}
  • 2) \begin{aligned} 1\frac{1}{5} \end{aligned}
  • 3) \begin{aligned} 1\frac{1}{4} \end{aligned}
  • 4) \begin{aligned} 1\frac{1}{3} \end{aligned}
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Ans.   C
Explanation :
\begin{aligned} = \sqrt{\frac{25}{16}} \end{aligned} \begin{aligned} = \frac{\sqrt{25}}{\sqrt{16}} \end{aligned} \begin{aligned} = \frac{5}{4} \end{aligned} \begin{aligned} = 1\frac{1}{4} \end{aligned}

13) Evaluate \begin{aligned} \sqrt{53824} \end{aligned}

  • 1) 132
  • 2) 232
  • 3) 242
  • 4) 253
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Ans.   B
Explanation :

14) Evaluate \begin{aligned} \sqrt{10+\sqrt{25+\sqrt{108+\sqrt{154+\sqrt{225}}}}} \end{aligned}

  • 1) 16
  • 2) 8
  • 3) 6
  • 4) 4
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Ans.   D
Explanation :
\begin{aligned} = \sqrt{10+\sqrt{25+\sqrt{108+\sqrt{154+\sqrt{225}}}}} \end{aligned} \begin{aligned} =\sqrt{10+\sqrt{25+\sqrt{108+\sqrt{154+15}}}} \end{aligned} \begin{aligned} =\sqrt{10+\sqrt{25+\sqrt{108+\sqrt{154+15}}}} \end{aligned} \begin{aligned} =\sqrt{10+\sqrt{25+\sqrt{108+\sqrt{169}}}} \end{aligned} \begin{aligned} =\sqrt{10+\sqrt{25+\sqrt{108+13}}} \end{aligned} \begin{aligned} =\sqrt{10+\sqrt{25+\sqrt{121}}} \end{aligned} \begin{aligned} =\sqrt{10+\sqrt{25+11}} \end{aligned} \begin{aligned} =\sqrt{10+\sqrt{36}} \end{aligned} \begin{aligned} =\sqrt{10+6} \end{aligned} \begin{aligned} =\sqrt{16} = 4 \end{aligned}

15) \begin{aligned} \sqrt{41 - \sqrt{21 + \sqrt{19 - \sqrt{9}}}} \end{aligned}

  • 1) 4
  • 2) 26
  • 3) 16
  • 4) 6
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Ans.   D
Explanation :
\begin{aligned} = \sqrt{41 - \sqrt{21 + \sqrt{19 - 3}}} \end{aligned} \begin{aligned} = \sqrt{41 - \sqrt{21 + \sqrt{16}}} \end{aligned} \begin{aligned} = \sqrt{41 - \sqrt{21 + 4}} \end{aligned} \begin{aligned} = \sqrt{41 - \sqrt{25}} \end{aligned} \begin{aligned} = \sqrt{41 - \sqrt{25}} \end{aligned} \begin{aligned} = \sqrt{41 - 5} \end{aligned} \begin{aligned} = \sqrt{36} = 6 \end{aligned}

16) \begin{aligned} (\frac{\sqrt{625}}{11} \times \frac{14}{\sqrt{25}} \times \frac{11}{\sqrt{196}}) \end{aligned}

  • 1) 15
  • 2) 7
  • 3) 5
  • 4) 9
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Ans.   C
Explanation :
\begin{aligned} = (\frac{25}{11} \times \frac{14}{5} \times \frac{11}{14}) \end{aligned} \begin{aligned} = 5 \end{aligned}

17) Find the value of x \begin{aligned} \frac{2707}{\sqrt{x}} = 27.07 \end{aligned}

  • 1) 1000
  • 2) 10000
  • 3) 10000000
  • 4) None of above
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Ans.   B
Explanation :
\begin{aligned} = \frac{2707}{27.07} = \sqrt{x} \end{aligned} \begin{aligned} => \frac{2707 \times 100}{2707} = \sqrt{x} \end{aligned} \begin{aligned} => 100 = \sqrt{x} \end{aligned} \begin{aligned} => x = 100^2 = 10000 \end{aligned}

18) What is the square root of 0.

  • 1) 0.4
  • 2) 0.04
  • 3) 0.004
  • 4) 4
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Ans.   A
Explanation :
as .4 * .4 = 0.16

19) The least perfect square, which is divisible by each of 21, 36 and 66

  • 1) 213414
  • 2) 213424
  • 3) 213434
  • 4) 213444
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Ans.   D
Explanation :
L.C.M. of 21, 36, 66 = 2772 Now, 2772 = 2 x 2 x 3 x 3 x 7 x 11 To make it a perfect square, it must be multiplied by 7 x 11. So, required number = 2 x 2 x 3 x 3 x 7 x 7 x 11 x 11 = 213444

20) Evaluate \begin{aligned} \sqrt{0.00059049} \end{aligned}

  • 1) 0.00243
  • 2) 0.0243
  • 3) 0.243
  • 4) 2.43
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Ans.   B
Explanation :
Very obvious tip here is, after squre root the terms after decimal will be half (that is just a trick), works awesome at many questions like this.
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