Square Root and Cube Root Questions Answers

• 8. \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

  Answer And Explanation

  Answer: Option C

  Explanation:

  \begin{aligned}
  = (\frac{25}{11} \times \frac{14}{5} \times \frac{11}{14})
  \end{aligned}
  
  \begin{aligned}
  = 5
  \end{aligned}

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• 9. 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

  Answer And Explanation

  Answer: Option 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}
  

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• 10. What is the square root of 0.16
  

  1. 0.4
  2. 0.04
  3. 0.004
  4. 4

  Answer And Explanation

  Answer: Option A

  Explanation:

  as .4 * .4 = 0.16

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• 11. The least perfect square, which is divisible by each of 21, 36 and 66 is

  1. 213414
  2. 213424
  3. 213434
  4. 213444

  Answer And Explanation

  Answer: Option 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

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• 12. Evaluate
  \begin{aligned}
  \sqrt{0.00059049}
  \end{aligned}

  1. 0.00243
  2. 0.0243
  3. 0.243
  4. 2.43

  Answer And Explanation

  Answer: Option 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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• 13. if a = 0.1039, then the value of
  \begin{aligned} \sqrt{4a^2 - 4a + 1} + 3a \end{aligned}

  1. 12.039
  2. 1.2039
  3. 11.039
  4. 1.1039

  Answer And Explanation

  Answer: Option D

  Explanation:

  Tip: Please check the question carefully before answering. As 3a is not under the root we can convert it into a formula , lets evaluate now :
  
  \begin{aligned}
  = \sqrt{4a^2 - 4a + 1} + 3a \end{aligned}
  
  \begin{aligned}
  = \sqrt{(1)^2 + (2a)^2 - 2x1x2a} + 3a \end{aligned}
  
  \begin{aligned}
  = \sqrt{(1-2a)^2} + 3a \end{aligned}
  
  \begin{aligned}
  = (1-2a) + 3a \end{aligned}
  
  \begin{aligned}
  = (1-2a) + 3a \end{aligned}
  
  \begin{aligned}
  = 1 + a = 1 + 0.1039 = 1.1039 \end{aligned}
  
  
  
  

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• 14. Find the value of X
  \begin{aligned} \sqrt{81} + \sqrt{0.81} = 10.09 - X \end{aligned}

  1. 0.019
  2. 0.19
  3. 0.9
  4. 0.109

  Answer And Explanation

  Answer: Option B

  Explanation:

  \begin{aligned}
  => \sqrt{81} + \sqrt{0.81} = 10.09 - X
  \end{aligned}
  
  \begin{aligned}
  => 9 + 0.9 = 10.09 - X
  \end{aligned}
  
  \begin{aligned}
  => X = 10.09 - 9.9 = 0.19
  \end{aligned}
  
  

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