Square Root and Cube Root Problems and Solutions

• 8. Evaluate
  \begin{aligned}
  \sqrt{6084}
  \end{aligned}

  1. 75
  2. 77
  3. 78
  4. 68

  Answer :

  Option C

• 9. Evaluate \begin{aligned} \sqrt[3]{\sqrt{.000064}} \end{aligned}

  1. 0.0002
  2. 0.002
  3. 0.02
  4. 0.2

  Answer :

  Option D

  Explanation:

  \begin{aligned} = \sqrt{.000064} \end{aligned}
  \begin{aligned} = \sqrt{\frac{64}{10^6}} \end{aligned}
  \begin{aligned} = \frac{8}{10^3} = .008 \end{aligned}
  \begin{aligned} = \sqrt[3]{.008} \end{aligned}
  \begin{aligned} = \sqrt[3]{\frac{8}{1000}} \end{aligned}
  \begin{aligned} = \frac{2}{10} = 0.2 \end{aligned}

• 10. 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}

  Answer :

  Option 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}

• 11. \begin{aligned} \sqrt{\frac{32.4}{x}} = 2 \end{aligned}
  

  1. 8
  2. 8.1
  3. 9
  4. 9.1

  Answer :

  Option B

• 12. The largest four digit number which is a perfect cube, is:

  1. 7000
  2. 8000
  3. 9261
  4. 9999

  Answer :

  Option C

  Explanation:

  21*21*21 = 9261

• 13. The cube root of .000216 is

  1. 0.6
  2. 0.006
  3. 0.06
  4. .0006

  Answer :

  Option C

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

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

  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.