Square Root and Cube Root Problems and Solutions

• 15. What is the smallest number by which 3600 be divided to make it a perfect cube.

  1. 450
  2. 445
  3. 440
  4. 430

  Answer :

  Option A

  Explanation:

  \begin{aligned}
  3600 = 2^3 \times 5^2 \times 3^2 \times 2
  \end{aligned}
  To make it a perfect cube it must be divided by
  \begin{aligned}
  5^2 \times 3^2 \times 2 = 450
  \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

  Answer :

  Option C

  Explanation:

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

• 17. Evaluate
  \begin{aligned}
  \sqrt{10+\sqrt{25+\sqrt{108+\sqrt{154+\sqrt{225}}}}}
  \end{aligned}

  1. 16
  2. 8
  3. 6
  4. 4

  Answer :

  Option 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}
  

• 18. \begin{aligned}
  \sqrt{41 - \sqrt{21 + \sqrt{19 - \sqrt{9}}}}
  \end{aligned}

  1. 4
  2. 26
  3. 16
  4. 6

  Answer :

  Option 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}
  

• 19. Evaluate
  \begin{aligned}
  \sqrt{248+\sqrt{64}}
  \end{aligned}

  1. 14
  2. 26
  3. 16
  4. 36

  Answer :

  Option 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}

• 20. 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 :

  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}
  

• 21. \begin{aligned} \sqrt{0.00059049} \end{aligned}

  1. 24.3
  2. 2.43
  3. 0.243
  4. 0.0243

  Answer :

  Option D