Square Root and Cube Root Problems and Solutions

• 1. What is the square root of 0.16
  

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

  Answer :

  Option A

  Explanation:

  as .4 * .4 = 0.16

• 2. Evaluate \begin{aligned}
  \sqrt{1471369}
  \end{aligned}

  1. 1213
  2. 1223
  3. 1233
  4. 1243

  Answer :

  Option A

• 3. 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 :

  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}
  
  
  
  

• 4. Evaluate
  \begin{aligned}
  \sqrt{53824}
  \end{aligned}

  1. 132
  2. 232
  3. 242
  4. 253

  Answer :

  Option B

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

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

  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

• 6. Evaluate
  \begin{aligned} \sqrt[3]{4\frac{12}{125}} \end{aligned}

  1. \begin{aligned} 1\frac{2}{5} \end{aligned}
  2. \begin{aligned} 1\frac{3}{5} \end{aligned}
  3. \begin{aligned} 1\frac{4}{5} \end{aligned}
  4. 1

  Answer :

  Option B

  Explanation:

  \begin{aligned}
  = \sqrt[3]{\frac{512}{125}} \end{aligned}
  \begin{aligned}
  = (\frac{8*8*8}{5*5*5})^{\frac{1}{3}} \end{aligned}
  
  \begin{aligned} = \frac{8}{5} = 1\frac{3}{5} \end{aligned}

• 7. 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 :

  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}