Square Root and Cube Root Questions Answers

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

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

  Answer And Explanation

  Answer: Option C

  Explanation:

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

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

  Answer And Explanation

  Answer: Option A

  Explanation:

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

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

  Answer And Explanation

  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}

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• 4. 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 And Explanation

  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}

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

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

  Answer And Explanation

  Answer: Option B

  Explanation:

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

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

  Answer And Explanation

  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}
  

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

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

  Answer And Explanation

  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}
  

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