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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