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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

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

    1. 1213
    2. 1223
    3. 1233
    4. 1243
    Answer And Explanation

    Answer: Option A

  • 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}

  • 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}

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

    1. 132
    2. 232
    3. 242
    4. 253
    Answer And Explanation

    Answer: Option B

  • 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}

  • 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}