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Q.

Find the cube root of 135 $\sqrt{3} - 87 \sqrt{6} .$

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a

\sqrt{3} - \sqrt{6}

b

3 \sqrt{3} - 3 \sqrt{6}

c

2 \sqrt{3} - 5 \sqrt{6}

d

3 \sqrt{3} - \sqrt{6}

answer is D.

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Detailed Solution

Concept- Solving for Cube roots.
Given,
135

\sqrt{3} - 87 \sqrt{6} .

This equation can be written as

= 81 \sqrt{3} + 54 \sqrt{3} - 81 \sqrt{6} - 6 \sqrt{6}

= {(3 \sqrt{3})}^{3} + {(- \sqrt{6})}^{3} + 3 \times 3 \sqrt{3} \times (- \sqrt{6}) (3 \sqrt{3} - \sqrt{6})

=

{(3 \sqrt{3} - \sqrt{6})}^{3}

Hence, Cube root is

3 \sqrt{3} - \sqrt{6}

Hence, the correct option is 4.

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Find the cube root of 1353-87 6.