Question
Find the cube root of $512$ by prime factorisation method.
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Answer
Prime factorisation of $512$ is
$2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 [grouping the factors in triplets]$
$=2^3 \times 2^3 \times 2^3=(2 \times 2 \times 2)^3=8^3$
Therefore, $\sqrt[3]{{512}} = 8$
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