Question
Find the cube root of $175616$ by prime factorisation method.
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Answer
Prime factorisation of $175616$ is
$2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 7 \times 7 \times 7$ [grouping the factors in triplets]
$=2^3 \times 2^3 \times 2^3 \times 7^3=(2 \times 2 \times 2 \times 7)^3=56^3$ Therefore, $\sqrt[3]{{175616}} = 2 \times 2 \times 2 \times 7 = 56 .$
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