Question
Find the cube root of $110592$ by prime factorisation method.
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Answer
Prime factorisation of $110592$ is
$2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times \times 3 \times 3 \times 3$ [grouping the factors in triplets]
$=2^3 \times 2^3 \times 2^3 \times 2^3 \times 3^3=(2 \times 2 \times 2 \times 2 \times 3)^3=24^3$
Therefore, $\sqrt[3]{{110592}} = 2 \times 2 \times 2 \times 2 \times 3 = 48 .$
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