Question
Find the cube root of $46656$ by prime factorisation method.
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Answer
Prime factorisation of $46656$ is
$2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 3 \times 3 \times 3 \times 3 \times 3 \times 3$ [grouping the factors in triplets]
$=2^3 \times 2^3 \times 3^3 \times 3^3=(2 \times 2 \times 3 \times 3)^3=36^3$ [by laws of exponents]
Therefore, $\sqrt[3]{{46656}} = 2 \times 2 \times 3 \times 3 = 36 .$
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