Question
Find the cube root of $91125$ by prime factorisation method.
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Answer
Prime factorisation of $91125$ is
$3 \times 3 \times 3 \times 3 \times 3 \times 3 \times 5 \times 5 \times 5$ [grouping the factors in triplets]
$=3^3 \times 3^3 \times 5^3=(3 \times 3 \times 5)^3=45^3$
Therefore, $\sqrt[3]{{91125}} = 3 \times 3 \times 5 = 45.$
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