Question
Find the cube root of $8000$.
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Answer
By prime factorisation,
$8000 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 5 \times 5 \times 5$ [grouping the factors in triplets]
$=2^3 \times 2^3 \times 5^3$[by laws of exponents]
$=(2 \times 2 \times 5)^3$
$=20^3$ which is a perfect cube.
Hence, $8000$ is a perfect cube.
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