Question
Is $46656$ a perfect cube?
✓
Answer
By prime factorisation,
$46656 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 3 \times 3 \times 3 \times3 \times 3 \times 3$ [grouping the factors in triplets]
$=2^3 \times 2^3 \times 3^3 \times 3^3$
$=36^3$ which is a perfect cube.
All the terms form triplets
Therefore, $46656$ is a perfect cube.
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