Question:
363 x 81 is a perfect cube.
Solution:
False
$\because \quad 363 \times 81=3 \times 11 \times 11 \times 3 \times 3 \times 3 \times 3$
$=3 \times 3 \times 3 \times 3 \times 3 \times 11 \times 11$
Grouping the factors in triplets of equal factors, we have
$363 \times 81=(3 \times 3 \times 3) \times 3 \times 3 \times 11 \times 11$
Clearly, in grouping, the factors in triplets of equal factors, we are left with two factors $3 \times 3$ and $11 \times 11$.
Hence, $363 \times 81$ is not a perfect cube.
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