Question

Question 82

State whether the following statement is true or false:

$363\times 81$ is a perfect cube.

Answer 1

False
$\because$ $363\times 81=3\times 11\times 11\times 3\times 3\times 3\times 3$
$=3\times 3\times 3\times 3\times 3\times 11\times 11$
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.