Question

Write true (T) or false (F) for the following statement:

392 is a perfect cube.

Answer 1

 False
On factorising 392 into prime factors, we get:

\[392 = 2 \times 2 \times 2 \times 7 \times 7\] On grouping the factors in triples of equal factors, we get: \[392 = \left\{ 2 \times 2 \times 2 \right\} \times 7 \times 7\] It is evident that the prime factors of 392 cannot be grouped into triples of equal factors such that no factor is left over. Therefore, 392 is not a perfect cube.