Question

Write true $\left(T\right)$ or false $\left(F\right)$ for the following statements:
$392$ is a perfect cube

Answer 1

Step: State true or false

Given statement: $392$ is a perfect cube

Resolving $392$ into prime factors:

$$\begin{array}{cc}2& 392\\ 2& 196\\ 2& 98\\ 7& 49\\ 7& 7\\ & 1\end{array}$$

$392=\{2\times 2\times 2\}\times 7\times 7$

Clearly, on grouping the factors in triplets of equal factors, we are left with two factors i.e., $7\times 7$

Therefore, $392$ is not a perfect cube.

Hence, the given statement is false.