Question

Write true $\left(T\right)$ or false $\left(F\right)$ for the following statements:
$8640$ is not a perfect cube

Answer 1

Step: State true or false
Given statement: $8640$ is not a perfect cube

Resolving $8640$ into prime factors:
$$\begin{array}{cc}2& 8640\\ 2& 4320\\ 2& 2160\\ 2& 1080\\ 2& 540\\ 2& 270\\ 3& 135\\ 3& 45\\ 3& 15\\ 5& 5\\ & 1\end{array}$$
$8640=\{2\times 2\times 2\}\times \{2\times 2\times 2\}\times \{3\times 3\times 3\}\times 5$

Clearly, on grouping the factors in triplets of equal factors, we are left with one factor i.e., $5$

Thus, $8640$ is not a perfect cube.

Hence, the given statement is true.