Question

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

8640 is not a perfect cube.

Answer 1

 True
On factorising 8640 into prime factors, we get:

\[8640 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 3 \times 3 \times 3 \times 5\] On grouping the factors in triples of equal factors, we get:

\[8640 = \left\{ 2 \times 2 \times 2 \right\} \times \left\{ 2 \times 2 \times 2 \right\} \times \left\{ 3 \times 3 \times 3 \right\} \times 5\] It is evident that the prime factors of 8640 cannot be grouped into triples of equal factors such that no factor is left over. Therefore, 8640 is not a perfect cube.