Question

Which of the following number is cube of negative integer - 1056 .

Answer 1

In order to check if a negative number is a perfect cube, first check if the corresponding positive integer is a perfect cube. Also, for any positive integer m, -m³ is the cube of - m.

On factorising 1056 into prime factors, we get:

\[1056 = 2 \times 2 \times 2 \times 2 \times 2 \times 3 \times 11\]

On grouping the factors in triples of equal factors, we get:​

\[1056 = \left\{ 2 \times 2 \times 2 \right\} \times 2 \times 2 \times 3 \times 11\]

It is evident that the prime factors of 1056 cannot be grouped into triples of equal factors such that no factor is left over. Therefore, 1056 is not a perfect cube. This implies that - 1056 is not a perfect cube as well.