Question

Which of the following number is cube of negative integer - 42875 .

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 42875 into prime factors, we get:

\[42875 = 5 \times 5 \times 5 \times 7 \times 7 \times 7\]

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

\[42875 = \left\{ 5 \times 5 \times 5 \right\} \times \left\{ 7 \times 7 \times 7 \right\}\]

It is evident that the prime factors of 42875 can be grouped into triples of equal factors and no factor is left over. Therefore, 42875 is a perfect cube. This implies that - 42875 is also a perfect cube.

Now, collect one factor from each triplet and multiply, we get: 

\[5 \times 7 = 35\] This implies that 42875 is a cube of 35.
Thus, - 42875 is the cube of - 35.