Question

Which of the following number is cube of negative integer - 2744 .

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 2744 into prime factors, we get:

\[2744 = 2 \times 2 \times 2 \times 7 \times 7 \times 7\] 

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

 

\[2744 = \left\{ 2 \times 2 \times 2 \right\} \times \left\{ 7 \times 7 \times 7 \right\}\] 

It is evident that the prime factors of 2744 can be grouped into triples of equal factors and no factor is left over. Therefore, 2744 is a perfect cube. This implies that - 2744 is also a perfect cube.

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

 \[2 \times 7 = 14\]

This implies that 2744 is a cube of 14.
Thus, - 2744 is the cube of -14.