Question

Find the cube root of the following integer −2744000 .

Answer 1

We have: \[\sqrt[3]{- 2744000} = - \sqrt[3]{2744000}\]

To find the cube root of 2744000, we use the method of factorisation.
On factorising 2744000 into prime factors, we get:

\[2744000 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 5 \times 5 \times 5 \times 7 \times 7 \times 7\]

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

\[2744000 = \left\{ 2 \times 2 \times 2 \right\} \times \left\{ 2 \times 2 \times 2 \right\} \times \left\{ 5 \times 5 \times 5 \right\} \times \left\{ 7 \times 7 \times 7 \right\}\]

It is evident that the prime factors of 2744000 can be grouped into triples of equal factors and no factor is left over.

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

 

\[2 \times 2 \times 5 \times 7 = 140\]

This implies that 2744000 is a cube of 140.

Hence,

\[\sqrt[3]{- 2744000} = - \sqrt[3]{2744000} = - 140\]