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:

$$2744000=\{2\times 2\times 2\}\times \{2\times 2\times 2\}\times \{5\times 5\times 5\}\times \{7\times 7\times 7\}$$

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,

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