Question

Show that the following integers are cubes of negative integers. Also, find the integer whose cube is the given integer:
(i) -5832 (ii) -2744000

Answer 1

(i) $-5832=-\left(5832\right)=-(\underset{–}{2\times 2\times 2}\times \underset{–}{3\times 3\times 3}\times \underset{–}{3\times 3\times 3})$

Grouping the factors in triplets of equal factors, we see that no factor is left
$\therefore -5832$ is a perfect cube
Now taking one factor from each triplet wwe find that
- 5832 is a cube of $-(2\times 3\times 3)=-18$
$\therefore$ Cube root of - 5832 = - 18
(ii)$-2744000=-\left(274000\right)=\underset{–}{2\times 2\times }\times \underset{–}{2\times 2\times 2}\times \underset{–}{5\times 5\times 5}\times \underset{–}{7\times 7\times 7}$

Grouping the factors in triplets of equal factors, we see taht no factor is left. Therefore it is a perfect cube.
Now takingone factor from each triplet, we find that.
$-2744000isacubeof-(2\times 2\times 5\times 7)i.e.-140$
$\therefore$ Cube root of $-2744000=-140$