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

5823 = 2 × 2 × 2 × 3 × 3 × 3 × 3 × 3 × 3

= 23 × 33 × 33

= 183

5832 is a perfect cube.

∴ -5832 is a cube of negative integer – 18.

(ii) -2744000

2744000 = 2 × 2 × 2 × 2 × 2 × 2 × 5 × 5 × 5 × 7 × 7 × 7

= 23 × 23× 53 × 73

2744000 is a perfect cube.

∴ -2744000 is a cube of negative integer – 140.