Show that the following integers are cubes of negative integers. Also,

1.	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» (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.

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»

(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.