Show that the following integers are cubes of negative integers. Also, find the integer whose cube is the given integer.
(i) -5832
(ii) -2744000
(i) -5832
Prime factors of 5832 = 2 × 2 × 2 × 3 × 3 × 3 × 3 × 3 × 3 = 23 × 33 × 33 = 183
We find that 5832 is a perfect cube.
Hence, - 5832 is a cube of negative integer – 18 .
(ii) -2744000
Prime factors of 2744000 = 2 × 2 × 2 × 2 × 2 × 2 × 5 × 5 × 5 × 7 × 7 × 7 = 23 × 23 × 53 × 73
We find that 2744000 is a perfect cube.
Hence, - 2744000 is a cube of negative integer – 140 .