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 .


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