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

To find: 

We have to show that the given numbers are cubes of negative integers and find the integer whose cube is the given integer.

Solution:

(i) $-5832=-(2\times2\times2\times3\times3\times3\times3\times3\times3)$

$=-[(2^3)\times(3^3)\times(3^3)]$

$=-(2\times3\times3)^3$

$=-(18)^3$

All the factors of 5832 can be grouped in triplets of equal factors completely.

Therefore,

$-5832$ is a perfect cube of a negative integer. It is the cube of $-18$.

(ii) $-2744000=-(2\times2\times2\times2\times2\times2\times5\times5\times5\times7\times7\times7)$

$=-[(2^3)\times(2^3)\times(5^3)\times(7^3)]$

$=-(2\times2\times5\times7)^3$

$=-(140)^3$

All the factors of 2744000 can be grouped in triplets of equal factors completely.

Therefore,

$-2744000$ is a perfect cube of a negative integer. It is the cube of $-140$.

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Updated on: 10-Oct-2022

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