# Which of the following numbers are cubes of negative integers.(i) $-64$(ii) $-1056$(iii) $-2197$(iv) $-2744$(v) $-42875$

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To find:

We have to find whether the given numbers are cubes of negative integer.

Solution:

(i) $-64=-(2\times2\times2\times2\times2\times2)$

$=-(2\times2\times2)\times(2\times2\times2)$

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

$=-(2\times2)^3$

$=-4^3$

All the factors of 64 can be grouped in triplets of equal factors completely.

Therefore,

$-64$ is a perfect cube of a negative integer.

(ii) $-1056=-(2\times2\times2\times2\times2\times3\times11)$

All the factors of 1056 cannot be grouped in triplets of equal factors completely.

Therefore,

$-1056$ is not a perfect cube of a negative integer.

(iii) $-2197=-(13\times13\times13)$

All the factors of 2197 can be grouped in triplets of equal factors completely.

Therefore,

$-2197$ is a perfect cube of a negative integer.

(iv) $-2744=-(2\times2\times2\times7\times7\times7)$

All the factors of 2744 can be grouped in triplets of equal factors completely.

Therefore,

$-2744$ is a perfect cube of a negative integer.

(v) $-42875=-(5\times5\times5\times7\times7\times7)$

All the factors of 42875 can be grouped in triplets of equal factors completely.

Therefore,

$-42875$ is a perfect cube of a negative integer.

Updated on 10-Oct-2022 12:46:26