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