Which of the following numbers are cubes of negative integers?
(a) -64 (b) -2197 (c) -1056 (d) -3888
(a) 64 = 2x2x2x2x2x2

... -64 is a cube of -4 a negative integer.
(b) 2197 = 13x13x13

... -2197 is a cube of -13 a negative integer.
(c) 1056 = 2x2x2x2x2x3x11In the above factorisation 2 x 3 x 3 x 11 x 11 remains after grouping in triplets. Therefore, 1056 is not a perfect cube. Hence -1056 is not a cube of negative integer.
(d) 3888 = 2 x 2 x 2 x 2 x 3 x 3 x 3 x 3 x 3 In the above factorisation 2 x 3 x 3 remains after grouping in triplets. Therefore, 3888 is not a perfect cube.
Hence -3888 is not a cube of negative integer.
... -64 is a cube of -4 a negative integer.
(b) 2197 = 13x13x13
... -2197 is a cube of -13 a negative integer.
(c) 1056 = 2x2x2x2x2x3x11In the above factorisation 2 x 3 x 3 x 11 x 11 remains after grouping in triplets. Therefore, 1056 is not a perfect cube. Hence -1056 is not a cube of negative integer.
(d) 3888 = 2 x 2 x 2 x 2 x 3 x 3 x 3 x 3 x 3 In the above factorisation 2 x 3 x 3 remains after grouping in triplets. Therefore, 3888 is not a perfect cube.
Hence -3888 is not a cube of negative integer.
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