Which of the following integers are cubes of negative integers
(i) -64
(ii) -1056
(iii) -2197
(iv) -2744
(v) -42875
Prime factors of 64 = 2 × 2 × 2 × 2 × 2 × 2 = 23 × 23 = 43
We find that 64 is a perfect cube of negative integer – 4 .
Prime factors of 1056 = 2 × 2 × 2 × 2 × 2 × 3 × 11
We find that 1056 is not a perfect cube.
Hence, - 1056 is not a cube of negative integer
Prime factors of 2197 = 13 × 13 × 13 = 133
We find that 2197 is a perfect cube.
Hence, - 2197 is a cube of negative integer – 13 .
Prime factors of 2744 = 2 × 2 × 2 × 7 × 7 × 7 = 23 × 73 = 143
We find that 2744 is a perfect cube.
Hence, - 2744 is a cube of negative integer – 14 .
Prime factors of 42875 = 5 × 5 × 5 × 7 × 7 × 7 = 53 × 73 = 353
We find that 42875 is a perfect cube.
Hence, - 42875 is a cube of negative integer – 35.