Find which of the following numbers are cubes of rational numbers: `(27)/(64)` (ii) `(125)/(128)` (iii) `0. 001331` (iv) `0. 04`

Explanation

(i)`(27)/(64)=(3 xx 3 xx 3)/(4 xx 4 xx 4)=(3/4)^3`
Hence,`27/64` is a perfect cube of `3/4`.

(ii) `(125)/(128)`
`=(5 xx 5 xx 5)/(2 xx 2 xx 2 xx 2 xx 2 xx 2 xx 2)`
Hence,`125/128` is not a perfect cube.

(iii) `0. 001331`
`=( 11 xx 11 xx 11)/(100 xx 100 xx 100)=(11/100)^3`
Hence,`0. 001331` is a perfect cube of `11/100`.

(iv) `0.04`
`=(2 xx 2)/(20 xx 5)`
Hence, `0.04` is not a perfect cube.