Find the cube root each of the following : `\ 216\ xx\ 1728` (ii) `-125\ xx-3375`

Explanation

(i) `216xx1728=8xx8xx8xx12xx12xx12`
`root(3)(216xx1728)=8xx12`
`root(3)(216xx1728)=96`

(ii) `-125xx-3375`
`−125=−1×5×5×5`
`-125=−1×5^3`
`−3375=−1×3×3×3×5×5×5`
`-3375=−1×3^3xx5^3`
`∴125×3375=−1×−1×5^3×3^3×5^3`
`125xx3375=1×5^3×3^3×5^3`
Cube root of `(-125)xx(-3375)` is:
`root(3)((−125)×(−3375))=root(3)(5^3×3^3×5^3)`
`=5×3×5=75`