Question

How do you find the cube roots of `1000`?

Answer 1

Cube roots of `1000` are `10`, `(-5+5sqrt3i)` and `(-5-5sqrt3i)`

Explanation:

Cube roots of `1` are well known namely

`1`, `-1/2+sqrt3/2i` and `-1/2-sqrt3/2i`

Hence cube roots of `1000=10^3` are

`10xx1=10`,

`10xx(-1/2+sqrt3/2i)=-5+5sqrt3i` and

`10xx(-1/2-sqrt3/2i)=-5-5sqrt3i`