Question

How do you simplify `root3(-16x^8)`?

Answer 1

`-2x^2root3(2x^2)`

Explanation:

We have:

`root3(-16x^8)`

I'm going to rewrite the terms under the root sign into terms of cubes:

`root3((-1)^3(2^3)2^1x^3x^3x^2)`

The cube root and the cubes inside the root are inverse functions, so we simply end up with the base term. Everything else is a "remainder" and stays within the root sign:

`-1(2)(x)(x)root3(2^1x^2)`

and cleaning this up a bit:

`-2x^2root3(2x^2)`

While there is the same term inside as outside the root sign, we can't really factor it more than where we are, so I'll leave it here.