Simplyfying roots - question

[user5196]

Hi Greg,

In the concept Simplifying Roots, there is an example where you simplify the cube root of 32.
You explained that this becomes the cube root of (8 × 4), and then you took out the cube root of 8 and wrote it as 2.

Earlier, under the root rules, you mentioned that for odd roots (like cube roots), the answer could be either positive or negative.
So I’m a bit confused: why didn’t you choose –2 here, and only used +2? Could you please explain why?

Thank you!

[cylverixxx]

@user5196

Earlier, under the root rules, you mentioned that for odd roots (like cube roots), the answer could be either positive or negative.

What is likely meant is that \sqrt[3]{x} can output either positive or negative numbers (or trivially zero) unlike something like \sqrt{x}.

@user5196

So I’m a bit confused: why didn’t you choose –2 here, and only used +2? Could you please explain why?

Because (-2)^3 \neq 2^3 = 8