Question

Why are functions biased towards the positive for square roots?

Answer 1

\[f(x)=\sqrt{x}\] If you look at x=4 it always seems to graphically show 2 and not -2. Why is the principal root of a number shown? I guess it's to keep the function continuous, but why is that important?

Answer 2

It's conventional usage and makes some other things, like inverses, easier to handle without special cases.

What's the cube root of -8? -2 or something else?