Question

How do I check for extraneous solutions?

Answer 1

\[\sqrt[3]{2x}+5=9\]

Answer 2

If you subtract 5 form both sides, you get sqrt(2x) = 4. If you now square it, you get 2x = 16, thus x = 8.

I am not sure what you mean by extraneous solutions. The square root function here, takes its domain as positive real numbers. It has only one solution.

Answer 3

Except I think it's the cube root, if I read it right.\[2x=64\]etc..