Can I square both sides of inequality for these functions?

Question

I have two functions $f(x)$ and $g(x)$ for $x>0$. Both functions are monotonically increasing and $f(x)>5$ and $g(x)>0$ .

I know that $f(x)>\sqrt{g(x)}$.

Then, can I conclude that $f(x)^2>g(x)$ for $x>0$?

Answer 1

Yes, because both $f$ and $\sqrt g$ are positive and $z\mapsto z^2$ is a strictly increasing function for positive $z$.