If the point $(3,6)$ is on the graph of $y=g(x)$, and $h(x)=(g(x))^2$ for all $x$, then there is one point that must be on the graph of $y=h(x)$. What is the sum of the coordinates of that point?
The fact that $(3,6)$ is on the graph of $y=g(x)$ means that $g(3)=6$. Therefore, $h(3)=(g(3))^2=6^2=36$, which tells us that $(3,36)$ is on the graph of $y=h(x)$. The sum of the coordinates of this point is $\boxed{39}$.