The Root Sign Groups

The long bar of a root sign reaches over everything under it, and it groups that whole expression, the way a fraction bar groups its top. So in $\sqrt{9+16}$ you add first: $9+16$ is 25, and $\sqrt{25}$ is 5.

The tempting shortcut takes each root on its own: $\sqrt{9}+\sqrt{16}$ is $3+4$, which is 7. But 7 squared is 49, not 25, so 7 cannot be the root of 25. A root does not split over a sum.

So on the board, finish everything under the sign first, one line at a time, until a single number sits there. Only then take the root.