Simplifying radicals inside radicals: $\sqrt{24+8\sqrt{5}}$ Simplify: $\sqrt{24+8\sqrt{5}}$
I removed the common factor 4 out of the square root to obtain $2\sqrt{6+2\sqrt{5}}$, but the answer key says it is $2+2\sqrt{5}$.
Am I missing out on some general rule here?

Hint. One may observe that
$$
6+2\sqrt{5}=(\sqrt{5})^2+2\sqrt{5}+1=(\sqrt{5}+1)^2.
$$
