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?

The nested radical:
$$
\sqrt{6+2\sqrt{5}}=\sqrt{6+\sqrt{20}}
$$
can be denested using the identity (that you can easely verify).
$$
\sqrt{a\pm \sqrt{b}}=\sqrt{\dfrac{a+ \sqrt{a^2-b}}{2}}\pm\sqrt{\dfrac{a- \sqrt{a^2-b}}{2}}
$$
that works if $a^2-b$ is a perfect square. In this case $a^2-b=16$
