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?

You can start from the identity
\begin{equation}
24+8 \sqrt{5} =24+8 \sqrt{5}
\end{equation}
And write
\begin{equation}
24+8 \sqrt{5} =20+4+8 \sqrt{5} = (2+2 \sqrt{5})^{2}
\end{equation}
Then:
\begin{equation}
\sqrt{24+8 \sqrt{5}}=\sqrt{(2+2 \sqrt{5})^{2}}=2+2 \sqrt{5}
\end{equation}
