\(\sqrt{12 + \sqrt{128}}\)
\begin{equation*}
{\color {blue} \sqrt{(a + b) + 2\sqrt{ab}} = \sqrt{a} + \sqrt{b}} \\
\end{equation*}
\begin{equation*}
\begin{split}
& \sqrt{12 + \sqrt{128}} \\\\
& \sqrt{12 + \sqrt{4 \:.\: 32}}
& \sqrt{12 + 2\sqrt{32}} \\\\
& \sqrt{(8 + 4) + 2\sqrt{8 \cdot 4}} \\\\
& \sqrt{8} + \sqrt{4} \\\\
& 2\sqrt{2} + 2
\end{split}
\end{equation*}