Answer
$20\sqrt2-5\sqrt3$
Work Step by Step
Factor each radicand so that one of the factors is a perfect square to obtain:
\begin{align*}
&=3\sqrt{4(2)}-\sqrt{16(2)}+3\sqrt{36(2)}-\sqrt{25(3)}\\
\end{align*}
Simplifiy each radical by taking out the square root of each perfect square factor inside the radical sign to obtain:
\begin{align*}
&=3(2)\sqrt2-4\sqrt2+3(6)\sqrt2-5\sqrt3\\
&=6\sqrt2-4\sqrt2+18\sqrt2-5\sqrt3\\
&=(6-4+18)\sqrt2-5\sqrt3\\
&=20\sqrt2-5\sqrt3
\end{align*}
