[tex]\bf \sqrt{8}+3\sqrt{2}+\sqrt{32}\qquad
\begin{cases}
8=2\cdot 2\cdot 2\\
\qquad 2^2\cdot 2\\
32=2\cdot 2\cdot 2\cdot 2\cdot 2\\
\qquad 2^4\cdot 2\\
\qquad (2^2)^2\cdot 2
\end{cases}
\\\\\\
\sqrt{2^2\cdot 2}+3\sqrt{2}+\sqrt{(2^2)^2\cdot 2}\implies 2\sqrt{2}+3\sqrt{2}+2^2\sqrt{2}
\\\\\\
\stackrel{like-terms}{2\sqrt{2}+3\sqrt{2}+4\sqrt{2}}\implies 9\sqrt{2}[/tex]
