[tex]\bf 3\sqrt{2}-\sqrt{50}+3-\sqrt{8}+\sqrt{288}-\sqrt{9}~~ \begin{cases} 50=2\cdot 5\cdot 5\\ \qquad 2\cdot 5^2\\ 8=2\cdot 2\cdot 2\\ \qquad 2^2\cdot 2\\ 288=2\cdot 2\cdot 2\cdot 2\cdot 2\cdot 3\cdot 3\\ \qquad 2^4\cdot 2\cdot 3^2\\ \qquad 2 (2^2)^2 3^2\\ \qquad 2(2^2 3)^2\\ \qquad 2(12)^2\\ 9=3^2 \end{cases}[/tex]
[tex]\bf 3\sqrt{2}-\sqrt{2\cdot 5^2}+3-\sqrt{2^2\cdot 2}+\sqrt{2\cdot 12^2}-\sqrt{3^2} \\\\\\ 3\sqrt{2}-5\sqrt{2}+3-2\sqrt{2}+12\sqrt{2}-3 \\\\\\ 3\sqrt{2}-5\sqrt{2}-2\sqrt{2}+12\sqrt{2}+3-3\implies \stackrel{\textit{adding like-terms}}{8\sqrt{2}}[/tex]
