[tex]3\sqrt{578}-\sqrt{162}+4\sqrt{32}=\\\\=3\sqrt{289\cdot2}-\sqrt{81\cdot2}+4\sqrt{16\cdot2}=\\\\=3\sqrt{17^2\cdot2}-\sqrt{9^2\cdot2}+4\sqrt{4^2\cdot2}=\\\\=3\cdot17\sqrt2-9\sqrt2+4\cdot4\sqrt2=\\\\=51\sqrt2-9\sqrt2+16\sqrt2=51\sqrt2+7\sqrt2=\boxed{58\sqrt2}[/tex]
