\[17\sqrt{2} - 3\sqrt{32} + \sqrt{50} =\]
\[= 17\sqrt{2} - 3\sqrt{16 \cdot 2} + \sqrt{25 \cdot 2} =\]
\[= 17\sqrt{2} - 12\sqrt{2} + 5\sqrt{2} = 10\sqrt{2}\]