$\phantom{XX}\dfrac{2\sqrt{50}\;-\;\sqrt[\Large 3]{8}\;-\;3\sqrt{2}\;-\;\sqrt{8}}{\sqrt{2}}\;=$
$\;=\,\dfrac{2\sqrt{2\centerdot25}\;-\;\sqrt[\Large 3]{2\centerdot2\centerdot2}\;-\;3\sqrt{2}\;-\;\sqrt{2\centerdot 4}}{\sqrt{2}}\;=$
$\;=\,\dfrac{2\centerdot 5 \centerdot \sqrt{2}\;-\;\sqrt[\Large 3]{2^{\large 3}}\;-\;3\sqrt{2}\;-\;2\sqrt{2}}{\sqrt{2}}\;=$
$\;=\,\dfrac{10\sqrt{2}\;-\;2\;-\;3\sqrt{2}\;-\;2\sqrt{2}}{\sqrt{2}}\;=$
$\;=\,\dfrac{5\sqrt{2}\;-\;2}{\sqrt{2}}\centerdot \dfrac{\sqrt{2}}{\sqrt{2}}\;=$
$\;=\,\dfrac{5(\sqrt{2})^{\large 2}\;-\;2\sqrt{2}}{(\sqrt{2})^{\large 2}}\;=$
$\;=\,\dfrac{5\centerdot 2\;-\;2\sqrt{2}}{(2)}\;=$
$\;=\,\dfrac{2\centerdot(5\;-\;\sqrt{2})}{2}\;=\;5\;-\;\sqrt{2}$
