\[\boxed{\mathbf{599\ (599).\ }Еуроки\ - \ ДЗ\ без\ мороки}\]
\[1)\ \sqrt{\left( \sqrt{5} - 4 \right)^{2}} = \left| \sqrt{5} - 4 \right| =\]
\[= 4 - \sqrt{5}\]
\[2)\ \sqrt{\left( \sqrt{8} - 3 \right)^{2}} - \sqrt{\left( \sqrt{2} - 3 \right)^{2}} =\]
\[= \left| \sqrt{8} - 3 \right| - \left| \sqrt{2} - 3 \right| =\]
\[= - \sqrt{8} + 3 - 3 + \sqrt{2} =\]
\[= \sqrt{2} - \sqrt{8} = \sqrt{2} - 2\sqrt{2} = - \sqrt{2}\]