\[\sqrt{\left( 3 - \sqrt{8} \right)^{2}} + \sqrt{\left( 1 - \sqrt{8} \right)^{2}} =\]
\[= \left| 3 - \sqrt{8} \right| + \left| 1 - \sqrt{8} \right| =\]
\[= 3 - \sqrt{8} + \sqrt{8} - 1 = 2.\]