Сравните числа:

\[\left( \sqrt{5} + \sqrt{3} \right)^{2} = 5 + 2\sqrt{15} + 3 =\]

\[= 8 + 2\sqrt{15}\]

\[\left( \sqrt{2} + \sqrt{8} \right)^{2} = 2 + 2\sqrt{16} + 8 =\]

\[= 10 + 2 \cdot 4 = 8 + 10\]

\[8 + 2\sqrt{15} < 8 + 10\]

\[\Longrightarrow \sqrt{5} + \sqrt{3} < \sqrt{2} + \sqrt{8}.\]