\[\left( \sqrt{6} + \sqrt{10} \right)^{2} = 6 + 2\sqrt{60} + 10 =\]
\[= 16 + \sqrt{240};\]
\[\left( 3 + \sqrt{7} \right)^{2} = 9 + 6\sqrt{7} + 7 =\]
\[= 16 + \sqrt{252};\]
\[3 + \sqrt{7} > \sqrt{6} + \sqrt{10}.\]