$$( \sqrt{ 6 } + \sqrt{ 2 } + \sqrt{ 3 } +1/2)/2$$
$\frac{\sqrt{2}}{2}+\frac{\sqrt{3}}{2}+\frac{\sqrt{6}}{2}+\frac{1}{4}\approx 3.047877056$
$\frac{2 \sqrt{2} + 2 \sqrt{3} + 2 \sqrt{6} + 1}{4} = 3.047877056362575$
