$$2+ \frac{ \sqrt{ 1 \sqrt{ 4 \sqrt{ 7 } } } }{ 2 }$$
$\frac{\sqrt{2}\sqrt[8]{7}}{2}+2\approx 2.901824972$
$\frac{\sqrt{2} \sqrt[8]{7} + 4}{2} = 2.901824972402568$
