# No, the answer is not 2.500

Algebra Level 5

$\begin{eqnarray} &&\sqrt{ \dfrac a{b+c+d+e}} + \sqrt{ \dfrac b{a+c+d+e}} + \sqrt{ \dfrac c{a+b+d+e}} \\ && + \sqrt{ \dfrac d{a+b+c+e}} + \sqrt{ \dfrac e{a+b+c+d}} \end{eqnarray}$

Over all non-negative real numbers $$a,b,c,d$$ and $$e$$, find the infimium value of the expression above.