# Minimum value

Algebra Level 5

If $$a,b,c,$$ and $$d$$ are positive real numbers, what is the infimum (minimum) value of

$\sqrt { \frac { a }{ b+c+d } } +\sqrt { \frac { b }{ a+c+d } } +\sqrt { \frac { c }{ a+b+d } } +\sqrt { \frac { d }{ a+b+c } } ?$