Minimum value

Algebra Level 5

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

\[ \sqrt { \frac { a }{ b+c+d } } +\sqrt { \frac { b }{ a+c+d } } +\sqrt { \frac { c }{ a+b+d } } +\sqrt { \frac { d }{ a+b+c } } ?\]

Round your answer to the nearest hundredth.

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