# Minimal Value

Algebra Level 3

Given positive reals $$a,b,c$$ and $$ab+bc+ca\ge 3$$. The minimum value of $$\frac{a}{\sqrt{b+c}}+\frac{b}{\sqrt{c+a}}+\frac{c}{\sqrt{a+b}}$$ is $$\frac{m}{\sqrt{n}}$$, where $$m,n$$ are square-free integers. Find the value of $$mn$$.

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