# The minimum is irrational?

Algebra Level 5

$\large \dfrac{c}{\sqrt{ab + 1 - c}} + \dfrac{b}{\sqrt{ca + 1 - b}} + \dfrac{a}{\sqrt{bc + 1 - a}}$

For positive real numbers $$a$$, $$b$$, and $$c$$, find the minimum value of the expression above, for $$a+b+c =1$$. If the answer is in the form of $$\dfrac{p\sqrt{q}}{r}$$, where $$\gcd(p,r) = 1$$ and $$q$$ is square free, find $$p+q+r$$.

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