How to solve this inequality question: $\sqrt{\frac{a}{a+8}} + \sqrt{\frac{b}{b+8}} + \sqrt{\frac{c}{c+8}} \ge 1$ for $abc=1$?

Question

$abc=1$ where $a$, $b$, $c$ are positive reals. Prove that $$\sqrt{\frac{a}{a+8}} + \sqrt{\frac{b}{b+8}} + \sqrt{\frac{c}{c+8}} \ge 1$$