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