Show that $\sqrt{\frac{a}{b+c}+ \frac{b}{c+a}}+ \sqrt{\frac{b}{c+a}+ \frac{c}{a+b}} + \sqrt{\frac{c}{a+b}+ \frac{a}{b+c}} \ge 3.$

Question

Suppose that $a,b,c>0$, show that $$\sqrt{\frac{a}{b+c}+ \frac{b}{c+a}}+ \sqrt{\frac{b}{c+a}+ \frac{c}{a+b}} + \sqrt{\frac{c}{a+b}+ \frac{a}{b+c}} \ge 3.$$

Appreciate any advice!