Question

Let a, b, c>=0. Prove that \[\sqrt{3(a+b+c)} \geq \sqrt{a}+\sqrt{b}+\sqrt{c}.\]
Which of AM-GM, Cauchy-Schwarz, and Chebyshev's Inequality should be used?

Answer 1

http://math.stackexchange.com/questions/128983/showing-fracxyz3-ge-sqrt3xyz-for-x-y-z-ge-0