TUYMAADA 2014 S8

Let positive integers $a,\ b,\ c$ be pairwise coprime. Denote by $g(a, b, c)$ the maximum integer not representable in the form $xa+yb+zc$ with positive integral $x,\ y,\ z$ . Prove that $$g(a, b, c)\ge \sqrt{2abc}$$

(M. Ivanov)