$a, b,$ and $c$ are not necessarily sides of a triangle, but they are positive numbers.
The question was:
Given that $a+b>c$ , does this imply that $\sqrt a +\sqrt b > \sqrt c$ , and that $a^2+b^2>c^2$ ?
The one with the square roots is easily proven by assuming it is true and squaring both sides. However, the one with the squares is giving be problems. I cannot arrive at a strong result. Of course sometimes $a^2+b^2$ will be equal to $c^2$ when $a, b$ are sides of a triangle, but I am not able to definitevly prove that $a^2+b^2$ is never $less$ than $c^2$ , so I am starting to believe that this statement is false. What is the way to solve this? Thanks.