Prove by epsilon delta definition $\lim_{x\to\infty} \sqrt x = \infty $

Question

I find myself a bit confused with the definition. This is my attempt:

Let $ m \in \mathbb R >0$.

Let $ A \in \mathbb R > m^2$ such that for any $ x>A \Rightarrow \sqrt x > m $.

Is this correct?

Answer 1

Almost. $m \in \mathbb R >0$ and $A \in \mathbb R > m^2$ are senseless.

Better: let $m \in \mathbb R$ and $m >0$. If $x >m^2 $, then $\sqrt x > m.$

You are done .