Analyzing q further

Hey guys, I've already seen how to prove this problem using continuity however I'd like to also understand how to do it another way

Suppose $a_n>0$ for all $n$ and $a_n\rightarrow 3$ show that $\sqrt{a_n}\rightarrow \sqrt{3}$ .

How would I begin to show this by first showing algebraically that $|\sqrt{a_n}-\sqrt{3}|<|a_n-3|$ ?