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|?