Question

Prove that if limit of f(x) as x approaches infinity is a, then limit of sqrt{f(x)} is sqrt{a}

Answer 1

\[|\sqrt{f(x)}-\sqrt{a}|=\frac{ |f(x)-a| }{ |\sqrt{f(x)}+\sqrt{a}| }<\frac{ |f(x)-a| }{ \sqrt{a} }<\frac{ \epsilon }{ \sqrt{a} }\]
Is this correct? Is this enough of a proof?