Finding a $\delta$ corresponding to $\epsilon = 0.01$ for $f(x) = \sqrt{x}$

Question

The answer I have is not aligning with that in the back of the book and I can't determine why. Here is my work thus far: \begin{align*} |f(x) - f(a)| &= |\sqrt{x} - \sqrt{2}| \\ &< |\sqrt{x}-\sqrt{2}||\sqrt{x}+\sqrt{2}|\\ &< |(\sqrt{x}-\sqrt{2})(\sqrt{x}+\sqrt{2})| \\ &< |x-2|< \epsilon \end{align*}

So $\delta=\epsilon=0.01$

Where am I going wrong here?