Normalizing an eigenvector to have unit length

I worked out a problem where one of the eigenvectors is $(1+ \sqrt{2}, 1)$. How do I normalize this vector? Should I use approximate values?

Here's the general formula for normalizing a vector: If $v$ is the non-zero vector $(a,b)$, then the normalized vector $v$ is
$$\frac{1}{\sqrt{a^2+b^2}}(a,b).$$