Answer
$2,622,950$ nurses
Work Step by Step
Let $x$ be the number of registered nurses in $2008.$
The conditions of the problem translate to the equation
\begin{array}{l}\require{cancel}
x+0.22x=3,200,000
.\end{array}
Using the properties of equality, the equation above is equivalent to
\begin{array}{l}\require{cancel}
1.22x=3,200,000
\\
x=\dfrac{3,200,000}{1.22}
\\
x=2622950.8196721311475409836065574
.\end{array}
Hence, the number of nurses in $2008$ was $
2,622,950
.$