The question is how to calculate $r$ from $r^2$. Now, I know that its just as simple as taking a square root but is it as simple as that?
A Pearson correlation is really only defined for two variable problems. If you happen to run a regression to obtain $R^2$, yes the square root will just convert back to the correlation. In a multivariate context, however, the square root of $R^2$ really doesn’t tell you much.