Whitening two correlated signals

Two trading signals have covariance matrix

You want to transform a signal vector $r$ into $z = Wr$ with uncorrelated, unit-variance components, using a symmetric $W$.

Find the symmetric square root $\Sigma^{1/2}$ (the symmetric positive definite matrix whose square is $\Sigma$) and $W = \Sigma^{-1/2}$. Then whiten today's reading $r = (3, 1)$.