Diagonalization & Matrix Powers · Challenge problem

Let $A = \begin{pmatrix}5 & 2 & 2\\2 & 5 & 2\\2 & 2 & 5\end{pmatrix}$. Let $B$ be the unique symmetric matrix with positive eigenvalues such that $B^2 = A$. Find the entry in row 1, column 2 of $B$.