Symmetric Matrices & Quadratic Forms · Hard problem

The positive definite matrix $A = \begin{pmatrix}9&3&0\\3&5&1\\0&1&3\end{pmatrix}$ has a Cholesky factorization $A=LL^{T}$ with $L$ lower triangular and positive diagonal entries. Find the entry of $L$ in row $3$, column $3$.