Find a matrix $B$ so that $A = BB^{T}$

Question

$A$ is $$A= \begin{pmatrix} 2 & 0 & 1 \\ 0 & 2 & 0 \\ 1 & 0 & 2 \\ \end{pmatrix} $$ Find a matrix $B$ so that $A=BB^{T}$. Hint: $A=PDP^{T}$.

Answer 1

Hint: since $D$ is diagonal, you can take its square root $\sqrt{D}$. Then define

$$B\equiv P\sqrt{D}$$