Have a matrix dot its transpose, what is the original matrix?

Question

I have a matrix that equals the dot product of a matrix A with its transpose. How do I get the matrix A?

Ex.: $AA^T$ = [a given matrix]

Answer 1

In general, you can't. For example, $$[1\ 8]\begin{pmatrix}1 \\ 8\end{pmatrix} = [4\ 7]\begin{pmatrix}4 \\ 7\end{pmatrix} = [65].$$