A matrix A belonging to $\displaystyle M_n$ is a square root of B belonging to $\displaystyle M_n$ if $\displaystyle A^2$=B. Show that every diagonalizable matrix in $\displaystyle M_n$ has a square root.

I know that a diagonal matrix has all zeros outside of the diagonal and the diagonal may or maynot have zeros. I want to say that these matrices must be similar as well.

I am not sure how to prove this. Any help would be great. Thanks!