1To obtain the square root of a matrix, say matrix C  , follow these steps.

Determine the eigenvalues λ  of the matrix.
For each eigenvalue λn  determine the correspending eigenvector Vn
Construct the Matrix N  whose columns are the eigenvectors Vn  . i.e. the first column will be the vector V1  etc...
Construct matrix M  with diagonal elements that contains the √ ---
  λn  . i.e.          √ --
M  (1,1) =  λ1  ,           √--
M  (2,2) =  λ2  , and so forth. (This is the Jordan form for real distinct eigenvalues)
Now √--
 C = N TM N

In Matlab, the command expm() can be used to calculate sqrt of a matrix.