matrix square root

I know that the square root of a matrix can be found by firstly
performing an eigen decomposition , so that the matrix appears in the
form A = PDP^ -1 , and then from this, the square root of A is given
by
PD^1/2 P^ -1

But what if the matrix cannot be diagonalised? Can the square root of
a matrix be found in this instance?

.

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