I think there is something wrong with what you have written because expressions like usually work for vector norms. Using a square matrix of any size will give you a vector back. Indeed, if , then

and taking the square root gives you the norm of thevector. Since you only have one index in the sum, I would assume you are talking about vectors . In that case you simply have that is a unit vector.

More generally, if is some norm (vector or matrix, if doesn't matter), then you have

Since is a constant, you have

You should check exactly what the question is asking you.

Now, if you are interested in the square roots of matrices, they are not numbers. If is a square matrix, we seek to find a matrix such that and we call . In general, is not unique. You may read more about it here Square root of a matrix - Wikipedia, the free encyclopedia