The square of an integer will always be an integer?

Yes, the square of an integer is always an integer.

Yes it will.

Yes.The square of an integer is just the number times itself. For any two whole numbers that are multiplied, the answer is always an integer (i.e. no decimals).

The square root of an integer is a CYCLOTOMIC integer.

no, the square root of an integer will not always be another integer. take the integer 27, for example. the square root of 27 is about 5.1961, which is not an integer.