The length of one side is 8 centimeters.
Extra information:
When the area is square, it means that all sides are the same size. When the area of the square is 64 centimeters, it means that the length of one side is the opposite of square: square root. Therefore if you take the square root of 64, you end up with 8. You can check this, by "imagining" the length of the sides (8 centimeters) and calculate the area. This is done by multiplying the length by width. The length and width are both 8, so the area will be 64. Therefore the length is correct!