Given the area of a square, its perimeter can be determined uniquely. For example, the perimeter of a square containing 9 square units is 12 units. How did we figure this out? First, we observed that 9 square units may be arranged into a square in only one way: a 3 unit by 3 unit square. Hence, its perimeter is 4⋅3 units = 12 units. This is not true of any other quadrilateral, e.g. the perimeter of a rectangle with area 9 square units could be 2⋅1 unit + 2⋅9 units = 20 units since a 1 unit by 9 unit rectangle has the required area. Try this with other quadrilaterals to see that their sides are not uniquely determined by their areas.
Since the sides of a square is uniquely determined by its area, we may well-define the concept of a square root.
Informal Definition: The square root of n is the side length of a square with area n.