Why is finding the square root of 36 the same as finding the side length of a square with an area of 36 square units?

Answer 1

Area of a square is (length) x (width) and in a square the length and width are the same and let's just call it "L"

So area of square is L x L = L-squared

So if the area of a square is given, its side is square root of the area. Thus if 36 square units represent the area of a square, then its square root which is 6 is the side of the square figure. This holds good for other areas like 4, 9, 16, 25, 49, 64,.... etc. whose quare roots are 2, 3, 4, 5, 7, 8,...etc.