The laws of exponents help you out here. We can write square root of a number n, as n^1/2 power. Now we know that raising and exponent to a powers is done according to the rule (a^b)^c=a^bc. That is...
When you square a number, you are referring to the area of a square, where the number you are squaring is a side length. The square root is a method of finding a side length when you know the area.