Square root

The square root of a number, also called the 2nd root of the number, is the most common nth root. It is either a (positive) number, or a (positive) multiple of i.

Square root of non-negative integers
The square root of an integer is either an irrational number, like $$\sqrt{2}$$, or an integer, like 2 or 3.

The square root of 1 is 1, and the square root of 0 is 0, even though $$\frac{0}{0}$$ is different, as it is not zero at all.

General
The square root of n is known as √n. There are two square roots of n, $$\pm\sqrt{n}$$.

Square root of square numbers
As the square numbers are the square of integers, and are positive (so 0, which is neither positive or negative, is not a square number) even though its square root is an integer. The first square number is 1 [add reference to confirm it. or else, change]. The first composite number, 4, is a square number.

There are two integer square roots of square numbers, $$\sqrt{n}$$ and $$-\sqrt{n}$$, so the square roots of 4 are 2 and (-2). This applies even for other integers.

Negative square root of number
As $$n\cdot n = n^2$$, $$-n \cdot {-n} = -[-(n\cdot n)]$$, and -[-(n)] = n, therefore $$-n \cdot {-n} = n\cdot n$$, which is equal to n2. This proves that a negative number squared is a positive number, and also proves that there are 2 integer square roots of square numbers.

Square root of negative integers
The square root of -1 is i, also called the imaginary unit. It also means the square root of -n is $$\sqrt{n}\cdot i$$.