In the equation

*n*\(^{2}\) =*N*, each real-number*n*whose square is equal to*N*is a square root of the real number*N*.### Symbols

The square roots of the number *N* are written as – \(\sqrt{N}\) and + \(\sqrt{N}\) which are read as “the negative square root of *N*” and “the positive square root of N”.

### Properties

- All positive real numbers
*N*have two square roots, written as – \(\sqrt{N}\) and + \(\sqrt{N}\)*.* - If
*N*is a positive real number, then*n*has two real values, with the same absolute value but with opposite signs. - If
*N*is a negative real number, then*n*has two imaginary values.

### Example

If *x*² = 100, then *x* = \(\sqrt{100}\) or *x* = – \(\sqrt{100}\).