# Square Roots of a Real Number

## Square Roots of a Real Number

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 x² = 100, then x = $$\sqrt{100}$$ or x = – $$\sqrt{100}$$.