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 = – \(\sqrt{100}\).