Square roots

The square root of a non-negative number $a$ is the non-negative number $x$ such that $x^2 = a$. This is written as $x = \sqrt{a}$. The square root symbol $\sqrt{\ }$ always refers to the principal (non-negative) root.

Important properties

• For any $a \geq 0$, $\sqrt{a} \geq 0$ and $\sqrt{a}^2 = a$.

• $\sqrt{ab} = \sqrt{a} \cdot \sqrt{b}$ for $a, b \geq 0$.

• $\sqrt{a^2} = |a|$ for any real number $a$.

• $\sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}}$ for $a \geq 0, b > 0$.