# Principal Value of a Square Root

A square root of a number $b$ is the solution of the equation ${x}^{2}=b$ .  It is a number that when multiplied by itself gives you $b$ .  Every positive number $b$ has two square roots , denoted $\sqrt{b}$ and $-\sqrt{b}$ .  The principal square root of $b$ is the positive square root, denoted $\sqrt{b}$ .

Example 1:

The square roots of $25$ are $\sqrt{25}=5$ and $-\sqrt{25}=-5$ since ${5}^{2}=25$ and ${\left(-5\right)}^{2}=25$ .

The principal square root of $25$ is $\sqrt{25}=5$ .

Example 2:

Find the real roots of the equation ${x}^{2}=100$ .

$x=±\sqrt{100}=±10$

Therefore, the roots are $10$ and $-10$ .

Example 3:

Simplify $\sqrt{36}$ .

$\sqrt{36}$  indicates the principal (or positive) square root so $\sqrt{36}=6$ .