# 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 ${x}^{2}=100$ .

$x=\pm \sqrt{100}=\pm 10$

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

**
Example 3:
**

Simplify $\sqrt{36}$ .

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