# How do you simplify sqrt(1/8)?

Mar 28, 2018

$\frac{\sqrt{2}}{4}$

#### Explanation:

Looking at the given expression:
$\sqrt{\frac{1}{8}}$

By: $\sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}}$

$\sqrt{\frac{1}{8}} = \frac{\sqrt{1}}{\sqrt{8}}$

Which is:

$\frac{\sqrt{1}}{\sqrt{8}} = \frac{1}{\sqrt{8}}$

Simplify:
$\frac{1}{\sqrt{8}} = \frac{1}{\sqrt{2 \cdot 4}}$

$\frac{1}{\sqrt{2 \cdot 4}} = \frac{1}{2 \sqrt{2}}$

Rationalize the denominator:
$\frac{1}{2 \sqrt{2}} \cdot \frac{\sqrt{2}}{\sqrt{2}} = \frac{\sqrt{2}}{4}$

Mar 28, 2018

sqrt(1/8)=color(blue)(sqrt2/4

#### Explanation:

Simplify:

$\sqrt{\frac{1}{8}}$

Apply square root rule: sqrt(a/b)=sqrta/sqrtb; b!=0

$\frac{\sqrt{1}}{\sqrt{8}}$

Simplify $\sqrt{1}$ to $1$.

$\frac{1}{\sqrt{8}}$

Rationalize the denominator.

$\frac{1}{\sqrt{8}} \times \frac{\sqrt{8}}{\sqrt{8}}$

$\frac{\sqrt{8}}{\sqrt{8} \sqrt{8}}$

Apply square root rule: $\sqrt{a} \sqrt{a} = a$

$\frac{\sqrt{8}}{8}$

Prime factorize $\sqrt{8}$.

$\frac{\sqrt{2 \times 2 \times 2}}{8} =$

$\frac{\sqrt{{2}^{2} \times 2}}{8}$

Apply square root rule: $\sqrt{{a}^{2}} = a$

$\frac{{\textcolor{red}{\cancel{\textcolor{b l a c k}{2}}}}^{1} \sqrt{2}}{\textcolor{red}{\cancel{\textcolor{b l a c k}{8}}}} ^ 4$

Simplify.

$\frac{\sqrt{2}}{4}$