# How do you simplify (8sqrt3 )/ sqrt6?

Mar 27, 2018

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

#### Explanation:

Recall that $\frac{\sqrt{a}}{\sqrt{b}} = \sqrt{\frac{a}{b}}$

So, we're looking to simplify $8 \sqrt{\frac{3}{6}}$

$\frac{3}{6} = \frac{1}{2} ,$ so we have

$8 \sqrt{\frac{1}{2}} = \frac{8 \sqrt{1}}{\sqrt{2}} = \frac{8}{\sqrt{2}}$

Mar 27, 2018

$4 \sqrt{2}$

#### Explanation:

$\frac{8 \sqrt{3}}{\sqrt{6}}$

Rationalize Denominator

$\frac{8 \sqrt{3} \sqrt{6}}{6}$

Combine Roots

$\frac{8 \sqrt{18}}{6}$

Factor

$\frac{8 \sqrt{9 \cdot 2}}{6}$

Take Out The Nine

$\frac{8 \cdot 3 \sqrt{2}}{6}$

Simplify

$\frac{24 \sqrt{2}}{6}$

Simplify

$4 \sqrt{2}$

Mar 27, 2018

$\frac{8 \sqrt{3}}{\sqrt{6}} = 4 \sqrt{2}$

#### Explanation:

Given:

$\frac{8 \sqrt{3}}{\sqrt{6}}$

Rationalize the denominator:

$\Rightarrow \frac{8 \sqrt{3}}{\sqrt{6}} \cdot \frac{\sqrt{6}}{\sqrt{6}}$

rArr [8 sqrt(3) sqrt(6)]/(sqrt(6) sqrt(6)

Observe that color(blue)(sqrt(m) * sqrt(m)=m and

rArr color(blue)(sqrt(mn)=sqrt(m)*sqrt(n)

$\Rightarrow \frac{8 \sqrt{3} \sqrt{3 \cdot 2}}{6}$

$\Rightarrow \frac{2 \cdot 4 \sqrt{3} \sqrt{3} \sqrt{2}}{2 \cdot 3}$

$\Rightarrow \frac{2 \cdot 4 \cdot 3 \cdot \sqrt{2}}{2 \cdot 3}$

$\Rightarrow \frac{\cancel{2} \cdot 4 \cdot \cancel{3} \cdot \sqrt{2}}{\cancel{2} \cdot \cancel{3}}$

$\Rightarrow 4 \sqrt{2}$

Hence,

color(red)((8 sqrt(3))/(sqrt(6)) = 4 sqrt2