# How do you simplify sqrt 8 /( 2 sqrt3)?

Feb 28, 2016

$\frac{\sqrt{8}}{2 \sqrt{3}} = \textcolor{b l u e}{\frac{\sqrt{6}}{3}}$

#### Explanation:

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

Simplify $\sqrt{8}$.

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

Rewrite the fraction.

$\frac{2 \sqrt{2}}{2 \sqrt{3}}$

Rationalize the denominator by multiplying the numerator and denominator by $\sqrt{3}$.

$\frac{2 \sqrt{2}}{2 \sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}}$

Simplify.

$\frac{2 \sqrt{2} \sqrt{3}}{2 \times 3}$

Simplify.

$\frac{2 \sqrt{6}}{2 \times 3}$

Simplify.

$\frac{\cancel{2} \sqrt{6}}{\cancel{2} \times 3}$

Simplify.

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

Feb 28, 2016

$\sqrt{\frac{2}{3}}$

#### Explanation:

$8 = {2}^{3}$
$\sqrt{8} = {2}^{\frac{3}{2}}$

Therefore we have

$\frac{{2}^{\frac{3}{2}} {.2}^{- 1}}{\sqrt{3}}$

Add the exponent coefficients for 2

$\frac{{2}^{\frac{1}{2}}}{\sqrt{3}}$

Same as $\sqrt{\frac{2}{3}}$

Feb 28, 2016

$\sqrt{\frac{2}{3}}$

#### Explanation:

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

We could see that

$\sqrt{8} = \sqrt{4 \cdot 2}$

So

=sqrt(4*2)/(2sqrt3_

$= \frac{\cancel{2} \sqrt{2}}{\cancel{2} \sqrt{3}}$

$= \frac{\sqrt{2}}{\sqrt{3}} = \sqrt{\frac{2}{3}}$

But wait ! We could not have irrational numbers in the denominator.

So,rationalize the denominator by multiplying with $\frac{\sqrt{3}}{\sqrt{3}}$

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

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