# How do you rationalize the denominator and simplify (2+sqrt2)/sqrt3?

Aug 2, 2017

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

#### Explanation:

$\text{to rationalise the denominator}$

$\text{multiply the numerator/denominator by } \sqrt{3}$

•color(white)(x)sqrtaxxsqrta=a

•color(white)(x)sqrtaxxsqrtb=sqrt(axxb)

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

$= \frac{\sqrt{3} \left(2 + \sqrt{2}\right)}{3} \leftarrow \textcolor{red}{\text{ rational denominator}}$

$= \frac{2 \sqrt{3} + \sqrt{6}}{3}$