# How do you simplify: (sqrt2+ 2sqrt2 +sqrt8) /sqrt3?

Aug 13, 2018

$\frac{\sqrt{2} + 2 \sqrt{2} + \sqrt{8}}{\sqrt{3}} = \frac{5}{3} \sqrt{6}$

#### Explanation:

As we have a surd in the denominator, here simplifying means rationalizing the denominator, which can be done by multiplying numerator and denominator by $\sqrt{3}$.

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

= $\frac{\sqrt{2} + 2 \sqrt{2} + \sqrt{\underline{2 \times 2} \times 2}}{\sqrt{3}}$

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

= $\frac{5 \sqrt{2}}{\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}}$

= $\frac{5 \sqrt{6}}{3}$

= $\frac{5}{3} \sqrt{6}$

Aug 13, 2018

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

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

Collect like terms

$\frac{5 \sqrt{2}}{\sqrt{3}}$

Rationalise the denominator

$\frac{5 \sqrt{2}}{\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}}$

$\frac{5 \sqrt{6}}{3}$