# What is (square root 2) + 2 (square root 2) + (square root 8) / (square root 3)?

Jun 2, 2015

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

$\sqrt{8}$ can be expressed as  color(red)(2sqrt2
the expression now becomes:

$\frac{\sqrt{2} + 2 \sqrt{2} + \textcolor{red}{2 \sqrt{2}}}{\sqrt{3}}$
$= \frac{5 \sqrt{2}}{\sqrt{3}}$

$\sqrt{2} = 1.414 \mathmr{and} \sqrt{3} = 1.732$

$\frac{5 \times 1.414}{1.732}$

$= \frac{7.07}{1.732}$

$= 4.08$