# How do you simplify 4 sqrt (81 / 8)?

$E = 4 \sqrt{\frac{81}{8}} = 4 \cdot \frac{\sqrt{81}}{\sqrt{8}} = 4 \cdot \frac{9}{\sqrt{4 \cdot 2}} = 4 \cdot \frac{9}{\sqrt{4} \cdot \sqrt{2}}$
$E = \stackrel{\textcolor{b l u e}{2}}{\cancel{4}} \cdot \frac{9}{\cancel{2} \cdot \sqrt{2}} = \frac{18}{\sqrt{2}}$
$E = \frac{18 \cdot \sqrt{2}}{\sqrt{2} \cdot \sqrt{2}} = \frac{18 \cdot \sqrt{2}}{2} = \frac{\stackrel{\textcolor{b l u e}{9}}{\cancel{18}} \cdot \sqrt{2}}{\cancel{2}} = \textcolor{g r e e n}{9 \sqrt{2}}$