# How do you simplify (sqrt2 * sqrt8)/2?

Apr 9, 2015

$\sqrt{2}$ $\cdot$ 2 $\sqrt{2}$ $\div$ 2 =

= 2

Apr 9, 2015

$\frac{\sqrt{2} \cdot \sqrt{\textcolor{b l u e}{8}}}{2}$

$= \frac{\sqrt{2} \cdot \sqrt{\textcolor{b l u e}{{2}^{3}}}}{2}$ (We write 8 as ${2}^{3}$)

$= \frac{\sqrt{2} \cdot \sqrt{\textcolor{b l u e}{{2}^{2} \cdot 2}}}{2}$ (We write ${2}^{3}$ as ${2}^{2} \cdot 2$)

$= \frac{\sqrt{2} \cdot \left(\cancel{2} \cdot \sqrt{2}\right)}{\cancel{2}}$ $\left(\sqrt{{2}^{2} \cdot 2} = \sqrt{{2}^{2}} \cdot \sqrt{2}\right)$

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

color(green)(= 2