# How do you solve the following? 6√1/6 - √2/3 the answer at the back of the book says 6√2, but I'm not sure how to get there.

Nov 1, 2014

Since

$6 \sqrt{\frac{1}{6}} = \frac{6}{\sqrt{6}} = \frac{{\left(\sqrt{6}\right)}^{2}}{\sqrt{6}} = \sqrt{6}$

and

$\sqrt{\frac{2}{3}} = \frac{\sqrt{2}}{\sqrt{3}} \cdot \frac{\sqrt{3}}{\sqrt{3}} = \frac{\sqrt{6}}{3}$,

we have

$6 \sqrt{\frac{1}{6}} - \sqrt{\frac{2}{3}} = \sqrt{6} - \frac{\sqrt{6}}{3} = \left(1 - \frac{1}{3}\right) \sqrt{6} = \frac{2}{3} \sqrt{6}$.

I hope that this was helpful.