How do you simplify (8sqrt 2)/ (sqrt 3)?

Feb 10, 2016

$\frac{8 \sqrt{6}}{3}$

Explanation:

We want to "rationalize" the denominator--that is, get all square roots out of the denominator. We can do this by multiplying the fraction by $\sqrt{3} \text{/} \sqrt{3}$.

$= \frac{8 \sqrt{2}}{\sqrt{3}} \cdot \frac{\sqrt{3}}{\sqrt{3}} = \frac{8 \sqrt{2} \sqrt{3}}{3}$

To simplify the numerator, recall that when $a , b$ are positive, $\sqrt{a} \sqrt{b} = \sqrt{a b}$. Hence

$= \frac{8 \sqrt{2 \times 3}}{3} = \frac{8 \sqrt{6}}{3}$