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

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

#### Explanation:

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

and now we can see that there is a square root in the denominator that doesn't belong. So let's get rid of that.

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

Apr 21, 2017

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

#### Explanation:

Note that if $a \ge 0$ and $b > 0$ then:

$\sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}}$

Also if $a \ge 0$ then:

$\sqrt{{a}^{2}} = a$

Instead of breaking up the square root then rationalising the denominator, we can make the denominator square first as follows:

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