# How do you simplify sqrt(5/3)?

Sep 18, 2017

$\sqrt{\frac{5}{3}} = \frac{\sqrt{15}}{3}$

#### Explanation:

Note that if $b > 0$ then:

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

The same is not true if $a > 0$ and $b < 0$.

Given to simplify:

$\sqrt{\frac{5}{3}}$

The way I have seen most people address this kind of problem is to separate the square root then rationalise the denominator by multiplying both numerator and denominator by $\sqrt{3}$, so:

$\sqrt{\frac{5}{3}} = \frac{\sqrt{5}}{\sqrt{3}} = \frac{\sqrt{5} \sqrt{3}}{\sqrt{3} \sqrt{3}} = \frac{\sqrt{15}}{3}$

Personally, I prefer to multiply the numerator and denominator by $3$ first, in order to make the denominator into a perfect square, thus:

$\sqrt{\frac{5}{3}} = \sqrt{\frac{15}{3} ^ 2} = \frac{\sqrt{15}}{\sqrt{{3}^{2}}} = \frac{\sqrt{15}}{3}$