# What is the simplest radical form of sqrt(10/6)?

Jul 23, 2015

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

#### Explanation:

To get the simplest radical form of $\sqrt{\frac{10}{6}}$, you first have to simplify the fraction that's under the radical, $\frac{10}{6}$.

$\frac{10}{6} = \frac{\cancel{2} \cdot 5}{\cancel{2} \cdot 3} = \frac{5}{3}$

$\sqrt{\frac{5}{3}}$
$\sqrt{\frac{5}{3}} = \frac{\sqrt{5}}{\sqrt{3}}$
Rationalize the denominator by multiplying the numerator and the denominator by $\sqrt{3}$ to get
$\frac{\sqrt{5} \cdot \sqrt{3}}{\sqrt{3} \cdot \sqrt{3}} = \frac{\sqrt{5 \cdot 3}}{\sqrt{3 \cdot 3}} = \textcolor{g r e e n}{\frac{\sqrt{15}}{3}}$