# How do you rationalize the denominator and simplify sqrt(245/3)?

Jul 11, 2016

$\sqrt{\frac{245}{3}} = \frac{7 \sqrt{15}}{3}$

#### Explanation:

$\sqrt{\frac{245}{3}} = \frac{\sqrt{245}}{\sqrt{3}}$

As we have $\sqrt{3}$ in denominator, we need to multiply it by $\sqrt{3}$, that will make the denominator $\sqrt{9} = 3$ and thus rationalise the denominator. But as we multiply denominator by $\sqrt{3}$. we should also multiply numerator by $\sqrt{3}$. Hence,

$\sqrt{\frac{245}{3}} = \frac{\sqrt{245}}{\sqrt{3}}$

= (sqrt245×sqrt3)/(sqrt3×sqrt3

= $\frac{\sqrt{735}}{3}$

= sqrt(3×5×ul(7×7))/3

= $\frac{7 \sqrt{15}}{3}$