# How do you simplify 5/(sqrt6+sqrt3)?

Aug 6, 2017

See a solution process below below:

#### Explanation:

To simplify this we can rationalize the denominator. Or, in other words, remove the radicals from the denominator.

To remove the radicals we need to multiply by the appropriate form of $1$. Remember that $\left(\textcolor{red}{x} + \textcolor{b l u e}{y}\right) \left(\textcolor{red}{x} - \textcolor{b l u e}{y}\right) = {\textcolor{red}{x}}^{2} - {\textcolor{b l u e}{y}}^{2}$ we can multiply this expression as:

$\frac{\sqrt{6} - \sqrt{3}}{\sqrt{6} - \sqrt{3}} \times \frac{5}{\sqrt{6} + \sqrt{3}} \implies$

$\frac{5 \left(\sqrt{6} - \sqrt{3}\right)}{{\left(\sqrt{6}\right)}^{2} - {\left(\sqrt{3}\right)}^{2}} \implies$

$\frac{5 \left(\sqrt{6} - \sqrt{3}\right)}{6 - 3} \implies$

$\frac{5 \left(\sqrt{6} - \sqrt{3}\right)}{3}$

Or

$\frac{5}{3} \left(\sqrt{6} - \sqrt{3}\right)$