# How do you rationalize the denominator and simplify 6/(sqrt4+sqrt5)?

Mar 24, 2016

$6 \left(\sqrt{5} \pm 2\right)$

#### Explanation:

Multiply numerator and denominator by the conjugate $\sqrt{5} - \sqrt{4}$ of the denominator and use $\left(a - b\right) \left(a + b\right) = \left({a}^{2} - {b}^{2}\right)$. Hence,

6/(sqrt5+2)=(6(sqrt5-2))/ ((sqrt5-2)(sqrt5+2)) or

$\frac{6 \left(\sqrt{5} - 2\right)}{5 - 4}$ or

$6 \left(\sqrt{5} - 2\right)$