# How do you rationalize the denominator and simplify 4/(6-sqrt5)?

Mar 27, 2016

$= \frac{24 + 4 \sqrt{5}}{31}$

#### Explanation:

$\frac{4}{6 - \sqrt{5}}$

To rationalize the denominator, we multiply the expression , by the conjugate of the denominator.

Conjugate , of  6 -sqrt5 = color(blue)( 6 + sqrt5

 4 / ( 6 -sqrt5) = (4 * (color(blue)( 6 + sqrt5))) / (( 6 -sqrt5) * color(blue)( 6 + sqrt5)

• Applying below mentioned property to simplify denominator:
color(blue)((a-b)(a+b) = a^2 - b^2

$= \frac{4 \cdot \left(\textcolor{b l u e}{6}\right) + 4 \cdot \left(\sqrt{5}\right)}{{\left(6\right)}^{2} - {\left(\sqrt{5}\right)}^{2}}$

= (24 + 4 sqrt5)/ ((36 - 5)

$= \frac{24 + 4 \sqrt{5}}{31}$