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

##### 1 Answer

Oct 11, 2015

Multiply both numerator and denominator by

#### Explanation:

#4/(6-sqrt(5)) = (4(6+sqrt(5)))/((6-sqrt(5))(6+sqrt(5))) =#

#=(24+4sqrt(5))/(6^2-sqrt(5)^2) = (24+4sqrt(5))/(36-5)#

#=(24+4sqrt(5))/31#

This uses the difference of squares identity to square any square roots in the binomial denominator.

#(a-b)(a+b) = a^2 - b^2#

In our case