How do you simplify #-20/(sqrt6 - sqrt2)#?

1 Answer
Feb 24, 2016

Answer:

Rationalize the denominator to find that

#-20/(sqrt(6)-sqrt(2))=-5(sqrt(6)+sqrt(2))#

Explanation:

We will use the fact that #(a-b)(a+b) = a^2-b^2# to rationalize the denominator.

#-20/(sqrt(6)-sqrt(2)) = -(20(sqrt(6)+sqrt(2)))/((sqrt(6)-sqrt(2))(sqrt(6)+sqrt(2))#

#=-(20(sqrt(6)+sqrt(2)))/((sqrt(6))^2-(sqrt(2))^2)#

#=-(20(sqrt(6)+sqrt(2)))/(6-2)#

#=-(20(sqrt(6)+sqrt(2)))/4#

#=-5(sqrt(6)+sqrt(2))#