How do you rationalize the denominator and simplify #5/(sqrt3+sqrt5)#?

1 Answer
Jan 18, 2017

Answer:

I got as far as: #-5/2*(sqrt(3)-sqrt(5))#

Explanation:

You can multiply and divide by #sqrt(3)-sqrt(5)# and take advantage of the fact that: #(a+b)(a-b)=a^2-b^2# and write:

#5/(sqrt(3)+sqrt(5))*color(red)((sqrt(3)-sqrt(5))/(sqrt(3)-sqrt(5))=#

#=(5*(sqrt(3)-sqrt(5)))/(3-5)=-5/2*(sqrt(3)-sqrt(5))#