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

1 Answer
Jun 4, 2017

Answer:

#5/(sqrt3+sqrt5)=(5sqrt5-5sqrt3)/2#

Explanation:

If you have a denominator of type #sqrta+sqrtb#, to rationalize multiply numerator and denominator by #sqrta-sqrtb# or vice-versa.

Hence to rationalize #5/(sqrt3+sqrt5)# multiply numerator and denominator by #sqrt3-sqrt5# and you get

#(5(sqrt3-sqrt5))/((sqrt3+sqrt5)(sqrt3-sqrt5))#

= #(5sqrt3-5sqrt5)/(3-5)#

= #(5sqrt3-5sqrt5)/(-2)#

= #5sqrt5-5sqrt3)/2#