How do you rationalize the denominator and simplify #5/(sqrt6+sqrt5)#?

1 Answer
May 10, 2016

Answer:

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

Explanation:

Use the difference of squares identity:

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

with #a=sqrt(6)# and #b=sqrt(5)#.

Multiply numerator and denominator by #sqrt(6)-sqrt(5)#

#5/(sqrt(6)+sqrt(5))#

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

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

#=(5(sqrt(6)-sqrt(5)))/1#

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