How do you simplify #(4+sqrt2)/(3+2sqrt3)#?

1 Answer
Apr 15, 2018

Answer:

I think you're asking for rationalizing?
Answer: #-12+11sqrt(2)-2sqrt(6)#

Explanation:

You rationalize it by multiply both numerator and denominator with its conjugate, which is: #3-sqrt(2)#

#(4+sqrt(2))/(3+sqrt(2)) ((3+sqrt(2))/(3+sqrt(2)))#
#=(12+3sqrt(2)-8sqrt(2)-2sqrt(2)sqrt(3))/(3^2-4(3)#
#=-(12-5sqrt(2)-2sqrt(6))/3#