How do you rationalize the denominator and simplify #(4sqrt5)/(3sqrt5+2sqrt2)#?

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Answer 1 · 2017-05-02T11:40:04

#1/37( 60-8sqrt10) #

To rationalize the denominator multiply by #(3sqrt5-2sqrt2)# in both numerator and denominator. we get ,

#((4sqrt5)* (3sqrt5-2sqrt2))/((3sqrt5+2sqrt2)*(3sqrt5-2sqrt2)#

#=(12*5 -8*sqrt10)/((3sqrt5)^2- (2sqrt2)^2) = (60-8sqrt10)/(45-8)#

#= (60-8sqrt10)/37 =1/37( 60-8sqrt10) # [Ans]

Answer 2 · 2017-05-02T12:05:09

we can multiply the fraction by 1 to rationalise the denominator

#(4sqrt5)/(3sqrt5 + 2sqrt2)##times (3sqrt5 - 2sqrt2)/(3sqrt5 - 2sqrt2)#

This gives #(60 - 8sqrt10)/(45 - 8)#

i think the remaining workings should be quite easy to complete