How do you rationalize the denominator #(8sqrt2)/(sqrt20-sqrt18)#?

1 Answer
Alan P.
May 27, 2015

To rationalize the denominator, multiply both the numerator and the denominator by the conjugate of the denominator.

#(8sqrt(2))/(sqrt(20)-sqrt(18))#

#= (8sqrt(2))/(sqrt(20)-sqrt(18))* (sqrt(20)+sqrt(18))/(sqrt(20)+sqrt(18))#

#= (8sqrt(40)+8sqrt(36))/(20-18)#

#= (8(2sqrt(10)+6))/2#

#= 24 + 8sqrt(10)#

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