How do you rationalize the denominator (8sqrt2)/(sqrt20-sqrt18)8√2√20−√18?

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))8√2√20−√18

= (8sqrt(2))/(sqrt(20)-sqrt(18))* (sqrt(20)+sqrt(18))/(sqrt(20)+sqrt(18))=8√2√20−√18⋅√20+√18√20+√18

= (8sqrt(40)+8sqrt(36))/(20-18)=8√40+8√3620−18

= (8(2sqrt(10)+6))/2=8(2√10+6)2

= 24 + 8sqrt(10)=24+8√10

Related questions
See all questions in Multiplication and Division of Radicals
Impact of this question
2302 views around the world
You can reuse this answer
Creative Commons License