How do you rationalize the denominator #(8sqrt2)/(2sqrt5-3sqrt2)#?

1 Answer
Jun 14, 2015

Answer:

Multiply both numerator and denominator by the conjugate #(2sqrt(5)+3sqrt(2))# to get:

#(8sqrt(2))/(2sqrt(5)-3sqrt(2)) = #

Explanation:

#(8sqrt(2))/(2sqrt(5)-3sqrt(2))#

#=(8sqrt(2))/(2sqrt(5)-3sqrt(2))*(2sqrt(5)+3sqrt(2))/(2sqrt(5)+3sqrt(2))#

#=(8sqrt(2)(2sqrt(5)+3sqrt(2)))/(20-18)#

#=4sqrt(2)(2sqrt(5)+3sqrt(2))#

#=8sqrt(2)sqrt(5)+24#

#=8sqrt(10)+24#

#=8(sqrt(10)+3)#