How do you rationalize the denominator and simplify #3/(6-sqrt5)#?

1 Answer
Apr 4, 2016

Answer:

#18/31+3/31sqrt5#

Explanation:

WE can rationalize the denominator in #3/(6-sqrt5)# by multiplying numerator and denominator by conjugate of the denominator. The conjugate of #(6-sqrt5)# is #(6+sqrt5)#.

Hence #3/(6-sqrt5)=(3*(6+sqrt5))/((6-sqrt5)(6+sqrt5))#

= #(18+3sqrt5)/(36-5)# or

= #18/31+3/31sqrt5#