How do you rationalize the denominator and simplify #6/(3-sqrt11)#?

1 Answer
Aug 31, 2016

Answer:

#6/(3-sqrt(11)) =-9-3sqrt(11)#

Explanation:

Multiply both numerator and denominator by the radical conjugate #3+sqrt(11)# of the denominator, then simplify...

#6/(3-sqrt(11)) =(6(3+sqrt(11)))/((3-sqrt(11))(3+sqrt(11)))#

#color(white)(6/(3-sqrt(11))) =(6(3+sqrt(11)))/(3^2-(sqrt(11))^2)#

#color(white)(6/(3-sqrt(11))) =(6(3+sqrt(11)))/(9-11)#

#color(white)(6/(3-sqrt(11))) =-3(3+sqrt(11))#

#color(white)(6/(3-sqrt(11))) =-9-3sqrt(11)#