# How do you rationalize the denominator and simplify #(10-sqrt3)/(6+sqrt6)#?

##### 1 Answer

Mar 15, 2016

#### Explanation:

#(10-sqrt(3))/(6+sqrt(6))#

#=(10-sqrt(3))/(6+sqrt(6))((6-sqrt(6))/(6-sqrt(6)))#

#=(60-10sqrt(6)-6sqrt(3)+sqrt(18))/(6+sqrt(6))(1/(6-sqrt(6)))#

#=(60-10sqrt(6)-6sqrt(3)+3sqrt(2))/(6+sqrt(6))(1/(6-sqrt(6)))#

#=(60-10sqrt(6)-6sqrt(3)+3sqrt(2))/(36-6)#

#=color(green)(|bar(ul(color(white)(a/a)(60-10sqrt(6)-6sqrt(3)+3sqrt(2))/30color(white)(a/a)|)))#