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)|)))#