Question

How do you rationalize the denominator `(2+sqrt3)/(5-sqrt3)`?

Answer 1

`(2 + sqrt(3))/(5 - sqrt(3)) = ((2 + sqrt(3))xx(5 + sqrt(3)))/((5 - sqrt(3))xx(5 + sqrt(3))`

`= (10 + 5sqrt(3) + 2sqrt(3) + (sqrt(3))^2)/(25 - (sqrt(3))^2)`

`= (10 + 3 + 8sqrt(3))/(25 - 3)`

`= (13 + 8sqrt(3))/(22)`