Question

How do you rationalize the denominator and simplify `(2+sqrt11)/(5-sqrt11)`?

Answer 1

To rationalize a denominator:
Multiply the numerator and denominator by the conjugate of the denominator.

`(2+sqrt(11))/(5-sqrt(11))xx(5+sqrt(11))/(5+sqrt(11))`

`=(10 +7sqrt(11)+11)/(25-11)`

`= (21+7sqrt(11))/(14)`

`= (3+sqrt(11))/2`