Question

How do you rationalize the denominator and simplify your answer `3/(2 + sqrt(12))`?

Answer 1

To rationalize the denominator multiply both the numerator and the denominator by the conjugate of the denominator

`3/(2+sqrt(12))`

`=3/(2+sqrt(12)) xx (2-sqrt(12))/(2-sqrt(12))`

`= (6-3sqrt(12))/(4-12)`

`=(6-6sqrt(3))/(-8)`

`= 3/4 (sqrt(3)-1)`