Question

How do you rationalize the denominator `sqrt6/(sqrt13+3)`?

Answer 1

Multiply both numerator (top) and denominator (bottom) by the conjugate `(sqrt(13)-3)` ...

`sqrt(6)/(sqrt(13)+3)`

`=sqrt(6)/(sqrt(13)+3)*(sqrt(13)-3)/(sqrt(13)-3)`

`=(sqrt(6)*(sqrt(13)-3))/((sqrt(13)+3)(sqrt(13)-3))`

`=(sqrt(6)*(sqrt(13)-3))/(13-9)`

`=(sqrt(6)*(sqrt(13)-3))/4`