Rationalize: `1/(sqrt x + sqrt y)`

Expert Answers
justaguide eNotes educator| Certified Educator

The expression `1/(sqrt x + sqrt y)` has to be rationalized.

`1/(sqrt x + sqrt y)`

=> `(sqrt x - sqrt y)/((sqrt x + sqrt y)(sqrt x - sqrt y))`

=> `(sqrt x - sqrt y)/((sqrt x)^2 - (sqrt y)^2)`

=> `(sqrt x - sqrt y)/(x - y)`

The rationalized form of `1/(sqrt x + sqrt y) = (sqrt x - sqrt y)/(x - y)`

=> (sqrt x - sqrt y)/((sqrt x + sqrt y)(sqrt x - sqrt y))