Question

How do you rationalize the denominator and simplify `3/(6-sqrt5)`?

Answer 1

`18/31+3/31sqrt5`

Explanation:

WE can rationalize the denominator in `3/(6-sqrt5)` by multiplying numerator and denominator by conjugate of the denominator. The conjugate of `(6-sqrt5)` is `(6+sqrt5)`.

Hence `3/(6-sqrt5)=(3*(6+sqrt5))/((6-sqrt5)(6+sqrt5))`

= `(18+3sqrt5)/(36-5)` or

= `18/31+3/31sqrt5`