Question

How do you rationalize the denominator and simplify `3/(sqrt5+sqrt6)`?

Answer 1

We multiply by `\frac{ sqrt{5} - sqrt{6} }{ sqrt{5} - sqrt{6} }` to rationalize the denominator.

Explanation:

`frac {3} {sqrt{5} + sqrt{6} }`

`= frac {3} {sqrt{5} + sqrt{6} } cdot \frac{ sqrt{5} - sqrt{6} }{ sqrt{5} - sqrt{6} }`

`= frac { 3 sqrt{5} - 3 sqrt{6} } { 5 - 6 }`

`= 3 sqrt{6} - 3 sqrt{5}`