Question

How do you rationalize the denominator and simplify `2/(sqrt6-sqrt5)`?

Answer 1

Refer to explanation

Explanation:

When you have a formula like `sqrta-sqrtb` in the denominator you multiply with `sqrta+sqrtb` so

`2/(sqrt6-sqrt5)=2*(sqrt6+sqrt5)/((sqrt6-sqrt5)*(sqrt6+sqrt5))=2*(sqrt6+sqrt5)/((sqrt6)^2-(sqrt5)^2)=2*(sqrt6+sqrt5)/(6-5)=2*(sqrt6+sqrt5)`

Remarks

We used the identity `a^2-b^2=(a-b)*(a+b)`