Question

Express of the following with rational denominator:

`1/(sqrt6 - sqrt5)`

Answer 1

We know that rationalization factor for `sqrt6 - sqrt5` is `sqrt6 + sqrt5`. We will multiply numerator and denominator of the given expression `1/(sqrt6 -sqrt5)` by `sqrt6 + sqrt5` to get

`1/(sqrt6 - sqrt5) xx (sqrt6 + sqrt5)/(sqrt6 + sqrt5) = (sqrt6 + sqrt6)/((sqrt6)^2 - (sqrt5)^2`

`= (sqrt6 + sqrt5)/(6 - 5)`

`= (sqrt6 + sqrt5)/(6 - 5)`

`= (sqrt6 + sqrt5)/1`

`= sqrt6 + sqrt5`

Hence the given expression is simplified with rational denominator to `sqrt6 + sqrt5`.