Question

Express the following with rational denominator:

`1/(2sqrt5 - sqrt3)`

Answer 1

We know that rationalization factor for `2sqrt5 - sqrt3` is `2sqrt5 + sqrt3`. We will multiply numerator and denominator of the given expression `1/(2sqrt5 - sqrt3)` by `2sqrt5 + sqrt3` to get

`1/(2sqrt5 - sqrt3) xx (2sqrt5 + sqrt3)/(2sqrt5 + sqrt3) = (2sqrt5 + sqrt3)/((2sqrt5)^2 - (sqrt3)^2)`

`= (2sqrt5 + sqrt3)/(4 xx 5 - 3)`

`= (2sqrt5 + sqrt3)/(20 - 3)`

`= (2sqrt5 + sqrt3)/17`

`= 5sqrt3 + 3sqrt5`

Hence the given expression is simplified with rational denominator to `(2sqrt5 + sqrt3)/17`