Question

Express the following with rational denominator:

`30/(5sqrt3 - 3sqrt5)`

Answer 1

We know that rationalization factor for `5sqrt3 - 3sqrt5` is `5sqrt3 + 3sqrt5`. We will multiply numerator and denominator of the given expression `30/(5sqrt3 - 3sqrt5)` by `5sqrt3 + 3sqrt5` to get

`30/(5sqrt3 - 3sqrt5) xx (5sqrt3 + 3sqrt5)/(5sqrt3 + 3sqrt5)` = `(30 xx 5 xx sqrt3 + 30 xx 3 xx sqrt5)/(5(sqrt3)^2 - (3sqrt3)^2)`

`= (30 xx 5 xx sqrt3 +  30 xx 3 xx sqrt5)/(25 xx 3 - 9 xx 5)`

`= (30 xx 5 xx sqrt3 + 30 xx 3 xx sqrt5)/30`

`= 5sqrt3 + 3sqrt5`

Hence the given expression is simplified with rational denominaor to  `5sqrt3  + 3sqrt5`