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Question
Express the following with rational denominator:
`30/(5sqrt3 - 3sqrt5)`
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Solution
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`
`(150sqrt3 + 90sqrt5)/30`
`(150sqrt3)/30 + (90sqrt5)/30`
`= 5sqrt3 + 3sqrt5`
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