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Question
Express of the following with rational denominator:
`1/(sqrt6 - sqrt5)`
Solution
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`.
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