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Question
Express the following with rational denominator:
`1/(3 + sqrt2)`
Solution
We know that rationalization factor for `3 + sqrt2` is `3 - sqrt2`. We will multiply numerator and denominator of the given expression `1/(3 + sqrt2)` by `3 - sqrt2` to get
`1/(3 + sqrt2) xx (3 - sqrt2)/(3 - sqrt2) = (3 - sqrt2)/(3^2 - (sqrt2)^2)`
`= (3 - sqrt2)/(9 - 2)`
`= (3 - sqrt2)/7`
Hence the given expression is simplified with rational denominator to `(3 - sqrt2)/7`
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