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Question
Rationales the denominator and simplify:
`(1 + sqrt2)/(3 - 2sqrt2)`
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Solution
We know that rationalization factor for `3 - 2sqrt2` is `3 + 2sqrt2`. We will multiply numerator and denominator of the given expression `(1 + sqrt2)/(3 - 2sqrt2)` by `3 + 2sqrt2`
`(1 + sqrt2)/(3 - 2sqrt2) xx (3 + 2sqrt2)/(3 + 2sqrt2) = (3 + 2sqrt2 + 3sqrt2 + 2 xx (sqrt2)^2)/((3)^2 - (2sqrt2)^2)`
` = (3 + 5sqrt2 + 4)/(9 - 4 xx 2)`
`= (7 + 5sqrt2)/(9 - 8)`
`= (7 + 5sqrt2)/1`
`= 7 + 5sqrt2`
Hence the given expression is simplified to `7 + 5sqrt2`
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