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Question
Rationales the denominator and simplify:
`(3 - sqrt2)/(3 + sqrt2)`
Solution
We know that rationalization factor for `sqrt3 + sqrt2` is "sqrt3 - sqrt2". We will multiply numerator and denominator of the given expression `(sqrt3 - sqrt2)/(sqrt3 + sqrt2)` by `sqrt3 - sqrt2` to get
`(sqrt3 - sqrt2)/(sqrt3 + sqrt2) xx (sqrt3 - sqrt2)/(sqrt3 - sqrt2) = ((sqrt3)^2 + (sqrt2)^2 - 2 sqrt3 xx sqrt2)/((sqrt3)^2 - (sqrt2)^2)`
`= (3 + 2 - 2sqrt6)/(3 - 2)`
`= (5 - 2sqrt6)/1`
`= 5 - 2sqrt6`
Hence the given expression is simplified to `5 - 2sqrt6`
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