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Question
Simplify by rationalising the denominator in the following.
`(3 - sqrt(3))/(2 + sqrt(2)`
Solution
`(3 - sqrt(3))/(2 + sqrt(2)`
= `(3 - sqrt(3))/(2 + sqrt(2)) xx (2 - sqrt(2))/(2 - sqrt(2)`
= `(3(2 - sqrt(2)) - sqrt(3)(2 - sqrt(2)))/((2)^2 - (sqrt(2))^2)`
= `(6 - 3sqrt(2) - 2sqrt(3) + sqrt(6))/(4 - 2)`
= `(6 - 3sqrt(2) - 2sqrt(3) + sqrt(6))/(2)`
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