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Question
Simplify by rationalising the denominator in the following.
`(2sqrt(3) - sqrt(6))/(2sqrt(3) + sqrt(6)`
Solution
`(2sqrt(3) - sqrt(6))/(2sqrt(3) + sqrt(6)`
= `(2sqrt(3) - sqrt(6))/(2sqrt(3) + sqrt(6)) xx (2sqrt(3) - sqrt(6))/(2sqrt(3) - sqrt(6)`
= `((2sqrt(3) - sqrt(6))^2)/((2sqrt(3))^2 - (sqrt(6))^2`
= `(12 + 6 - 4sqrt(18))/(12 - 6)`
= `(18 - 4sqrt(18))/(6)`
= `(9 - 2sqrt(18))/(3)`
= `(9 - 6sqrt(2))/(3)`
= 3 - 2`sqrt(2)`
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