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Question
Simplify by rationalising the denominator in the following.
`(42)/(2sqrt(3) + 3sqrt(2)`
Solution
`(42)/(2sqrt(3) + 3sqrt(2)`
= `(42)/(2sqrt(3) + 3sqrt(2)) xx (2sqrt(3) - 3sqrt(2))/(2sqrt(3) - 3sqrt(2)`
= `(42(2sqrt(3) - 3sqrt(2)))/((2sqrt(3))^2 - (3sqrt(2)^2)`
= `(84sqrt(3) - 126sqrt(2))/(12 - 18)`
= `(84sqrt(3) - 126sqrt(2))/(-6)`
= `-14sqrt(3) + 21sqrt(2)`
= `21sqrt(2) - 14sqrt(3)`
= `7(3sqrt(2) - 2sqrt(3))`
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