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Question
Rationalise the denominator and simplify `(5sqrt(3) + sqrt(2))/(sqrt(3) + sqrt(2))`
Solution
`(5sqrt(3) + sqrt(2))/(sqrt(3) + sqrt(2)) = ((5sqrt(3) + sqrt(2))(sqrt(3) - sqrt(2)))/((sqrt(3) + sqrt(2))(sqrt(3) - sqrt(2))`
= `(5(3) - 5sqrt(3) xx sqrt(2) + (sqrt(2)sqrt(3) - (2)))/((sqrt(3))^2 - (sqrt(2))^2`
= `(15 - 5sqrt(6) + sqrt(6) - 2)/(3 - 2)`
= `(13 - 4sqrt(6))/1`
= `13 - 4sqrt(6)`
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