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Question
Rationalise the denominator and simplify `(sqrt(48) + sqrt(32))/(sqrt(27) - sqrt(18))`
Solution
`(sqrt(48) + sqrt(32))/(sqrt(27) - sqrt(18)) = (sqrt(16 xx 3) + sqrt(16 xx 2))/(sqrt(9 xx 3) - sqrt(9 xx 2))`
= `(4sqrt(3) + 4sqrt(2))/(3sqrt(3) - 3sqrt(2))`
= `(4(sqrt(3) + sqrt(2)))/(3(sqrt(3) - sqrt(2))`
= `(4(sqrt(3) + sqrt(2)))/(3(sqrt(3) - sqrt(2))) xx ((sqrt(3) + sqrt(2)))/((sqrt(3) + sqrt(2)))`
= `(4(sqrt(3) + sqrt(2))^2)/(3[(sqrt(3))^2 - (sqrt(2))^2])`
= `(4[(sqrt(3))^2 + 2sqrt(3) xx sqrt(2) + (sqrt(2))^2])/(3(3 - 2))`
= `4/3(3 + 2sqrt(6) + 2)`
= `4/3(5 + 2sqrt(6))`
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