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Question
Simplify by rationalising the denominator in the following.
`(sqrt(12) + sqrt(18))/(sqrt(75) - sqrt(50)`
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Solution
`(sqrt(12) + sqrt(18))/(sqrt(75) - sqrt(50)`
= `(sqrt(12) + sqrt(18))/(sqrt(75) - sqrt(50)) xx (sqrt(75) + sqrt(50))/(sqrt(75) + sqrt(50)`
= `((2sqrt(3) + 3sqrt(2))(5sqrt(3) + 5sqrt(2)))/((sqrt(75))^2 - (sqrt(50))^2`
= `(30 + 10sqrt(6) + 15sqrt(6) + 30)/(75 - 50)`
= `(60 + 25sqrt(6))/(25)`
= `(12 + 5sqrt(6))/(5)`
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