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Question
Simplify by rationalising the denominator in the following.
`(7sqrt(3) - 5sqrt(2))/(sqrt(48) + sqrt(18)`
Solution
`(7sqrt(3) - 5sqrt(2))/(sqrt(48) + sqrt(18)`
= `(7sqrt(3) - 5sqrt(2))/(sqrt(48) + sqrt(18)) xx (sqrt(48) - sqrt(18))/(sqrt(48) - sqrt(18)`
= `(7sqrt(144) - 7sqrt(54) - 5sqrt(96) + 5sqrt(36))/((sqrt(48))^2 - (sqrt(18))^2`
= `(84 - 21sqrt(6) - 20sqrt(6) + 30)/(48 - 18)`
= `(144 - 41sqrt(6))/(30)`
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