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Question
Simplify by rationalising the denominator in the following.
`(5sqrt(3) - sqrt(15))/(5sqrt(3) + sqrt(15)`
Solution
`(5sqrt(3) - sqrt(15))/(5sqrt(3) + sqrt(15)`
= `(5sqrt(3) - sqrt(15))/(5sqrt(3) + sqrt(15)) xx (5sqrt(3) - sqrt(15))/(5sqrt(3) - sqrt(15)`
= `((5sqrt(3) - sqrt(15))^2)/((5sqrt(3))^2 - (sqrt(15))^2`
= `(75 + 15 - 10sqrt(45))/(75 - 15)`
= `(90 - 10sqrt(45))/(60)`
= `(9 - 1sqrt(45))/(6)`
= `(9 - 3sqrt(5))/(6)`
= `(3 - sqrt(5))/(2)`
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