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Question
Rationalise the denominator of the following:
`(3sqrt(5) + sqrt(3))/(sqrt(5) - sqrt(3))`
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Solution
Let `E = (3sqrt(5) + sqrt(3))/(sqrt(5) - sqrt(3))`
For rationalising the denominator, multiplying numerator and denominator by `sqrt(5) + sqrt(3)`,
`E = (3sqrt(5) + sqrt(3))/(sqrt(5) - sqrt(3)) xx (sqrt(5) + sqrt(3))/(sqrt(5) + sqrt(3))`
= `(3sqrt(5)(sqrt(5) + sqrt(3)) + sqrt(3)(sqrt(5) + sqrt(3)))/((sqrt(5))^2 - (sqrt(3))^2` ...[Using identity, (a + b)(a – b) = a2 – b2]
= `(15 + 3sqrt(15) + sqrt(15) + 3)/(5 - 3)`
= `(18 + 4sqrt(15))/2`
= `9 + 2sqrt(15)`
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