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Question
Rationalize the denominator.
`(sqrt 5 - sqrt 3)/(sqrt 5 + sqrt 3)`
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Solution
`(sqrt 5 - sqrt 3)/(sqrt 5 + sqrt 3)`
`= (sqrt 5 - sqrt 3)/(sqrt 5 + sqrt 3) xx (sqrt 5 - sqrt 3)/(sqrt 5 - sqrt 3)`
`= (sqrt 5 - sqrt 3)^2/((sqrt 5)^2 - (sqrt 3)^2) ....[because (a + b)(a - b) = a^2 - b^2]`
`= ((sqrt 5)^2 - 2(sqrt 5)(sqrt 3) + (sqrt 3)^2)/(5-3) ...[because (a - b)^2 = a^2 - 2ab + b^2]`
`= (5 - 2sqrt15 + 3 )/2`
`= (8 - 2sqrt 15)/2`
`= (2 (4 - sqrt15))/2`
`= 4 -sqrt15`
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