Question

Rationalize the denominator.

`(sqrt 5 - sqrt 3)/(sqrt 5 + sqrt 3)`

Answer 1

`(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`