Question

खालील संख्यांच्या छेदांचे परिमेयीकरण करा.

`(sqrt5 - sqrt3)/(sqrt5 + sqrt3)`

Answer 1

`(sqrt5 - sqrt3)/(sqrt5 + sqrt3)`

= `(sqrt5 - sqrt3)/(sqrt5 + sqrt3) xx (sqrt5 - sqrt3)/(sqrt5 - sqrt3)`

`(sqrt5 - sqrt3)^2/((sqrt5)^2 - (sqrt3)^2)   ...[(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 - 2sqrt15)/2`

= `(2(4 - sqrt15))/2`

= `4 - sqrt15`