Question

Rationalise the denominator of `(2 - sqrt(3))/(2 + sqrt(3))`.

Answer 1

To rationalise the expression:

`(2 - sqrt(3))/(2 + sqrt(3))`

Step 1: Multiply numerator and denominator by the conjugate of the denominator `(2 - sqrt(3))`:

`(2 - sqrt(3))/(2 + sqrt(3)) xx (2 - sqrt(3))/(2 - sqrt(3)) = (2 - sqrt(3))^2/((2 + sqrt(3))(2 - sqrt(3))`

Step 2: Denominator

`(2 + sqrt(3))(2 - sqrt(3))`

= `2^2 - (sqrt(3))^2`

= 4 – 3

= 1

Step 3: Numerator

`(2 - sqrt(3))^2`

= `4 - 4sqrt(3) + 3`

= `7 - 4sqrt(3)`