Question

Rationalise the denominator:

`6/(2 + sqrt(3))`

Answer 1

To rationalise the denominator of the expression `6/(2 + sqrt(3))`, we need to multiply both the numerator and the denominator by the conjugate of the denominator, which is `2 - sqrt(3)`.

`6/(2 + sqrt(3)) xx (2 - sqrt(3))/(2 - sqrt(3)) = (6(2 - sqrt(3)))/((2 + sqrt(3))(2 - sqrt(3))`

Now, simplify the denominator using the identity (a + b)(a – b) = a² – b²:

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

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

= 4 – 3

= 1

So the expression simplifies to:

`(6(2 - sqrt(3)))/1`

= `6(2 - sqrt(3))`

= `12 - 6sqrt(3)`