Question

Rationalise the denominator of the following:

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

Answer 1

Let `E = (2 + sqrt(3))/(2 - sqrt(3))`

For rationalising the denominator, multiplying numerator and denominator by `2 + sqrt(3)`,

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

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

= `(2^2 + (sqrt(3))^2 + 2 xx 2 xx sqrt(3))/(4 - 3)`  ...[Using identity, (a – b)(a + b) = a² – b²]

= `4 + 3 + 4sqrt(3)`  ...[Using identity (a + b)² = a² + 2b + b²]

= `7 + 4sqrt(3)`