Question

Rationalise the denominator:

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

Answer 1

We are asked to rationalise the denominator `6/(sqrt(5) - sqrt(3))`

Step 1: Multiply numerator and denominator by the conjugate of the denominator:

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

= `(6(sqrt(5) + sqrt(3)))/((sqrt(5) - sqrt(3))(sqrt(5) + sqrt(3))`

Step 2: Simplify the denominator using (a – b)(a + b) = a² – b²:

`(sqrt(5))^2 - (sqrt(3))^2`

= 5 – 3

= 2

Step 3: Final expression:

`(6(sqrt(5) + sqrt(3)))/2`

= `3(sqrt(5) + sqrt(3))`