Question

Rationalise the denominator:

`8/(sqrt(7) + sqrt(3)`

Answer 1

We are asked to rationalise the denominator `8/(sqrt(7) + sqrt(3)`

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

`8/(sqrt(7) + sqrt(3)) xx (sqrt(7) - sqrt(3))/(sqrt(7) - sqrt(3))`

= `(8(sqrt(7) - sqrt(3)))/((sqrt(7) + sqrt(3))(sqrt(7) - sqrt(3))`

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

`sqrt(7)^2 - sqrt(3)^2`

= 7 – 3

= 4

Step 3: Final expression:

`(8(sqrt(7) - sqrt(3)))/4`

= `2(sqrt(7) - sqrt(3))`