Question

Rationalise the denominator:

`(sqrt(7) - sqrt(6))/(sqrt(7) + sqrt(6))`

Answer 1

To rationalise the denominator `(sqrt(7) - sqrt(6))/(sqrt(7) + sqrt(6))`,

we multiply both the numerator and the denominator by the conjugate of the denominator, which is `sqrt(7) - sqrt(6)`:

`((sqrt(7) - sqrt(6))^2)/((sqrt(7) + sqrt(6))(sqrt(7) - sqrt(6))`

Step 1: Denominator

`(sqrt(7) + sqrt(6))(sqrt(7) - sqrt(6))`

= 7 – 6

= 1

Step 2: Numerator

`(sqrt(7) - sqrt(6))^2`

= `7 - 2sqrt(42) + 6`

= `13 - 2sqrt(42)`