Question

Rationalise the denominator of `5/(3 - sqrt(2))`.

Answer 1

To rationalise the denominator of `5/(3 - sqrt(2))`

Multiply numerator and denominator by the conjugate of the denominator:

`5/(3 - sqrt(2)) xx (3 + sqrt(2))/(3 + sqrt(2)) = (5(3 + sqrt(2)))/((3 - sqrt(2))(3 + sqrt(2))`

Now compute:

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

= 9 – 2

= 7

Numerator: `5(3 + sqrt(2))`

= `15 + 5sqrt(2)`

So, `(15 + 5sqrt(2))/7`