Question

Rationalise the denominator of the following:

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

Answer 1

Let `E = sqrt(6)/(sqrt(2) + sqrt(3))`

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

`E = sqrt(6)/(sqrt(2) + sqrt(3)) xx (sqrt(2) - sqrt(3))/(sqrt(2) - sqrt(3))`

= `(sqrt(6)(sqrt(2) - sqrt(3)))/((sqrt(2))^2 - (sqrt(3))^2)`  ...[Using identity, (a – b)(a + b) = a² – b²]

= `(sqrt(6) (sqrt(2) - sqrt(3)))/(2 - 3)`

= `(sqrt(6)(sqrt(2) - sqrt(3)))/(-1)`

= `sqrt(6)(sqrt(3) - sqrt(2))`

= `sqrt(18) - sqrt(12)`

= `sqrt(9 xx 2) - sqrt(4 xx 3)`

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