Question

How do you simplify `1/(sqrt2+sqrt7)`?

Answer 1

`1/(sqrt2+sqrt7)=(sqrt7-sqrt2)/5`

Explanation:

We simplify `1/(sqrt2+sqrt7)` by rationalizing the denominator i.e. multiplying numerator and denominator by conjugate of denominator.

As `(sqrt2+sqrt7)` can be written as `(sqrt7+sqrt2)` and its conjugate is (sqrt7-sqrt2)#, hence

`1/(sqrt2+sqrt7)=1/(sqrt7+sqrt2)`

= `(1xx(sqrt7-sqrt2))/((sqrt7+sqrt2)(sqrt7-sqrt2))`

= `(sqrt7-sqrt2)/(7-2)=(sqrt7-sqrt2)/5`