Question

How do you rationalize the denominator and simplify `7/(sqrt3-sqrt2)`?

Answer 1

Multiply both numerator and denominator by `sqrt(3)+sqrt(2)` to find:

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

Explanation:

Note that `(a-b)(a+b) = a^2-b^2`

So: `(sqrt(3)-sqrt(2))(sqrt(3)+sqrt(2)) = 3 - 2 = 1`

So we find:

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