Rationalize denominator of 6/2-squareroot3

Question

Rationalize denominator for this equation:

6/2-squareroot3

Answer 1

6 / (2- sqrt(3))

The trick is that (a-b)(a+b) = a^2 - b^2

To get rid of the square root on the bottom we want to multiply it by (2+sqrt(3)).

If we want to multiply the bottom by something, we have to multiply the top by the same thing, because something/something = 1

We're going to multiply the top and bottom by (2+sqrt(3))

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

(12 + 6sqrt(3)) / (4 - 3)

(12 + 6sqrt(3)) / 1

12 + 6sqrt(3)