Question

How do you simplify `(2+ sqrt3)(2- sqrt3)`?

Answer 1

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

Explanation:

The difference of squares identity can be written:

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

Putting `a=2` and `b=sqrt(3)` we find:

`(2+sqrt(3))(2-sqrt(3)) = 2^2-(sqrt(3))^2 = 4 - 3 = 1`