How do you simplify $(2 + \sqrt{3}) (2 - \sqrt{3})$ $(2+ sqrt3)(2- sqrt3)$ ?

Question

3264 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-11-01T15:00:14

$(2 + \sqrt{3}) (2 - \sqrt{3}) = 1$ $(2+sqrt(3))(2-sqrt(3)) = 1$

The difference of squares identity can be written:

$a^{2} - b^{2} = (a + b) (a - b)$ $a^2-b^2 = (a+b)(a-b)$

Putting $a = 2$ $a=2$ and $b = \sqrt{3}$ $b=sqrt(3)$ we find:

$(2 + \sqrt{3}) (2 - \sqrt{3}) = 2^{2} - {(\sqrt{3})}^{2} = 4 - 3 = 1$ $(2+sqrt(3))(2-sqrt(3)) = 2^2-(sqrt(3))^2 = 4 - 3 = 1$

How do you simplify (2+√3)(2−√3) (2+ sqrt3)(2- sqrt3) ?