Question

How do you simplify `(2- sqrt 2) (2 + sqrt2)`?

Answer 1

`(2-sqrt(2))(2+sqrt(2))=color(green)(2)`

Explanation:

Remember the general equation for the difference of squares:
`color(white)("XXX")(a^2-b^2)=(a-b)(a+b)`

Given `(2-sqrt(2))(2+sqrt(2))`
we can treat `a` as `2`
and `b` as `sqrt(2)`

So
`color(white)("XXX")(2-sqrt(2))(2+sqrt(2))`
`color(white)("XXXXX")=(2^2-(sqrt(2))^2)`
`color(white)("XXXXX")=4-2`
`color(white)("XXXXX")=2`