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

1 Answer
Alan P.
Jun 10, 2016

(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

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