How do you simplify #(2-sqrt2)^2#?

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Answer 1 · 2015-07-15T12:29:36

The answer is #6-4sqrt 2# .

#(2-sqrt 2)^2# is in the form of the square of a difference, in which

#(a-b)^2=a^2-2ab+b^2#, where #a=2 and b=sqrt2#.

Substitute the given values into the equation #a^2-2ab+b^2#.

#2^2-2*2*sqrt 2+sqrt 2^2# =

Simplify the terms.

#4-4sqrt 2+2# =

#6-4sqrt2#