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

1 Answer
Jun 10, 2016

Answer:

#(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#