How do you simplify #(5 - 2sqrt2)^2#?

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Answer 1 · 2016-04-09T03:10:37

#=5^2-2xx5xx2sqrt2+(2sqrt2)^2#
#=25-20sqrt2+8#
#=33-20sqrt2#

Answer 2 · 2016-04-09T07:25:33

#33-20sqrt2#

#color(blue)((5-2sqrt2)^2#

Use the identity

#color(brown)((a-b)^2=a^2-2ab+b^2#

So,we can say that

#color(purple)(a=5,b=2sqrt2#

Then,

#rarr(5-2sqrt2)^2=(5)^2-2(5)(2sqrt2)+(2sqrt2)^2#

#rarr25-10(2sqrt2)+(4*2)#

#rarr25-20sqrt2+8#

#color(green)(rArr33-20sqrt2#