(Sqrt{10} - sqrt{2})^2 Simplified to b-c sqrt {5}?

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Answer 1 · 2018-05-20T01:58:17

yes

#(sqrt10 - sqrt2)^2#

#=(sqrt10 - sqrt2)(sqrt10 - sqrt2)# FOIL

#=sqrt10*sqrt10+sqrt10*(-sqrt2) + sqrt10*(-sqrt2)+(-sqrt2)*(-sqrt2)#

#=10 - 2sqrt10sqrt2+2#

#=12 - 2sqrt10sqrt2#

#=12 - 2sqrt5*sqrt2*sqrt2# #lArr "because: " sqrt10 = sqrt2*sqrt5#

#=12 - 2sqrt5 *2#

#=12 - 4sqrt5#

#=4(3 - sqrt5)#