Question #6766a

1 Answer
Oct 13, 2016

Answer:

Show that

#(4sqrt(5)-3sqrt(2))^2=98-sqrt(10)#

Explanation:

Using that #(a-b)^2 = a^2-2ab+b^2#, and #sqrt(a)sqrt(b) = sqrt(ab)# for #a, b >=0#, we have

#(4sqrt(5)-3sqrt(2))^2 = (4sqrt(5))^2-2(4sqrt(5))(3sqrt(2))+(3sqrt(2))^2#

#=4^2(sqrt(5))^2-24sqrt(5)sqrt(2)+3^2(sqrt(2))^2#

#=16(5)-24sqrt(5*2)+9*2#

#=98-24sqrt(10)#