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The number (\sqrt{2}+\sqrt{3}+1)^3 can be written in the form a\sqrt{2} + b\sqrt{3} + c\sqrt{6} + d, where a, b, and c are integers. What is a+b+c+d?

 Jul 24, 2022
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\( (\sqrt{2}+\sqrt{3}+1)^3\)

 

\(a\sqrt{2} + b\sqrt{3} + c\sqrt{6} + d \)

 

[ sqrt 2 + sqrt 3  + 1)^3  =

 

16 + 14 sqrt(2) + 12 sqrt(3) + 6 sqrt(6)                                                   

 

 

a= 14

b = 12

c = 6

d = 16

 

Sum =  48

 

cool cool cool

 Jul 24, 2022

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