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

 Apr 19, 2019
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\( (\sqrt{2}+\sqrt{3})^3\)

 

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

 

We just have a binomial expansion  .....

 

( √2)^3  +  3(√2)^2(√3)  + 3(√2)(√3)^2  + (√3)^3       simplify

 

2√2 + 6√3  + 9√2  + 3√3  =

 

11√2 + 9√3 + 0√6

 

So.....a + b + c  =   20

 

cool cool cool

 Apr 19, 2019

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