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Stumped :(

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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

#1
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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

Apr 19, 2019