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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 $a+b+c$?

 May 7, 2021
 #1
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Expanding the binomial theorem, we get (sqrt(2) + sqrt(3))^3 = 15*sqrt(2) + 8*sqrt(3).  So a + b + c = 15 + 8 + 0 = 23.

 May 7, 2021
 #2
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Not to be rude but those two sides of the equation aren't equal. The first one is equal to around 31 and the second is equal to around 35.

 May 7, 2021
edited by nousername  May 7, 2021

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