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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 $a+b+c$?

 Jun 6, 2019
 #1
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\((\sqrt{2}+\sqrt{3})^3\)        ⇒     \( a\sqrt{2} + b\sqrt{3} + c\sqrt{6}\)

 

( √2 + √3)^3  = 

 

(√2)^3 + 3*(√2)^2 *(√3) + 3 * (√2) *(√3)^2  + ( √3)^3  =

 

2√2 + 3*2*√3 + 3*3*√2 + 3√3  =

 

2√2 + 9√2 + 6√3 + 3√3  =

 

11√2 + 9 √3  + 0 √6

 

a + b + c  =

 

11 + 9 + 0  =

 

20

 

 

cool cool cool

 Jun 6, 2019

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