We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.
 
+0  
 
0
92
1
avatar

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
avatar+104899 
+1

\( (\sqrt{2}+\sqrt{3})^3\)

 

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

 

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

23 Online Users

avatar