Express $\sqrt 3(2+\sqrt 3)$ in the form $ a + b \sqrt3 $.

I have expanded parentheses to get: $2\cdot \sqrt{3}+3$.
How would I go from there and write it in the form mentioned above?

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You've already finished.

$\color{red}{2}\sqrt{3}+\color{blue}{3}$ is in the form $\color{blue}{a}+\color{red}{b}\sqrt{3}$.

  • $\begingroup$ THANK YOU haha I feel so stupid. So It doesn't nessecarily have to be written out in the form a+b root 3? Like exactly like that? $\endgroup$ – M. Anderson Jun 12 '16 at 3:56
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    $\begingroup$ With addition the order you write something is not important as $a+b=b+a$ due to associativity. So your answer of $2\sqrt{3}+3$ is exactly the same as $3+2\sqrt{3}$ and hence it is in the form required. $\endgroup$ – Ian Miller Jun 12 '16 at 4:04
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    $\begingroup$ @IanMiller don't you mean commutativity...? $\endgroup$ – gebruiker Jun 12 '16 at 7:23
  • $\begingroup$ Yeh I do. Thanks for the correction. $\endgroup$ – Ian Miller Jun 12 '16 at 9:41
  • $\begingroup$ According to that logic, $\sqrt{3}(2+\sqrt{3})$ is already in the required form as well. $\endgroup$ – John Joy Jun 12 '16 at 15:21

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