How do I get from 2a+a+sqrt(3a^2)=20 to.... a=8.453?

- anonymous

How do I get from 2a+a+sqrt(3a^2)=20 to.... a=8.453?

- jamiebookeater

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- anonymous

How did you arrive at that answer?

- anonymous

wolframalpha.com

- anonymous

are you sure you plugged it in correctly?

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## More answers

- anonymous

I entered the equation exactly how it here.

- anonymous

Then you must've typed it here wrong. That is not the correct answer.

- anonymous

Double check

- anonymous

http://www.wolframalpha.com/input/?i=2a%2Ba%2B+sqrt%283a%5E2%29%3D20 are you able to see this, my friend?

- anonymous

\[2a+a+\sqrt(3a^2)=20\]

- anonymous

Yes, that correct.

- anonymous

It doesn't say the answer is 8.453

- anonymous

It does, in the solution: a=-10/3(sqrt(3)-3).

- anonymous

That comes out to approximately 4.2265

- anonymous

Not 8.453

- anonymous

You're right I made a mistake, my answer is two times 4.2265.

- anonymous

OK i will show you how to do the work correctly.

- anonymous

I am still wondering how I get there though.

- anonymous

\[3a+\sqrt(3a^2)=20\]
\[a(3+\sqrt(3))=20\]
\[a=\frac{20}{(3+\sqrt(3))}\]

- anonymous

From here we rationalize the denominator

- anonymous

I am confused in the second step.

- anonymous

\[\frac{20}{3+\sqrt(3)} * \frac{3-\sqrt(3)}{3-\sqrt(3)}\]

- anonymous

In the second step i simply factored out an a because \[\sqrt(a^2)=a\]

- anonymous

so it would be \[3a+a \sqrt(3)\]

- anonymous

Then you can factor out an a here, see?

- anonymous

okay, i see now thank you very much !

- anonymous

Do you know how to rationalize the denominator?

- anonymous

You must do that to get to the final answer

- anonymous

I do, i need to try it to make sure i get the mechanics of it.

- anonymous

The numberator should be 60-20sqrt(3), correct? And I am having difficulties with the denominator? Could you help please?

- anonymous

Nevermind, I figured it out, thank you.

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