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Math Help - √Combine Like Terms?

  1. #1
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    √Combine Like Terms?

    This is my first post, thank you for your consideration.

    My question regards the process of adding radicals.

    If it follows that
    √8 = √2+4 = 2√2.

    When why doesn't 2√2 + 2√2 = 2+2+√2+√2; instead of the correct answer of 4√2. How come the other like terms are discarted?

    I know there is a super simple answer to this which will make me look like a complete mule, but I would rather be an informed mule than a proud fool.
    Last edited by Enthusiast; December 7th 2012 at 07:44 PM. Reason: Syntax errors
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  2. #2
    MHF Contributor MarkFL's Avatar
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    Re: √Combine Like Terms?

    What you want is:

    \sqrt{8}=\sqrt{4\cdot2}=\sqrt{4}\cdot\sqrt{2}=2 \sqrt{2}

    and:

    2\sqrt{2}+2\sqrt{2}=2\sqrt{2}(1+1)=2(2\sqrt{2})=4 \sqrt{2}
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  3. #3
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    Re: √Combine Like Terms?

    Hello, Enthusiast!

    Welcome aboard!



    Why doesn't 2√2 + 2√2 = 2 + 2 + √2 + √2 ?

    It should be obvious that we don't add like that.


    2\sqrt{2} is simply "two times a thing".

    Let x = thing.

    Then you have: . 2x + 2x

    Got it?
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  4. #4
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    Re: √Combine Like Terms?

    I think I got really focused upon the deconstruction of the radicand and some how my "brain head" as Trippy would say got addition and multipication mixed up....I don't know. Thanks for the clarification everyone.
    Last edited by Enthusiast; December 8th 2012 at 04:38 PM. Reason: citing
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