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Math Help - simplifying radical

  1. #1
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    simplifying radical

    \sqrt{4x^4+36x^2+81}

    shrug, i should know how to do this lol

    help :P

    2x^2+9\sqrt{36x^2}

    I get lost at this point
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  2. #2
    Lord of certain Rings
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    Quote Originally Posted by silencecloak View Post
    \sqrt{4x^4+36x^2+81}

    shrug, i should know how to do this lol

    help :P

    2x^2+9\sqrt{36x^2}

    I get lost at this point
    \sqrt{4x^4+36x^2+81} = \sqrt{(2x^2+9)^2} = 2x^2+9
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  3. #3
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    Quote Originally Posted by Isomorphism View Post
    \sqrt{4x^4+36x^2+81} = \sqrt{(2x^2+9)^2} = 2x^2+9
    can you explain to me your thought process as you look at and go through this radical
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  4. #4
    Super Member angel.white's Avatar
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    For future reference:
    9*\sqrt{36x^2}

    =9*\sqrt{36}*\sqrt{x^2}

    =9*6*x

    =54x



    Another way of doing this:
    9*\sqrt{36x^2}

    =\sqrt{9^2}*\sqrt{36x^2}

    =\sqrt{81}*\sqrt{36x^2}

    =\sqrt{36*81*x^2}

    =\sqrt{2916*x^2}

    =\sqrt{2916}*\sqrt{x^2}

    =54x
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  5. #5
    Lord of certain Rings
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    Quote Originally Posted by silencecloak View Post
    can you explain to me your thought process as you look at and go through this radical
    Well I am acquainted with the formula
    a^2 + 2ab + b^2 = (a+b)^2

    So when I see 4x^4+36x^2+81,I ask myself if 4x^4 is a square of something and if 81 is a square of something. The answer is yes!

    So it take 2x^2 and 9 and check if 36x^2 is the expected 2(2x^2)9. It is...

    So yay!
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