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Math Help - Help for some (probably easy) radicals!?

  1. #1
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    Exclamation Help radicals!?

    I'd be grateful for any helpful hints, explanations, or explained solutions. Thank you for looking and (hopefully) for replying!!
    Attached Thumbnails Attached Thumbnails Help for some (probably easy) radicals!?-alg1.gif   Help for some (probably easy) radicals!?-alg2.gif   Help for some (probably easy) radicals!?-alg3.gif   Help for some (probably easy) radicals!?-alg4.gif  
    Last edited by MathGuru; November 14th 2005 at 07:34 AM.
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  2. #2
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    I know I haven't been a member of this forum for very long, but it seems like a nice and helpful place.
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  3. #3
    hpe
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    Since for each real number has exactly one cube and you get the number back by computing the cube root, this is true for all n. This would be different for squares and square roots.

    First compute y-x, then the square root, then raise it to the third power, then take the reciprocal.

    The expression under the square root is an instance of the formula a^2 -2ab+b^2 = (a-b)^2 So you need to write this as a square (of a difference). The square root of a square is ... not quite the term you squared in the first place, but the absolute value of this term: \left({A^2}\right)^{1/2} = |A|.

    Here's a simpler case:  \left({x^2y^7}\right)^{1/2} = \left({xy^3xy^3y}\right)^{1/2}  = |xy^3|\left(y\right)^{1/2} Use the same sort of argument.
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  4. #4
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    THANK YOU! Your information was very useful. I think I understand now
    Last edited by Christina03; November 15th 2005 at 02:57 AM.
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  5. #5
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    I got 7|x y| for the square root of the perfect-square polynomial, and:

    for the square root of (a^5b^6). Just wondering if those are correct.... I think so, but I just want to make sure. Thanks!
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  6. #6
    hpe
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    Quote Originally Posted by Christina03
    I got 7|x y| for the square root of the perfect-square polynomial, and:

    for the square root of (a^5b^6). Just wondering if those are correct.... I think so, but I just want to make sure. Thanks!
    Looks correct to me.
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  7. #7
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    ok, thank you for all your help!
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