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Thread: Square root Question in doubt

  1. #1
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    Square root Question in doubt

    Hi Dr.Math,

    Recently i have argument with my colleague for equations below

    √[(-2)^2] = x

    a) x = -2
    b) x = 2
    c) x = 2 or -2


    just wondering which answer of that? a,b or c?

    btw, if my equation assignment is

    √[(-2)^2] = -2

    Can they state my equation with Math Error?


    thank you
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  2. #2
    MHF Contributor

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    Re: Square root Question in doubt

    It is simply a matter of the definition of the square root function. Functions of real numbers are always defined so that f(x) has one value for a given x. That is the part of the definition of "function itself". And because of that \sqrt{a} is defined as "the positive number, x, such that x^2= a.

    Yes, if you are claiming that \sqrt{(-2)^2}= -2 you are definitely in error. (-2)^2= 4 and \sqrt{4}= 2, not -2.
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  3. #3
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    Re: Square root Question in doubt

    Quote Originally Posted by maxowlpang View Post
    Hi Dr.Math,

    Recently i have argument with my colleague for equations below

    √[(-2)^2] = x

    a) x = -2
    b) x = 2
    c) x = 2 or -2


    just wondering which answer of that? a,b or c?

    btw, if my equation assignment is

    √[(-2)^2] = -2

    Can they state my equation with Math Error?


    thank you
    \sqrt{x^2} = |x| ,so if x = -2 ,then \sqrt{(-2)^2} = |-2|=2

    If x=2,then again \sqrt {2^2} =|2|=2
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