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Math Help - A question on square rooths in polynomials

  1. #1
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    A question on square rooths in polynomials

    Hi : http://img841.imageshack.us/img841/9800/hviw.png

    I was wondering, I undestand what the text in the given link says, but I don't understand why we don't consider square rooth of variables valid?

    It says that a polynomials can only be constructed with addition, divison and substraction. The square rooth of two is a number, like any other, which can be used to construct a polynomial with these basic operation. Why can't we consider it in the same manner with square rooths of variables ????

    Thank you.
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  2. #2
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    Re: A question on square rooths in polynomials

    remember polynomials are defined as algebraic expression wherein variables have only non-negative integers as powers. if the coefficients are reals ( that is rationals or irrationals ) then it is a polynomial over reals otherwise over complex / imaginary. also please note that in case of division we will get a rational exprssion and not a polynomial.
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