By using only positive integer powers they now have a class of functions that we know everything about. This is very useful in higher mathematics.

]]>We could take that square root but it just would not be a polynomial.

Yes, but that's what I find weird... I don't see the logic behind it. But if it's the way it is, to play the game of mathematics, then we have to consider it that way.

]]>Each term consists of the product of a constant -- called the coefficient of the term and a finite number of variables (usually represented by letters), also called indeterminates, raised to whole number powers.

The above is a definition. We agree to abide by it to play the game called mathematics. It is a rule.It was a wise decision to define them like that.

(√a + √b) is not a polynomial because the variables a and b are not raised to a positive integer value.

]]>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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