A number r is algebraic if there is a nonzero polynomial p(x) with integer coefficients such that r is a root of p(x) = 0. Prove that every kth root of a rational number r is an algebraic number.
Follow Math Help Forum on Facebook and Google+
Let be the k'th root of a rational number where and are integers and is not 0. (i.e. )
We know that is a polynomial with a root at
To ensure the coefficients are all integer we simply multiply the right hand side by
View Tag Cloud