Intermediate value theorem/Existence of roots/2/Remark

The existence of arbitrary roots of nonnegative real numbers follows also from the Intermediate value theorem, since, for ${}c\geq 0$, the continuous function ${}X^{k}-c$ attains negative and positive values and has therefore also a zero. The proof of fact rests on the method of the Intermediate value theorem, even though continuity is not explicitly used.