# Article

**Keywords:**

Galois theory; finite group; permutation; radical

**Summary:**

We illustrate the main idea of Galois theory, by which roots of a polynomial equation of at least fifth degree with rational coefficients cannot general be expressed by radicals, i.e., by the operations $+,\,-,\,\cdot,\,:\,$, and $\root n \of{\cdot}$. Therefore, higher order polynomial equations are usually solved by approximate methods. They can also be solved algebraically by means of ultraradicals.