At the root of numbers

Extracting a root, for the famous scholar Cosinus, is a calculation session… at the dentist's. In maths, the methods for extracting square roots are multiple: exact or approximate, using sequences or functions, a calculator – it has become the modern reflex –, but also by hand, like at school for divisions, except that it's a bit more complicated. This will be an opportunity to discover a little-known technique for manually extracting cube roots! One can then easily generalize to complex roots, thanks to Euler, always him: their definition, the regular polygons they allow to draw, and what are called primitive roots with the concept of cyclotomic polynomial.