When reading about Galois theory concerning the solution by radicals of algebraic equations, one notices the following: One considers field extensions $L/K$ by adjunction of radicals. It is also required that the field $K$ contain "sufficient many roots of unity".
What does this mean, sufficient many roots of unity ? What roots of unity are about, what is their role ?
Since $K$ can be $Q$, I dont believe it is about complex roots of unity. But at the other hand roots of unity in $R$ are trivial. So I am not sure. Why you need to have "sufficient many roots of unity" ?
Why not all of them but only "sufficient many", and how many is sufficient, how do we know how many is sufficient ?
Can somebody elaborate on these questions ?
Many thanks.