12 1 7 5 2 221-2221 EON
A key is a tonal center. The key is the central tone that a piece of music finally rests (tonality) in our ear.
Chords are a combination of '3' or more tones played together (harmony). 2 tones work just fine too. Ultimately, a single ringing tone is a chord [harmonics].
Scales are a series of individual tones played one after another - alphabetically (whether naturals or sharped/flatted tones) ascending & descending. They are tone groups or sets.
Arpeggios are chords played one note at a time (ringing or not ringing together). An arpeggio is a 'broken chord.'
A root is a tone that names a key, chord, or scale. It is the starting point for building something. It is the number 1 [or zero with Numera] in our traditional music theory system for building anything. It can also be denoted R or 1 (or 0 in numberical chromatics).
We are running against music dictionarys with our definition of the word root. Dictionaries call the base tone of a chord, a root, while calling the base tone of a scale, a tonic. This is a semantic point, yet important. Our basic point is that if a tone of a scale can be a root of a chord, it can also be a root to a scale. We can build anything from a given root. Scale tones are often called degrees (& have their own corresponding names).
When we play an instrument that can sound all the tones of a scale at the same time, is that not a chord?
The naming of a scale degree as a root doesn't inflict any theoretical damage, rather, it creates one less boundary. You can call it Frank if musicianers you work with also call it Frank. The purpose of theory is to create a language that is capable of communicating musical ideas. The only worthwhile theory for us, is applied theory. In musicianer's applications, root is used as we are defining it. Usage dictates meaning, not musicologists defining boundaries.
With our definition, there is more intellectual freedom & the understanding that chords & scales are ultimately the same thing.