Where is the root note in a guitar chord?

Music theory is the exact same for all instruments (at least Western instruments with half-note intervals). So, everything will be the same on guitar as it is on piano... with the only difference being the positions/technique you use to play it on each respective instrument (ie: on a piano you have keys, on a guitar you have strings and a fretboard... but the notes/relation between notes/notes in chords are the exact same).

So yes, A is the root note of an A chord on guitar.

I know what you're trying to ask.

According to structure, when guitar is in standard tune, the basic A's root note is just the 5th string.

The basic C's root note is the 3rd fret of the 5th string.

E's is just the 6th string.

D's is just the 4th string.

F's is the 3rd fret of the 4th string. Or the 1st fret of the 6th string.

G's is the 3rd fret of the 6th string.

It's the note that a chord is built on. For example, in a C major triad (C,E,G) C is the root note.

Pretty much the same theory you learn in piano.