Root beer is NOT alcoholic. Root beer includes the term “beer” because of antiquated marketing reasons stemming from the last 1800’s when Charles Hires started selling it.
Interestingly enough, many breweries making beer DO produce root beer as a non-alcoholic option. And some root beer flavored liquor and hard root beer DOES exist now, although those are all very clearly marked as alcoholic. The normal kind of root beer found in stores is non-alcholic. Or, at least: as non-alcoholic as other drinks like orange juice, which actually have very, very small amounts of alcohol (not enough to affect you) due to trace amounts of naturally occurring yeast, which may ferment a small amount of the sugar. It’s science!