How does yeast carbonate home brewed root beer, and other soft drinks without creating alcohol?
Yeast produces alcohol, whether in beer, root beer, or bread. In bread the ethanol is evaporated due to heat. In root beer the alcohol stops at around a half-percent alcohol by volume, which is legally non-alcholic in most jurisdictions. It stops at that point due to the buildup of carbon dioxide (many CO2-related factors here, but simplifying for the purposes of explanation), and the relatively scarcity of nutrients in root beer compared to fermenting beer. BTW, it is safest to bottle your root beer in plastic bottles rather than gas, since the carb levels are less controllable than with normal primed beer bottling scenarios.