The United States of America is a REPUBLIC. It was designed as a republic based on the First Republic (Rome), which had some democratic processes but was not a DIRECT DEMOCRACY like Athens or Sparta, something most people who are actually educated in history more rigid than Social Studies actually get. Perhaps you ought to pay more attention to people who find your idea of a democratic republic "difficult."
I've listened to people harp on these particular and parochially US-centered definitions for more than 25 years but it seems like they will be around as long as there is AM talk radio. L'Iguana
already gave it in a nutshell: a republic is a government where the supreme power resides with the people, IOW not a monarchy, and a democracy is where the people exercise that power directly or indirectly through elected representatives
. Madison made a distinction between the two in Federalist 10, using republic to mean representative democracy. Some people hold to that, fine, but that does not corner the market on what the words mean to most of the world, as reflected even in US-published dictionaries.
Alidar Warlock wrote:
Sparta wasn't a direct democracy.
Something most people who are actually educated in history more rigid than Social Studies actually get.