[snowwrestler]

We have a representative democracy in the U.S. We also have a republic. The two terms are not contradictory.

"Representative democracy" tells you how decisions are made--we select a few citizens to make decisions on our behalf. "Republic" tells you who is sovereign--in the U.S. the individual citizens have the right and power to rule, and have used that to construct our own government.

Counter examples:

The U.K. is a representative democracy, but not a republic. It's a monarchy.

North Korea is a republic but it's not a democracy. It's an autocracy.