And you would still be wrong.
The word Republic simply means that it i s not a monarchy, and it is 'goverened.' China is also a Republic. It is NOT a monarchy.
Whether it is a democracy or not has nothing to do with being a Republic.
As for the 'complicated system of checks and balances,' The UK has a House of Lords and the House of Commons - an upper house and a lower house. South Africa has an exuctive executive, a judicial executive, and Legisilative authority. This is a normal system of checks and balances.
Where the United States is different to a normal reprsentative democracy is that it has an electroal college. The electoral college removes the power of the people in that it can overthrow the vote of the people - that was its intention.
The United States is NOT a democracy - I would agree. Princeton says it's an Oligarchy. However, that has nothing to do with the fact that it is a Republic.