Final answer:
Roosevelt believed that the success of the U.S. is important for the idea of democracy around the world because he wanted the U.S. to serve as a model for democratic governance.
Step-by-step explanation:
Roosevelt believed that the success of the U.S. is important for the idea of democracy around the world because he saw the United States as a model for democratic governance. He wanted the U.S. to serve as an example to other nations, showing that democracy can bring success, stability, and prosperity to a country and its people. By maintaining democracy and economic prosperity within the U.S., Roosevelt hoped to inspire other nations to adopt democratic principles as well.