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It is a Federal constitutional presidential republic. So, yes the US is a republic.
Brazil, officially known as the Federative Republic of Brazil, is the fifth largest country in the world. Its type of government is a Presidential system, Federal republic, Constitutional republic.
Depending on how strictly you define "Federal Republic"--yes. Strictly speaking, the United States is a constitutional republic (not a democracy as is often said). Generally speaking, a federal republic is a system in which the central government is above state/local governments, but state/local governments maintain a degree of power in their own domains. In this way, the U.S. government closely approximates a federal republic.
Constitutional federal courts are either created or allowed to be created under Article III of the Constitution. For instance, federal district courts and circuit court of appeals are Constitutional federal courts. The Supreme Court also falls under the category of Constitutional Federal Courts and it is the highest court in America. Legislative federal courts, on the other hand, are established by Congress using implied power. For instance, the Court of Military Appeals is a legislative federal court.
In a federal political system, state governments are given the ability to try new ideas by passing laws that are within its scope of power. The United States is a federal presidential constitutional republic.