What is the term used to refer to the official approval of the constitution by the states?

Ratification

The consent from the congressional branch needed to approve government contracts. In the United States, reforms to the Constitution demand the ratification of state legislatures, global treaties and also required the ratification by the Senate.The Constitution was formally approved by the United States when it was ratified by New Hampshire on June 21, 1788.  

Ratification is the formal way to validate something, ordinarily by vote. It is the legal validation of a purposed law.

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