How did the philosophies of Rousseau, Locke, and Montesquieu influence the U.S constitution?
With all of these three political thinkers, a major theme was the idea of the social contract. All three felt that the only way that a government could be legitimate was for it to be based on the consent of the people. They believed that the people consented to be ruled by the government in return for the government protecting their rights to (in Locke's words) life, liberty, and property.
The Constitution was written in such a way as to reflect this contract. The government is prohibited from taking away people's life, liberty, or property without due process of law. The government is also set up in such a way (separation of powers, which was Montesquieu's idea, etc) as to make it less likely that it will try to take rights away.
Thus, the Constitution is written to reflect the idea of a social contract between the people and their government.
These Enlightenment thinkers held much in the way of persuasion over the Framers in the construction of the Constitution. On one hand, the notion of individual and unalienable rights that Locke developed would represent a major benchmark of the Constitution. The idea that there are specific rights that cannot be taken away by any external force is an underlying assumption behind the Bill of Rights. At the same time, the idea of Roussau's general will, that political self determination is the only possible way to achieve an sense of internal liberation and freedom is vitally important to the principle of popular sovereignty, which is present in the Constitution. Finally, Montesquieu's vision of divided government with specific branches and outlined responsibilities is vitally important to the structure and purpose of government as present in the Constitution.