Final answer:
John Locke and Adam Smith are the key figures in establishing classical liberalism, with Locke's focus on natural rights and the consent of the governed and Smith's advocacy for free markets and laissez-faire economics.
Step-by-step explanation:
The two thinkers most closely associated with setting the roots of classical liberalism are John Locke and Adam Smith. Locke laid the philosophical groundwork with his emphasis on natural rights, such as the right to life, liberty, and property, and the idea that governments should function with the consent of the governed. Later, Adam Smith built upon these ideas with his economic theories, advocating for free markets and the principle of laissez-faire in his seminal work, The Wealth of Nations.