Conservatism and Radicalism are two different categories altogether.
Conservatives are those that wish to affect a more gradual, beneficient change in our country, while maintaining whole, pure, and simplistic ideals. There have been those who have compared it to "Right Wing Politics" in the sense that it supports liberty, free markets, limited government, a strong national defense, and high moral and religious values. But, Conservatism is more than that. According to Viscount Hailsham. The Conservative Case. Middlesex: Penguin Books, 1959:
Conservatism is not so much a philosophy as an attitude, a constant force, performing a timeless function in the development of a free society, and corresponding to a deep and permanent requirement of human nature itself."
Radicalism, on the other hand, seeks political reform in more drastic, dramatic (often violent) ways. Radicals seek to enact more government control, more regulated markets and economy, and fewer freedoms for the masses. Often called Liberals (or Left Wing), they are the ones who want to eliminate prayer in the schools, allow abortions and same sex marriages, mandate health care for all, and enact more gun control laws.