Radical

Radical is a much-misunderstood (and therefore much-misused) term. It literally means "at root" and thus was used to describe those whose political stance is either a) targeted at the roots of social convention, or b) is so deeply felt as to feel radically part of the view-holder. Radicals are often mistaken by American conservatives for liberals. The difference is that liberals are still invested in the political status quo and seek only to fine-tune the system while radicals — at least those of the anarchist or communist left — seek to tear the system down and replace it with one that they believe would allow for "real" egalitarianism. Many conservatives fail to see this nuance and thus tend to lump people like Michael Moore — a populist Democrat — in with Marxists. The opposite of a radical is a reactionary, a person who wants to actively repeal and remove liberal reforms and changes.

Historical
The historical meaning of (classical) radicalism or radical liberalism refers to hard-line republicanism, anti-clericalism and proto-social liberalism in the 18th and 19th centuries. Many left-wing to far-left classical liberal thinkers, including Maximilien Robespierre, Jeremy Bentham, Thomas Paine, Theodore Roosevelt and John Stuart Mill have defined themselves as 'radical'.

In the United States, Radical Republicans showed this tendency.

Hilariously, many left-liberal parties in Europe still name themselves "radical" but come across as rather center to center-left social liberal. Since left-wing socialists emerged as the mainstream of world politics, radicalists have become center to center-left social liberal. (Especially in France, "radical" is used in a similar sense to "center" or "liberal". Their philosophical roots can be found in the "republican" traditions that originated from the French Revolution.)

Radical left
The radical left has usually been used to describe moonbat anti-capitalist groups who want to abolish private property in favor of public ownership of most goods and property, along with the abolishment of all forms of inequality. Though some were pacifist in their methods, the ideology itself has come to be associated with those who want a fairly violent revolution that will destroy the bourgeoisie. The term has most frequently been used by academics to describe Maoists, Communists, anarchists and various socialists. However, note that it has also been used to describe left-wingers who did change society in a significant way, such as much of the leadership of the civil rights movement. As such the term "radical left" is somewhat broad and confusing, which isn't helped by the fact that conservatives in the U.S. use it as a pejorative to describe anything remotely social liberal. Although today's Social-Liberal has historically been called Radical, and this classical radical tradition still remains in Europe, conservatives in the United States will not use it in this sense. (In the context of modern international politics, social liberalism is located on the 'centre-left' of the political spectrum or even on the 'center' and is not considered a very hard 'left-wing'.)

Radical center
Radical centrism is an ideology that fervently promotes both left-wing and right-wing values. A "communitarian" is sometimes described as radically centrist due to being right-wing on social issues and left-wing on economic issues. Similarly, some American libertarians described themselves as being left-wing on social issues and right-wing on economic issues. It may also be used to describe an ideology that puts political pragmatism above all else, making it popular among Very Serious People. The Third Way, the Liberal Democrats and few European political parties are often identified as this. Many radical centrists tend to strike a trade-off between classical liberal(or fiscal conservative) and social liberal tendencies.

A few people have argued that fascism is "radically centrist" when it comes to economics, even if it's far-right on social issues. This is where third positionism sets in. Successful fascist movements are also "radically centrist" in the sense that their radicalism pervades even into the "center" of society, i.e. middle class and educated folks. This is something that people often fervently deny about past fascism in their country.

Radical right
See also: Reactionary

The term radical right has been used to refer to wingnuts who are extremely conservative, fervently anti-socialist, borderline xenophobic, nationalistic and have a weakness for right-wing conspiracy theories. For instance, many Tea Partiers are less extreme than the "far-right" on social policy (though many are still homophobes), but try to make up for it by being more radical than even much of the far-right when it comes to economic policy, resulting in support for nearly total deregulation of the economy, a comedic opposition to progressive taxation in favor of the flat tax or "FairTax", anti-environmentalism and the urge to dismantle much of welfare state and privatize most of the government's public services.

The term has been used to apply to the Liberty Lobby, John Birch Society, the Tea Party, UKIP and as of late much of the U.S. Republican Party. Barry Goldwater, due to his hawkish foreign policy and support for privatization, was also accused of being a reactionary by LBJ, though by the standards of today he would be considered a moderate Republican. The once leading political party in Switzerland, the Swiss People's Party, has also fallen under this label before, but luckily they were kept in check (for the most part). The "token" ultra-nationalistic party in Japan, the Japan Restoration Party, has been labeled this as well.

Other interpretations of radical
In the 1970s, teenagers referred to (for example) what today would be called extreme sports as "totally radical, man!". As of 2020, the term "radical" (or "rad") occurs only in parodies of teenage behavior.

People who dislike the connotations of "radical" change (so extreme!) have a new euphemism (courtesy of New-Age mealy-mouthed spin-doctors): "transformational" change.

Examples in history

 * John Brown, Harriet Tubman, and other abolitionists in the antebellum period of American history
 * Vladimir Lenin and the Bolsheviks before the October Revolution in Russia
 * Mao Zedong, Karl Marx, Leon Trotsky and other communist thinkers
 * Maximilien de Robespierre and other key figures in the radical phase of the French Revolution
 * The New Left self-identified as radical, putting forth a left critique against the prevailing post-World War II liberal consensus
 * The John Birch Society, who even William F. Buckley considered crazy, would be a right-wing example.

In math
It's a number to a fractional power such as $$\sqrt{10}$$ or $$7^{2/3}$$.

In chemistry
A radical is an atom, molecule or ion with an unpaired valence electron. Much like the above, they are known to react aggressively.