"Radical" can mean right, left or centre. The Neo-Cons are (or should that be "were") radical. Whether they should be counted as being conservative is another matter, but they were definitely well to the right.

Being radical is about advocating trying to sort things out by going to the root of the problem and digging that out.

Sometimes that's what needs to be done. Sometimes it is the worst thing in the world. The Nazis were radical as they come...