Why this is interesting to me, is it's another clear example of "radical" referring to a root. "Radical-changing verb" is referring to changes in the root of the word, as well as the ending. With numbers, an example is the square root of a number, like how "radical 9" means "the square root of 9." The symbol for which is , and that symbol is derived from a stretched out "r." The rationale I've heard for this word choice is, picture an upright square resting on the ground:
So I went and looked up "radical," and behold the first definition:
rad·i·cal adjective /ˈradikəl/(esp. of change or action) Relating to or affecting the fundamental nature of something; far-reaching or thorough
not, as I might have guessed, extreme or far-fetched, which are included in the definition, but farther down.
Anyway, you all probably knew that already. But I thought it was a neat connection.