I'm confused about why this mathematical operation has two different names.
Why is a square root also called a radical?
I am not surprised you are confused, because it is a new term for an old operation. We did not use the term "radical" in my math classes back in the 1950's or 1960's for anything. Take the "square root," "cube root,"or "nth root" operations were both concise and consistent with each other.
Jay, that's a great resource! This concept is kind of like "all squares are rectangles, but not all rectangles are squares."
"A radical is a root of a number. A square root is a radical. Roots can be square roots, cube roots, fourth roots and so on."
Hope this is of some help! :)