Ask a question

Why is a square root also called a radical?

I'm confused about why this mathematical operation has two different names.

4 Answers by Expert Tutors

Tutors, sign in to answer this question.
Jay S. | Victor Needlework Tutor AvailableVictor Needlework Tutor Available

"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! :)



A radical is actually the square root symbol.  A leading superscript number can indicate a higher order root, such as a cube root, fourth root, etc.   3√ indicates a cube root. The dictionary doesn't show a source root word for this definition of the word radical, so I don't know where it comes from or why it's called that. Most English words are derived from Latin, Greek or ancient Middle European languages.

I guess I should have also pointed out that while the radical is the symbol, the math operation is taking a root. The operation doesn't have two names. You can think of "subtraction" and "minus sign" as a parallel.

Jonathan F. | Math and Computer Tutor for All AgesMath and Computer Tutor for All Ages
5.0 5.0 (332 lesson ratings) (332)
Notice the word, "root", in square root? The word, "radical", comes from the Latin word, "radix", which means "root". "Radix" is also Latin for "radish", which is a root vegetable. So, "radical 3" is just another way of saying "the square root of 3".
Joseph H. | Math, Chemistry, Physics, Biology, and *Complete* SSAT, SAT, ACT ExamsMath, Chemistry, Physics, Biology, and *...
5.0 5.0 (40 lesson ratings) (40)

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.

Mike J. | Math Tutor in NJ okMath Tutor in NJ ok
5.0 5.0 (4 lesson ratings) (4)

Jay, that's a great resource! This concept is kind of like "all squares are rectangles, but not all rectangles are squares."