Definition and Origin of the Word "Radical"
Date: 06/22/2005 at 18:35:27 From: Heather Subject: Definition and origin of the word radical? I was curious what the exact definition of "radical" was and also where and when the word originated? I have found only a few general definitions, such as square root symbol, which I already know.
Date: 06/22/2005 at 23:09:32 From: Doctor Peterson Subject: Re: Definition and origin of the word radical? Hi, Heather. The word "radical" comes from the Latin word "radix", meaning "root", from which we get not only the word "radical", but also "radish"! The other use of "radical" means "by the roots" or "from the roots", that is, complete, such as a "radical" change in a person. A political "radical" is someone who wants radical change by radical means, that is, an extremist. Another word from the same source is "eradicate" (originally, to "root out" or "pull out by the roots"). Now, why is a square root called a root in the first place? Answer: a root is the source of something; if you square a number, the number it came from is the root, as if the square grew from it. You can check a dictionary for the details of the history (when and where); here are two sources that are listed in our FAQ: Math Words, and Some Other Words, of Interest http://www.pballew.net/etyindex.html Earliest uses of mathematical words http://jeff560.tripod.com/mathword.html The latter says RADICAL. The word radical was used in English before 1668 by Recorde and others to refer to an irrational number. RADICAL SIGN appears in English in 1669 in An Introduction to Algebra edited in 1668 by John Pell (1611-1685): In the quotient subjoyn the surd part with its first radical Sign. You may also find these pages helpful Etymology of the Word Radical http://mathforum.org/library/drmath/view/52670.html History of Radicals http://mathforum.org/library/drmath/view/59082.html History of the Radical Sign http://mathforum.org/library/drmath/view/52525.html As for an exact definition, you can of course check a dictionary; I find that the term is used somewhat loosely, but in my usage it refers to the symbol itself or the function represented by the symbol. A "radical expression" would then be an expression involving a radical, that is, any kind of root. Merriam-Webster says 5 a : a mathematical expression indicating a root by means of a radical sign b : RADICAL SIGN If you have any further questions, feel free to write back. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/
Search the Dr. Math Library:
Ask Dr. MathTM
© 1994- The Math Forum at NCTM. All rights reserved.