History of the Root of an Equation

Date: 11/01/2007 at 17:32:28
From: Greg
Subject: Why roots?

Why are solutions to equations called roots?  Is it because the 
solutions to some equations, e.g., x^2 = 16, are in fact roots of the
number specified in the equation?

Date: 11/01/2007 at 23:04:04
From: Doctor Peterson
Subject: Re: Why roots?

Hi, Greg.

This use of the word "root" originates with al-Khwarizmi, the Arabic
mathematician who wrote the first algebra book (coining our word
"algebra" in the process, and giving us the word "algorithm" from his
name).  He saw the variable as the root out of which an equation
grows; solving the equation is finding ("extracting") the root.  This
was more specifically applied to the equation x^n = k, from which we
get the idea of the nth root, and the square root in particular.  So
both uses of "root" in math come from the same "root" idea, that of
the hidden source of a plant.

I've had trouble in the past looking for confirmation of the fact that
both uses of root originated there; it's hidden in a footnote in
Smith's History of Mathematics (Vol. 2, p. 393).  But here is a quote
from Ball, A Short Account of the History of Mathematics, p. 157,
referring to the book Al-jabr:

  The unknown quantity is termed either "the thing" or "the root"
  (that is, of a plant), and from the latter phrase our use of the
  word root as applied to the solution of an equation is derived.
  The square of the unknown is called "the power".

If you have any further questions, feel free to write back.

- Doctor Peterson, The Math Forum
  http://mathforum.org/dr.math/