[Phys-l] principal square root; was: what shall we do about math?

[Krishna Chowdary <chowdark@gmail.com>]

On Thu, Jul 16, 2009 at 12:13 PM, Steve Highland<shighlan@uslink.net> wrote:
> The class I met today had a dispute going (good!) over what they saw as a
> contradiction in the book.  It defined the square roots of a number a to be
> the solutions of
>
> X^2 = a
>
> -- so that both the positive and negative values qualify.
>
> But then it said the value of {radical sign}a was just the positive value.
> So the text defined "square root" written out in words one way and square
> root written as a radical a different way.   It seemingly made a distinction
> between "a square root" and "the square root."
>
> Man, that's confusing.  Does anybody have a better way out of this language
> dilemma?

"principal square root"

http://en.wikipedia.org/wiki/Square_root

http://mathworld.wolfram.com/SquareRoot.html

http://mathworld.wolfram.com/PrincipalSquareRoot.html

My suggestion would be to (as Chuck mentions in a previous message) to
use this for a discussion of convention and language.

I'd probably introduce the term "principal square root" in this
context, with its definition, and then remind students to consider the
context and details of the phrases:  square root, square roots, the
square root, etc.  And then I'd ask the instructor to be careful and
consistent with the language in assessments:  "Find all square roots"
versus "Find a square root" versus "Find the principal square root"
versus "Find the square root".

sincerely,
Krishna

Krishna Chowdary
Faculty, Math & Physics
The Evergreen State College
Olympia WA 98505