conjugation (mnemonic)

In pre-college mathematics, students typically learn how to rationalize the denominator (or, in some cases, numerator) of expressions such as $\displaystyle\frac{3}{\sqrt{11}+2}$ and $\displaystyle\frac{\sqrt{x+h}-\sqrt{x-h}}{2h}$ . In to do this, they multiply the numerator and denominator of the fraction by an algebraic conjugate (or, in some cases, its negative) to eliminate the square root(s) (http://planetmath.org/SquareRoot) in the appropriate part of the fraction. Typically, the only algebraic conjugates that pre-college students encounter are those in some quadratic extension.

Most students who have advanced far enough in mathematics to encounter rationalizing denominators or numerators have also encountered some (usually Indo-European) foreign . Such students are familiar with the concept of of verbs, in which the ending of the verb changes to make agreement with the person and number of the subject. A helpful mnemonic for students to the algebraic conjugates that they need to use is pointing out to them that the procedure in mathematics is (and actually easier) than in foreign . The algebraic conjugates (or their negatives) that they need are nothing more than changing the ending of the number. For example, the way that a pre-college student is taught to rationalize the denominator of an expression such as $\displaystyle\frac{3}{\sqrt{11}+2}$ is:

$\begin{array}[]{rl}\displaystyle\frac{3}{\sqrt{11}+2}&\displaystyle=\frac{3}{% \sqrt{11}+2}\cdot\frac{\sqrt{11}-2}{\sqrt{11}-2}\\ &\\ &\displaystyle=\frac{3\sqrt{11}-6}{11-4}\\ &\\ &\displaystyle=\frac{3\sqrt{11}-6}{7}\end{array}$

Title	conjugation (mnemonic)
Canonical name	Conjugationmnemonic
Date of creation	2013-03-22 16:00:59
Last modified on	2013-03-22 16:00:59
Owner	Wkbj79 (1863)
Last modified by	Wkbj79 (1863)
Numerical id	6
Author	Wkbj79 (1863)
Entry type	Definition
Classification	msc 97D40
Classification	msc 11R04
Related topic	AlgebraicConjugates
Related topic	Division
Related topic	DifferenceOfSquares
Defines	rationalize the denominator
Defines	rationalize the numerator