In pre-college mathematics, students typically learn how to rationalize the denominator (or, in some cases, numerator) of expressions such as and . In order 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) 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 language. Such students are familiar with the concept of conjugation 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 calculate the algebraic conjugates that they need to use is pointing out to them that the procedure in mathematics is similar (and actually easier) than in foreign languages. 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 is: