# conjugation (mnemonic)

In pre-college mathematics, students typically learn how to rationalize the denominator (or, in some cases, numerator) of expressions such as $\frac{3}{\sqrt{11}+2}$ and $\frac{\sqrt{x+h}-\sqrt{x-h}}{2h}$. 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 $\frac{3}{\sqrt{11}+2}$ is:

$\begin{array}{cc}\hfill {\displaystyle \frac{3}{\sqrt{11}+2}}& ={\displaystyle \frac{3}{\sqrt{11}+2}}\cdot {\displaystyle \frac{\sqrt{11}-2}{\sqrt{11}-2}}\hfill \\ & \\ & ={\displaystyle \frac{3\sqrt{11}-6}{11-4}}\hfill \\ & \\ & ={\displaystyle \frac{3\sqrt{11}-6}{7}}\hfill \end{array}$

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 |