A remnant of pre-calculator days, the topic of rationalizing denominators remains entrenched in algebra textbooks and finds its way into standardized tests of all levels. And so I teach it, with the caveat that my students will never have to rationalize any denominators in my class unless they choose to do so.
I teach this unit with a bit of a history lesson, describing the choice that mathematicians once made (though it was not a difficult decision to make): should I divide by radical 2 (or some other irrational root), or should I divide by 2 (or some other rational denominator)? I talk to kids about square root tables and how they, along with tables of squares, trigonometric ratios, logarithms, etc., were once a mainstay of the mathematician's toolkit.
So I showed them slides with these images:
It took them a second to realize that I was joking, but still several students bewilderedly exclaimed, "Oh, man! At first I thought that mathematicians used to use those tables to help them do math!"
(photos from http://www.behance.net/gallery/square-root-table/282218)
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