radical thoughts

What is it about some topics that just never seem to leave the curriculum? People, do we realize what a waste of time it is to spend a week or two simplifying arcane radical expressions?

The purpose of rationalizing denominators predates four function calculators. In those days, one could benefit from transforming an irrational number from the denominator to the numerator. Root 2/2 could be more easily be calculated by hand because you could divide a whole number into 1.414, as opposed to dividing 1.414 into 1.

I also see a lot of algebra II students spending loads of time simplifying the nth root of x to the m, where n does not divide into m evenly. What can be gained from simplifying the fourth root of 32x^6y^9?

Now, I am not above doing "useless" math in class. I love doing mental math, calculation tricks made obsolete by our technology. I love number patterns, e.g. perfect squares can't end in any digit other than 0, 1, 4, 5, 6, 9. I love the Ramanujan story about the number 1729.* And you never know, "useless" math almost always proves to be useful at some later date. We should learn math that is either useful or enjoyable. I can't say that simplifying radicals qualifies on either ground.

Does anyone else have a topic they think is worthless to teach?

*Ramanujan, dying of TB, was paid a visit by his friend and benefactor Hardy, who complained that the number on the cab he took over was most uninteresting--1729. Ramanujan countered that it is the smallest number that could be expressed as the sum of two cubes in two different ways!