I’ll admit that, after 20 years of teaching at the university level, I sometimes get lazy. But…as I age, I must resist that temptation even though at times I find myself muttering “I don’t have 30 extra f*cking minutes to figure out how to do this…”
But often if I stick with it, it doesn’t take 30 “f*cking” minutes. 🙂
Here is an example: I was trying to remember how to calculate and was trying to remember instead of think. I looked at an old calculus book…no avail…then I was shamed into thinking. About 2-3 minutes later it struck me:
“you know how to simplify don’t you?”
Problem solved…shame WIN.
of course things like are easily converted to things like , etc.
This leads to another point. Often when we teach we use the “conjugate trick” which only works for square roots. The above method works for the other fractional powers.