In a message dated 3/13/2008 8:46:37 A.M. Pacific Daylight Time,
pcollinge@... writes:
We still
teach rationalizing denominators, though I have trouble
"rationalizing"
that topic. Clearly, the historic reason of "it's tough
to divide by a
messy decimal approximation" no longer applies. The only
real advantage I
can now see to rationalizing is that if everyone
changes their result to a
standard form, it's easier to compare answers
to see whether they
agree.
-----------------------------------
Yeah, what he said!
I was going to write out just about the same thing... Then, I thought
I should read the responses first.
Yes, it's a completely outdated (pre-calculator) technique for when
things were done by hand and you couldn't do long division by a radical.
Now that we have calculators, it's no longer needed -- except for the fact that
it's still in all the books and on all "standardized" exams. So, I still
show it to them... and test them on two problems. But, other than that, I
happily except unrationalized answers on my tests.
What's MUCH worse, if you ask me, is changing sqrt(8) to 2sqrt(2).
Another outdated technique. I ask you: Which one takes longer to
punch into a calculator? I refuse to call the second option "simplified"
because it isn't!
Karen
Coolmath.com
