rationalizing the denominator

[John & Mary Harrison]

Reasons to teach this process:
1. makes it easier to teach division of complex numbers
2. useful for solving limit problems before L'Hopital's rule is introduced
3. used when using the definition to find deriv of square root (x).
4. nice extension is using the definition to find cube root (x)

Mary Harrison
Salem High School
Va. Beach, Va.

[lee kucera]

My point exactly--none of these are Algebra I material. I have no objection to teaching it in Algebra II--just not Algebra I.

lk

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lee kucera
a.p. statistics
leek...@gmail.com

[Jim Wysocki]

Yes, but even then it seems that rationalizing the denominator remains in the "nice to know" category rather than the "need to know" category of math topics. Even in Algebra 2.

jim w

[Steve Phelps]

That is a good point about complex numbers, especially from a
geometric point of view, where a+ib is a point and the result of an
operation like division is another point in the complex plane. If you
can't rationalize a complex denominator, it is difficult to see the
point.

Another geometry idea is the distance between lattice points. By
rationalizing the denominator, you can express values of expressions
as a rational multiple of the distance between two lattice points
(with the exception of sqrt(11) and such).

Personally, I like to have my students rationalize the denominator
when they run across it in geometry. There are a bunch of patterns
that are usually hidden until you rationalize.

That said...is it useful? probably not. Is it testable? don't think
so. Is there a place for it? Absolutely!

[Theresa Rice]

I agree with Jim.  There are too many "nice to know" items as it is in our curriculum.  I long to see the day when we can teach to understanding and not just "cover" way too many objectives.