why-do-we-rationalize-the-denominator-kristakingmath

Our math teachers always tell us to "rationalize the denominator", but most of the time they don't tell us why. I'll leave it up to you to decide whether or not you think the reasons for rationalizing are good ones, but here are some of the reasons why we do it.

0:13 What we mean when we say "rationalize the denominator" // We're basically just saying "get the root out of the denominator". To do this, we have to multiply both the numerator and denominator by the root that's in the denominator. That way, the roots will cancel. Pro tip: If you have more than just a single root in your denominator, try conjugate method to eliminate the root from the denominator.

1:28 Why should be bother rationalizing the denominator at all? // We'll go over a few reasons why it might be a good idea:

1:34 It's easier for teachers to grade work when everyone's giving their answers in the same format.

1:51 Historically, we think about rationalized fractions as being reduced to lower terms, compared with non-rationalized fractions. And we always want to have our fractions reduced to the lowest possible terms. The reason rationalized fractions are in lower terms is because, before we had calculators, it was easier to do the long division for a rationalized fraction, than it was to do the long division for a non-rationalized fraction.

2:35 Agreeing to rationalize our fractions means we can always recognize like-terms when we have them, which might help us further simplify our answers.

3:00 Summary

Music by Joakim Karud: http://soundcloud.com/joakimkarud

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Hi, I’m Krista! I make math courses to keep you from banging your head against the wall. ;)

Math class was always so frustrating for me. I’d go to a class, spend hours on homework, and three days later have an “Ah-ha!” moment about how the problems worked that could have slashed my homework time in half. I’d think, “WHY didn’t my teacher just tell me this in the first place?!”

So I started tutoring to keep other people out of the same aggravating, time-sucking cycle. Since then, I’ve recorded tons of videos and written out cheat-sheet style notes and formula sheets to help every math student—from basic middle school classes to advanced college calculus—figure out what’s going on, understand the important concepts, and pass their classes, once and for all. Interested in getting help? Learn more here: http://www.kristakingmath.com

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