Timeline for How to justify teaching students to rationalize denominators?
Current License: CC BY-SA 3.0
24 events
| when toggle format | what | by | license | comment | |
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| Nov 28, 2023 at 3:38 | comment | added | Michael G | to add to what @Fantini said, I tell my (US high school) Algebra students the historical reason as stated. I then follow up by asking them to do the required long divisions by hand, no calculator allowed. In the first case they need to divide 1 by 1.41421.. (it can even be as few as 2 or 3 decimals to become tedious). In the second case they need to divide 1.41421... by 2. Most can do this second, rationalized, version in their head. The first one, not so easy. More generally, a simple fraction of a radical is usually easier to intuit the value of than whole number divided by a radical. | |
| Nov 26, 2023 at 19:36 | answer | added | Gerald Edgar | timeline score: 2 | |
| Nov 30, 2018 at 8:38 | comment | added | Watson | Related: math.stackexchange.com/questions/1084891 | |
| Sep 13, 2014 at 16:48 | answer | added | Sherwood Botsford | timeline score: 2 | |
| Apr 27, 2014 at 15:04 | answer | added | David Ebert | timeline score: 5 | |
| Apr 25, 2014 at 18:58 | answer | added | Dave L Renfro | timeline score: 15 | |
| Apr 24, 2014 at 14:28 | vote | accept | Dan Drake | ||
| Apr 24, 2014 at 6:42 | comment | added | André Nicolas | Amusingly enough, rationalizing the numerator is at least as frequently useful, for instance is finding $\lim_{h\to 0}\frac{\sqrt{x+h}-\sqrt{x}}{h}$. | |
| Apr 24, 2014 at 5:23 | answer | added | Jyrki Lahtonen | timeline score: 23 | |
| Apr 22, 2014 at 18:32 | vote | accept | Dan Drake | ||
| Apr 24, 2014 at 14:28 | |||||
| Apr 22, 2014 at 12:51 | comment | added | Jack M | My very first college math professor specifically criticized this tendency and called it "root-o-phobia". She said "Roots in the denominator have the right to live as well!". It might be a handy trick in some cases, but I think some students end up thinking it's somehow wrong to leave roots in the denominator. | |
| Apr 22, 2014 at 5:25 | answer | added | Confutus | timeline score: 1 | |
| Apr 22, 2014 at 2:47 | comment | added | user173 | You ask "how" and I'd say "don't". It won't help them much in other classes, it won't even help them with the SAT. It's a good subject to remove from the jr high and high school curriculum: we have better things to teach. | |
| Apr 22, 2014 at 2:16 | answer | added | paul garrett | timeline score: 11 | |
| Apr 22, 2014 at 2:03 | answer | added | SimonT | timeline score: 6 | |
| Apr 22, 2014 at 1:06 | answer | added | MasB | timeline score: 13 | |
| Apr 22, 2014 at 0:25 | answer | added | Mark Fantini | timeline score: 14 | |
| Apr 22, 2014 at 0:05 | comment | added | JRN | @Fantini, you should write your comment as an answer. I think it is the correct answer. In the old days (before calculators), you would have tables containing the values of, say, $\sqrt 2$, but none containing the values of, say, $1/\sqrt 2$, with the result that it became easier to multiply by $\sqrt 2$ than it is to divide by $\sqrt 2$. | |
| Apr 21, 2014 at 23:04 | comment | added | Benjamin Dickman | One reason is that it allows you to verify quickly whether two answers are equal; if students are going to share their solutions with you and one another, or compare them to those found in a textbook, then it might be wise to streamline the form in which answers are presented. | |
| Apr 21, 2014 at 22:15 | comment | added | Mark Fantini | I've once heard the justification that rationalizating denominators was useful when computations weren't so readily available (e.g. with computers). Then division using integers was way more feasible than dividing by rationals. | |
| Apr 21, 2014 at 22:12 | comment | added | mbork | IMHO rationalizing denominators is a purely aesthetic thing. It's just that e.g. every member of $\mathbb{Q}(\sqrt{2})$ can be canonically represented in the form $a+b\sqrt{2}$ with $a,b\in\mathbb{Q}$, so using this "canonical" representation is a Nice Thing To Do™. (And I strongly encourage my students not to rationalize denominators until the final solution, since it might be waste of time! | |
| Apr 21, 2014 at 22:12 | comment | added | Alexander Gruber | I've always personally leaned more towards a "lowest terms" approach, for example I prefer $1/\sqrt{2}$ to $\sqrt{2}/2$. If our intention is just to teach how to use exponent laws, why isn't it done more directly? | |
| Apr 21, 2014 at 22:09 | review | First posts | |||
| Apr 21, 2014 at 23:56 | |||||
| Apr 21, 2014 at 21:51 | history | asked | Dan Drake | CC BY-SA 3.0 |