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## Sunday, March 18, 2012

### Nerding Out with the Dictionary

In my Spanish studies, I recently came across radical-changing verbs. When Mark, the teacher (I'm using, among other sources, the excellent Coffee Break Spanish) first said "radical-changing" I first thought WHOA, RADICAL, they must be really extremely different. But here's how it works. In conjugating a standard verb, the stem stays the same, and the ending changes. For example, bailar - to dance: bailo, bailas, baila, bailamos, bailáis, bailan mean I dance, you dance, he dances, we dance, you-all dance, they dance. The stem stays the same and the ending changes. But in a radical-changing verb, there are spelling changes to the stem as well. For example pensar - to think, the "e" changes to "ie" sometimes: pienso, piensas, piensa, pensamos, pensáis, piensan mean I think, you think, he thinks, we think, you-all think, they think.

Why this is interesting to me, is it's another clear example of "radical" referring to a root. "Radical-changing verb" is referring to changes in the root of the word, as well as the ending. With numbers, an example is the square root of a number, like how "radical 9" means "the square root of 9." The symbol for which is $\sqrt{9}$, and that symbol is derived from a stretched out "r." The rationale I've heard for this word choice is, picture an upright square resting on the ground:
If the square has an area of 9, the root, the part resting on the ground, has a length of 3. The square root of 9 is 3.

So I went and looked up "radical," and behold the first definition:

(esp. of change or action) Relating to or affecting the fundamental nature of something; far-reaching or thorough

not, as I might have guessed, extreme or far-fetched, which are included in the definition, but farther down.

Anyway, you all probably knew that already. But I thought it was a neat connection.

1. (Spanish Math teacher here)
I think you will find this reference interesting:
Earliest Known Uses of Some of the Words of Mathematics (R)
Scroll down till you get to Radix, Root, Unknown, Square Root.
In Spanish we talk about the "raíz" (your root)of the words in a colloquial way, much more formal is the term "lexema" (pretty the same as lexeme).
Generally speaking, "raíz" works for almost everything related with origin.
A warning in advance: my blog would not be useful for your language purposes, because it's not written in Spanish, but another of the 3 languages spoken in Spain :(

2. Yep, radicals get to the root of the problem. ;^)

3. I recently taught radicals as well, and had a similar discussion about the origins or the word (and why people use the word radical to mean cool).

I like your visual showing why the side is the foundation of the square.

4. I recently taught radicals as well, and had a similar discussion about the origins or the word (and why people use the word radical to mean cool).

I like your visual showing why the side is the foundation of the square.

5. Nice!

- Elizabeth (aka @cheesemonkeysf on Twitter)

6. I had never heard that the root symbol may have started out as a stretched out "r"! I'm not sure why this intrigued me so, but it did. So I did a little more research on it (aka I flipped through some Wikipedia pages). The "r" was introduced by Christoph Rudolff (1500s) perhaps to represent "radix" (which I also had to look up--synonyms include root, base, radical, foundation). My question: did the "r" really represent radix...or Rudolff? Seems an interesting coincidence to me. ;)

7. Cool, I have to show my 8th graders the visual of a square resting on its root, anything to help the students who still simplify radical 20 as 10. Being a science major, I think of the highly reactive free radicals in chemistry. One word, multiple rad meanings :)

8. The common name "radish" is derived from Latin (Radix = root).

9. That's so cool! And I'm blown away by Anonymous's comment about the word "radish." :)

Hi! I will have to approve this before it shows up. Cuz yo those spammers are crafty like ice is cold.