# Square roots **URL:** \ **Category:** Factual Questions\ **Created:** [May 21, 2003, 3:03am UTC](https://boards.straightdope.com/t/square-roots/176479 "2003-05-21T03:03:38Z")\ **Posts on this page:** 9\ **Page:** 1
**Author:** ![optimystique](https://avatars.discourse-cdn.com/v4/letter/o/b38774/32.png) [@optimystique](https://boards.straightdope.com/u/optimystique)\ **Post date:** [May 21, 2003, 3:03am UTC](https://boards.straightdope.com/t/square-roots/176479/1 "2003-05-21T03:03:38Z")
I was once told that for all real x, Square root of (x^2) = modulus (x) Thus if e.g. x = -2, x^2 = 4, then square root of 4 would be modulus (-2) = 2 I was wondering if the above is the correct definition of a square root. If so, then the definition would imply that square roots always yield a positive number (i.e. although (-2)^2 = 4, square root of 4 = 2). Please correct me if I’m wrong! ---
**Author:** ![g8rguy](https://avatars.discourse-cdn.com/v4/letter/g/7cd45c/32.png) [@g8rguy](https://boards.straightdope.com/u/g8rguy)\ **Post date:** [May 21, 2003, 3:15am UTC](https://boards.straightdope.com/t/square-roots/176479/2 "2003-05-21T03:15:16Z")
That’s certainly what we mean colloquially when we say “the square root.” But every number of course has two distinct square roots (except for zero, which brings up the minor nitpick that the principle square root is never negative rather than always positive). For some useful information, see [here](http://mathworld.wolfram.com/SquareRoot.html). ---
**Author:** ![Jinx](https://avatars.discourse-cdn.com/v4/letter/j/c6cbf5/32.png) [@Jinx](https://boards.straightdope.com/u/Jinx)\ **Post date:** [May 21, 2003, 4:06am UTC](https://boards.straightdope.com/t/square-roots/176479/3 "2003-05-21T04:06:04Z")
Hmm…I always thought MOD() was shorthand for a function defined for taking the modulus of a number. Specifically, I used to use MOD() to tell me the remainder from a division problem. For example, 5 MOD(5) = 0 because there would be no remainder. Likewise, 10 MOD(5) = 0, as well. However, 12 MOD(5) = 2, for example. It is useful in some BASIC programs I used to write to predict when a very specific event of interest to me (in astronomy) would occur…as a sub-calculation to a larger program of astronomical events. Also, IIRC: Truncation, known as TRUNC(), was a mathematical function serving as the counterpart to MOD() yielding not the remainder, but the whole number of the answer to a division problem…truncating off the decimal portion. Neither MOD() not TRUNC() yielded solutions to square roots… Isn’t this correct? - Jinx ---
**Author:** ![ultrafilter](https://avatars.discourse-cdn.com/v4/letter/u/3d9bf3/32.png) [@ultrafilter](https://boards.straightdope.com/u/ultrafilter)\ **Post date:** [May 21, 2003, 4:12am UTC](https://boards.straightdope.com/t/square-roots/176479/4 "2003-05-21T04:12:53Z")
Modulus is an alternate term for absolute value. It’s a bit of a convenient fiction that a number has only one square root, or cube root, or nth root. For the purposes of real variable calculus, a function must be single-valued, so we take the positive value of the square root. Now, once you get into complex variable calculus, you can’t ignore the other values, but that gets really ugly really fast, so let’s leave that as is. ---
**Author:** ![CurtC](https://avatars.discourse-cdn.com/v4/letter/c/ce73a5/32.png) [@CurtC](https://boards.straightdope.com/u/CurtC)\ **Post date:** [May 21, 2003, 4:32am UTC](https://boards.straightdope.com/t/square-roots/176479/5 "2003-05-21T04:32:13Z")
But ultrafilter, you can’t ignore the other roots even when doing simple high school algebra. They pound into your head that if you have a square root, you need to keep in mind that there can be up to two (real) roots. ---
**Author:** ![Jinx](https://avatars.discourse-cdn.com/v4/letter/j/c6cbf5/32.png) [@Jinx](https://boards.straightdope.com/u/Jinx)\ **Post date:** [May 21, 2003, 4:57am UTC](https://boards.straightdope.com/t/square-roots/176479/6 "2003-05-21T04:57:36Z")
> [@](#): > > \*Originally posted by ultrafilter \* > **Modulus is an alternate term for absolute value…** Ultrafilter, just wondering… What do you know about my other meaning for Modulus, in math? How do mathematicians distinguish between these functions? - Jinx ---
**Author:** ![Donut](https://avatars.discourse-cdn.com/v4/letter/d/e19adc/32.png) [@Donut](https://boards.straightdope.com/u/Donut)\ **Post date:** [May 21, 2003, 5:12am UTC](https://boards.straightdope.com/t/square-roots/176479/7 "2003-05-21T05:12:54Z")
> [@](#): > > How do mathematicians distinguish between these functions? There are quite a few places in mathematics where terms have two (or more) conflicting meanings. Generally, one has to pick the appropriate meaning from the context. A good author will ensure the context is unambiguous, or supply an explicit definition. ---
**Author:** ![DarrenS](https://avatars.discourse-cdn.com/v4/letter/d/977dab/32.png) [@DarrenS](https://boards.straightdope.com/u/DarrenS)\ **Post date:** [May 21, 2003, 6:04am UTC](https://boards.straightdope.com/t/square-roots/176479/8 "2003-05-21T06:04:16Z")
In the real world, it’s often convenient to take the positive square (or nth) root and discard the negative. For example, a square room is 36 square feet - how long is each wall? 6 feet of course. The “-6” answer doesn’t have a real world interpretation - how long is “-6 feet” as a distance? (as a displacement, perhaps, but that’s another story). For a real world interpretation of “-6 feet”, without cheating and interpreting the minus sign as a direction, you’ll need a science fiction writer 😉 ---
**Author:** ![ultrafilter](https://avatars.discourse-cdn.com/v4/letter/u/3d9bf3/32.png) [@ultrafilter](https://boards.straightdope.com/u/ultrafilter)\ **Post date:** [May 21, 2003, 2:38pm UTC](https://boards.straightdope.com/t/square-roots/176479/9 "2003-05-21T14:38:08Z")
> [@](#): > > \*Originally posted by Jinx \* > \*\*Ultrafilter, just wondering… What do you know about my other meaning for Modulus, in math? How do mathematicians distinguish between these functions? - Jinx \*\* “modulus” referring to absolute value is pretty rare, IME, except when you get to complex numbers. Your mod function is one of the more important things out there. There’s usually very little room for confusion, as there are symbols–|z| and a mod b–for each operation, and the context makes them clear. > [@](#): > > _Originally posted by CurtC_ > **But ultrafilter, you can’t ignore the other roots even when doing simple high school algebra. They pound into your head that if you have a square root, you need to keep in mind that there can be up to two (real) roots.** Yes, but when you’re doing calculus, sqrt(x) means the positive root. That’s what I had in mind.