# Cubed Root of 6,636,363 **URL:** \ **Category:** Factual Questions\ **Created:** [October 26, 2001, 5:19am UTC](https://boards.straightdope.com/t/cubed-root-of-6-636-363/89732 "2001-10-26T05:19:21Z")\ **Posts on this page:** 14\ **Page:** 1
**Author:** ![Gooneybird](https://avatars.discourse-cdn.com/v4/letter/g/839c29/32.png) [@Gooneybird](https://boards.straightdope.com/u/Gooneybird)\ **Post date:** [October 26, 2001, 5:19am UTC](https://boards.straightdope.com/t/cubed-root-of-6-636-363/89732/1 "2001-10-26T05:19:21Z")
Hello, I don’t have a calculator on hand. Would some kind soul please help me out and provide me with the cubed root of 6,636,363? Hey, and while we’re at it, does anyone know what meconium is? ---
**Author:** ![Mikahw](https://avatars.discourse-cdn.com/v4/letter/m/e9bcb4/32.png) [@Mikahw](https://boards.straightdope.com/u/Mikahw)\ **Post date:** [October 26, 2001, 5:24am UTC](https://boards.straightdope.com/t/cubed-root-of-6-636-363/89732/2 "2001-10-26T05:24:26Z")
According to the windows calculator 6,636,363[sup]1/3[/sup] = 187.921604177903247450066475892493 Don’t know anything about meconium, though. ---
**Author:** ![bibliophage](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/bibliophage/32/7615_2.png) [@bibliophage](https://boards.straightdope.com/u/bibliophage)\ **Post date:** [October 26, 2001, 5:25am UTC](https://boards.straightdope.com/t/cubed-root-of-6-636-363/89732/3 "2001-10-26T05:25:43Z")
[http://www.calculator.com/calcs/calc\_sci.html](http://www.calculator.com/calcs/calc_sci.html) > **[Dictionary by Merriam-Webster: America's most-trusted online dictionary](https://www.merriam-webster.com/)** > > The dictionary by Merriam-Webster is America's most trusted online dictionary for English word definitions, meanings, and pronunciation. #wordsmatter ---
**Author:** ![Gooneybird](https://avatars.discourse-cdn.com/v4/letter/g/839c29/32.png) [@Gooneybird](https://boards.straightdope.com/u/Gooneybird)\ **Post date:** [October 26, 2001, 5:29am UTC](https://boards.straightdope.com/t/cubed-root-of-6-636-363/89732/4 "2001-10-26T05:29:14Z")
Thanks, folks. I think my windows calc is only capable of doing square roots. Much appreciated. ---
**Author:** ![Earthling](https://avatars.discourse-cdn.com/v4/letter/e/90db22/32.png) [@Earthling](https://boards.straightdope.com/u/Earthling)\ **Post date:** [October 26, 2001, 5:36am UTC](https://boards.straightdope.com/t/cubed-root-of-6-636-363/89732/5 "2001-10-26T05:36:40Z")
Within Windows Calculator, go up to the menu bar and click View, then choose Scientific. Lots more functions there. ---
**Author:** ![hibernicus](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/hibernicus/32/2802_2.png) [@hibernicus](https://boards.straightdope.com/u/hibernicus)\ **Post date:** [October 26, 2001, 7:06am UTC](https://boards.straightdope.com/t/cubed-root-of-6-636-363/89732/6 "2001-10-26T07:06:04Z")
> [@](#): > > \*Originally posted by Mikahw \* > **According to the windows calculator 6,636,363[sup]1/3[/sup] = 187.921604177903247450066475892493** Strange; my Windows 95 calculator only displays the first 10 decimal places. ---
**Author:** ![Why\_A\_Duck](https://avatars.discourse-cdn.com/v4/letter/w/13edae/32.png) [@Why\_A\_Duck](https://boards.straightdope.com/u/Why_A_Duck)\ **Post date:** [October 26, 2001, 11:53am UTC](https://boards.straightdope.com/t/cubed-root-of-6-636-363/89732/7 "2001-10-26T11:53:57Z")
I’m not sure what this cube root and meconium have in common, but meconium is the blackish, sticky, proto-poop that babies produce in the first couple of days after birth. ---
**Author:** ![CalMeacham](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/calmeacham/32/35_2.png) [@CalMeacham](https://boards.straightdope.com/u/CalMeacham)\ **Post date:** [October 26, 2001, 12:05pm UTC](https://boards.straightdope.com/t/cubed-root-of-6-636-363/89732/8 "2001-10-26T12:05:56Z")
**meconium** is the Cosmolene the Human Digestive System comes packed in. ---
**Author:** ![HeyHomie](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/heyhomie/32/207_2.png) [@HeyHomie](https://boards.straightdope.com/u/HeyHomie)\ **Post date:** [October 26, 2001, 12:16pm UTC](https://boards.straightdope.com/t/cubed-root-of-6-636-363/89732/9 "2001-10-26T12:16:54Z")
What is the formula for computing a square root (by hand, that is)? And for a cube root? ---
**Author:** ![hibernicus](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/hibernicus/32/2802_2.png) [@hibernicus](https://boards.straightdope.com/u/hibernicus)\ **Post date:** [October 26, 2001, 1:08pm UTC](https://boards.straightdope.com/t/cubed-root-of-6-636-363/89732/10 "2001-10-26T13:08:59Z")
If you’re not allowed log tables, then you can get there quite quickly by iteration. This is a method of solving transcendental equations (but it works for any equation where you don’t know the formula). It basically involves guessing, putting the guess into the formula and using the answer as the next guess. The values quickly converge on the correct answer. It sounds primitive, but it’s really powerful. in general it goes like this: x[sub]1[/sub]=x[sub]0[/sub]-f(x[sub]0[/sub])/f´(x[sub]0[/sub]) So in this case: f(x)=x[sup]3[/sup]-6,636,363 f´(x)=d[f(x)]/dx=3x[sup]2[/sup] Let’s say we guess the answer is 200, and call that x[sub]0[/sub]. To get the next guess we say: So x[sub]1[/sub]= 200-[(8000000-6636363)/120000]=200-11.4=188.6 Feeding in 188.6 as x[sub]1[/sub] to give x[sub]2[/sub]: 188.6-[(6708494-6636363)/106710]=188.6-0.676=187.924 And finally: 187.924-[(6636621.75-6636363)/105946]=187.924-0.0024= **187.9216** If that isn’t close enough for you (after only three iterations), you can do one more and get **187.921604178**. Now, are you sorry you asked? ---
**Author:** ![ultrafilter](https://avatars.discourse-cdn.com/v4/letter/u/3d9bf3/32.png) [@ultrafilter](https://boards.straightdope.com/u/ultrafilter)\ **Post date:** [October 26, 2001, 1:22pm UTC](https://boards.straightdope.com/t/cubed-root-of-6-636-363/89732/11 "2001-10-26T13:22:06Z")
> [@](#): > > \*Originally posted by rastahomie \* > \*\*What is the formula for computing a square root (by hand, that is)? And for a cube root? \*\* I remember learning special procedures for both in high school. In general, you don’t want to know these things, as they’re pretty horrible. ---
**Author:** ![Zyada](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/zyada/32/3028_2.png) [@Zyada](https://boards.straightdope.com/u/Zyada)\ **Post date:** [October 26, 2001, 6:57pm UTC](https://boards.straightdope.com/t/cubed-root-of-6-636-363/89732/12 "2001-10-26T18:57:30Z")
I remember using a heuristic technique in school to get square roots. It was easy to do, but non-intuitive so hard to remember. The easiest technique to use and remember if you have a calculator is successive approximations. For example, if you want to get the cube root of 15: 2 \* 2 \* 2 = 8 3 \* 3 \* 3 = 27 15 is between 8 and 27, so 2.5 \* 2.5 \* 2.5 = ? etc. until you get close enough for your purpose. ---
**Author:** ![sailor](https://avatars.discourse-cdn.com/v4/letter/s/a587f6/32.png) [@sailor](https://boards.straightdope.com/u/sailor)\ **Post date:** [October 26, 2001, 8:10pm UTC](https://boards.straightdope.com/t/cubed-root-of-6-636-363/89732/13 "2001-10-26T20:10:19Z")
I believe “cubed root” is incorrect because cubed means “elevated to exponent 3”. Also I will remind you that extracting the third root is the same as elevating to exponent 1/3 which you can do with the Windows calculator. You can elevate to any exponent as it has the function X^Y. ---
**Author:** ![rowrrbazzle](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/rowrrbazzle/32/414_2.png) [@rowrrbazzle](https://boards.straightdope.com/u/rowrrbazzle)\ **Post date:** [October 26, 2001, 11:17pm UTC](https://boards.straightdope.com/t/cubed-root-of-6-636-363/89732/14 "2001-10-26T23:17:35Z")
Another method: for cube roots, on the Windows calculator in scientific view, first check the “Inv” (inverse) box, then click on the “x^3” button. Square roots are similar.