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?
According to the windows calculator 6,636,363[sup]1/3[/sup] = 187.921604177903247450066475892493
Don’t know anything about meconium, though.
Thanks, folks. I think my windows calc is only capable
of doing square roots. Much appreciated.
Within Windows Calculator, go up to the menu bar and click View, then choose Scientific. Lots more functions there.
Strange; my Windows 95 calculator only displays the first 10 decimal places.
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.
meconium is the Cosmolene the Human Digestive System comes packed in.
What is the formula for computing a square root (by hand, that is)? And for a cube root?
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?
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.
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.
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.
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.