*sighs*
 

...didn't quite know where to ask this...though i suppose it could fit in here...

ok...i give up...so just how do you go about finding the nth root of a number without a calulator... for instance, the cube root of 27? yeah, it's 3, but how would you get that with just a pencil and some paper? ...i used to know, but i've been doing it with the calculator for so long, that i just...forgot. unlike your other basic math ops, it's not exactly something that's called for on a regular basis...

I pity you poor souls that have to know this stuff.
Work hard = $$$$$$$$$

Thats all I need to know.

GO HERE MY FRIEND

don't have to know it...just want to. i've just been thinking about for a while...thanx though.
:)

how do you get it for a square root? Might help for people here to jog their memory :)

(also: I'd like to know that as well :p )

bah, i used to know it too.

i can start this, but i dont konw if i'm doin it right

27^(1/3) = x
wouldnt u now turn this to log's?

ok, if it's just about whole powers that you want to take the n-th root of, then it's rather easy. (I actually jogged my own memory about that :) )

like The_Dude said, just take 27^(1/3) power. Now 27 is 3³
so you get 3^((1/3)*3) equals 3¨1 equals 3.

but as for numbers that aren't true powers... No idea.

Here's an easy to follow page that will help...

http://www.qc.edu.hk/it-school/homep...0Secondary.htm

You have to know the squares, cubes, whatever before you can start deriving roots.

Using your example, we know the cube root of 27 is 3, but suppose you asked what is the cube root of 28?

Well, we start by finding the nearest lower perfect cube, which is 27, and its root, which is 3.

So the first number of the cube root of 28 is 3, with a remander of 1.

next, what is the next lowest cube of 10 (1.0)? That is 8 or root 2, remainder of 2. (we are now at 3.2).

now what is the next lowest cube of 20 (.20)? That is still 8 or root 2, remainder 12 (we are now to 3.22)

what is the lowest cube of 120 (.120)? That is 64 or root 4, remainder 56 (we are now at 3.224)

and so on until you get the accuracy you desire.

Great link. My dad taught me how to do this a long time ago but I had forgotten.

thats pretty cool. I've never seen that before. As for numbers other than the square root (like that other method wouldn't work) all i can think of is using logs. Like if you had a log table and anti-log tale, or a calculator with only log functions and no root function.

anyways for the example its:

27^(1/3) = x

(1/3)log27 = logx

note: log27 = 1.43 (this is what you'd look up)

(1/3)*1.43 = logx

0.48= logx

note: the anti log is just 10 to the power of a number ie 10^
you'd also look this up!

10^.48 = x

3 = x

lebell explained it the way i learned it many, many years ago...

Yup! Just like long division!

and calculators were a thing of the future...(they used to teach us how to use our brains back then...)

yes...i see now. thanx. thanx much:)

I learned it this way not too many years ago.. and it works best!!!

You can actually set it up on your piece of paper like long division and it works great. It also keeps things organized when you are using crazy big numbers, and when you get into vectors and all that shit too. God i am glad i didn't continue with Algebra and Geometry.

Wow guys, I haven't done anything math related since I took my _____ (I don't want to sound like anything, so you can fill in whatever math you think I might've taken) as a juinor in high school, but after getting into all of this (I mean reading your helpful hints and stuff) I feel like pursuing math again. At least on my own...