Mathematics - cube root

[martinjr]

Can any member provide a method for calculating a cube root for numbers with 4 or more digits, e.g., 2345, 23456, 234567 etc?

[factor-fiction]

Are you allowed to use a calculator or spreadsheet?
Do you know a method for a number that has fewer than 3 digits because I don't.
I can do square roots in my head and on paper using iteration but not cube roots

[factor-fiction]

I can do cube roots by iteration too but I need a basic calculator (no cube root key) to do some division. Is that acceptable? To how many decimal places do you need to be able to work the answer out?

[Calibax]

Log Tables?

[The Builder]

Just a thought ........... am I right in saying that if the 4 digit number ends in 7, then the cube root must end in 3
If it ends in 5 then the cube root must end in 5 etc etc
Then divide by the factor, and go from there ........... not sure where though :o(

[factor-fiction]

2345
Take an estimate: say 12
Calculate 2345/(12 x12)
That is 16.285.
Add your estimate twice to 16.285. That is 40.285.
Divide that by 3: that gives 13.428

Repeat using 13.428 as your guess

2345/(13.428x13.428) = 13.005
Add that to 13.428 +13.428.
That gives 39.861
Divide it by 3. Gives 13.287
That is pretty much the cube root (I think the answer is 13.286)

[bibblebub]

the last digit of the cube can only give you the last digit of the root, that digit is not a factor

e.g. 13³ = 2197 but neither 3 nor 7 are factors

[The Builder]

Number ends in 0 then cube root must end in 0
1 1
2 8
3 7
4 4
5 5
6 6
7 3
8 2
9 9

[The Builder]

........... oh poop Bibbles .............. you're right not necessarily a factor :o(

[Jonathan-Joe]

The tricks suggested, ie looking at the last digit, won't help as the OPer isn't asking just about cubes of integers. He gave example 2345 whiuch has a cube root 13.285593158578324, wich I found using http://www.csgnetwork...cuberootcubecalc.html

[Spotty Dog]

Just Google "Cube root of xxxx" and the answer will appear at the top of the page. Save the grey cells.

[factor-fiction]

I assumed martinjr wanted a method for any number with more than 4 digits and had just used numbers with consecutive digits for his examples.

Hi the builder- what you say works the other way round but not always your way round. So yes if you take a number ending in 5 its cube will also end in 5
Similarly the cube of a number ending in 8 will end with a 2.

But it doesn't always work in reverse. The cube root of 2345 doesn't end in a 5 because the answer is not a whole number

[factor-fiction]

I think my method should always work but you need a calculator. Certainly if I'd done a third iteration I'd have got the answer to at least 3 decimal places

[bibblebub]

There is a way using a long division technique similar to one that can be used to find square roots, but I found out about it so long ago that I can't recall the details (yet).

[factor-fiction]

23456
Estimate is 25
23456/(25x25)=37.53
(37.53+25+25)/3= 29.177

Repeat using 29.177 as estimate
23456/(29.177x29.177)= 27.553
(27.553+29.177+29.177)/3 = 28.63

Correct to 2 decimal places. Check it on Excel

[factor-fiction]

I was hoping matinjr might have returned to this thread,

[martinjr]

I've just returned to my thread right now (Sat 12th @17.46). Lots of interesting replies but factor30 is correct in assuming what I needed was a method for calculating the cube root of any number with more than 4 digits. I'm really only looking for the old arithmetic method which involved splitting the number into sets of three but the method escapes me. If it helps:- calculating the square root involves splitting the number into pairs and bringing down next pair alongside the remainder after finding the square of 1st pair of numbers. I know I've explained this badly so sorry about that.

[Jonathan-Joe]

Somethng like this http://xlinux.nist.gov/dads/HTML/cubeRoot.html ?

[zebo]

I'm not sure there is a chunking method, similar to square roots, I will now be up all night trying! Thanks!

[zebo]

http://www.wikihow.co...ate-Cube-Root-by-Hand

Having said that, found this which seems to work!

[martinjr]

Thanks for that Zebo. You need not stay up all night after all but I will trying to prove that Wikihow is correct!!