what is the mathod of getting cube root of any given number manually?

Question

say i want to find the cube root of 23456 manually. how do i do it?

Answer 1

Here is an interactive page that discusses one way to do it:

http://dilc.upd.edu.ph/loDeploy/math/math10a.html

For large numbers, bequalmings technique using logs is an easier way to go.

Answer 2

Hi:

Here are eight different way to find the cube root:

1) take the log of the number you want to cube root and divide by 3 get the result and take the antilog of it

2 ) use the power key( Y^X) key ( example: 23456Y^X (1/3)

3 ) Take a number to be cube root and divide it by a Guess Number squared and add it to two times the Guess number get the result divide by 3 get the result

store in memory or write down the result and use it for the new guess number ( example down below)

repeat this for about five or ten times

4) use the Newton -Taylor method

5) Graph it and interpolate it

6 ) trial and error method by cubing your number and average it out and continue do it until the number equal the cube root

7) get a Mathematical handbook of tables and formulas and look up cube and cube root of number

8) Visit the following website for the schoolboy or manual method:

www.nist.gov/dads/HTML/cubeRoot.html





Example for Number 3:

((23456/ (28^2) +(2*28) )/3) = Gn

((23456/ 784 + 56)/3)= Gn

(29.918367346 + 56)/3) = Gn

85.918367346 /3 = Gn

28.639455782 = Gn




((23456/ 28.639455782 ^2) + (2* 28.639455782))/3 )= Gn

(((23456/820.218427374)+ (2* 28.639455782) /3) = Gn

(( 28.597260457+ 57.278911564) /3) = Gn

( 85.876172021)/3 = Gn

28.625390673= Gn


((23456/ 28.625390673^2) +(2* 28.625390673)/3)= Gn

((28.625369932) + (57.250781346) /3) = Gn

85.876151278 / 3 = Gn

28.625383759 = Gn

Repeat this process about two more times and the approximate cube root should be accurate to 9 decimal places
the Gn is the Cube Root when your done

Good luck and best wishes to you

Answer 3

Find the prime factors of your number.
In this case, the prime factors of 23456 are:
2^5 * 733

To find the cube root, just find factors that appear three times. In this case, the number 2. That number goes outside the radical, and the other prime factors, the ones that are leftover, get multiplied together and stay inside the radical.
So, the cube root is 2 (cube root) 2932

Answer 4

Calculate a Taylor series expansion for the function f(x) = x^1/3 and substitute 23456 into it and it'll give you an approximation. The more terms you use in the series the more accurate your solution will be.

Answer 5

All the answers given for your question except the one from mc7e are good and valid. But there is another very famous method to get the cube root and that goes by the name CARDAN's method. Any handbook on mathematic contains the discription of this method, e.g. Taschenbuch der Mathematik - Bronstein-Semendjajew. This book is a German book, but there are English translations of this book.

Answer 6

There are many ways..one is prime factorization of the given number writing it as a^3 * b^3 * c^3 etc..then you can get it.but this works only for perfect numbers..
for others you will have to find the root of x^3- given number=0 where x are the three possible roots.this can be solved by newton raphson method.
The logarithmic method is another way.

Answer 7

guess nobody thought of finding the cube root using complex numbers . obviously that wud need the help of trigonometric tables. by the way 2 students in INDIA have discovered 1 method to find it manually. its gonna come out soon.

Answer 8

If this goes to voting, I'm voting for Carbon-based's solution.

The logarithmic method may be more effective, plus it works for roots or powers other than just cubes, but the origami method is pretty cool.

I'm going to have to play with that and see if I can figure out why it works.

Answer 9

x^3=23456.
3log x = log 23456
log x = (log 23456) /3
x=10^((log23456)/3)