how do you find the cube root of a number?
Your subject is not geometry.
These days, almost everyone uses a pocket calculator for roots. A table of logarithms or a slide rule can also be used, but no one does that anymore.
Since you are using a computer, you can also raise the number to the 1/3 power, using Google. For example: for the cube root of 27, write in the search box
27^(1/3) =
and you should get the answer, 3.
suppose you want the cube root of k
take a reasonable guess, call it x
sub that guess into (2x^3+k)/(3x^2)
if the result differs from x, make the result your new x and repeat the process.
After a few loops of this process, your result will get closer to your input of x.
This is called Newton's Method
e.g. find cube root of 30, so k=30
my starting guess is x=3
guess -- result
3 .....3.11111111
3.1111111 3.10723734
3.10723734 3.107232505
3.107232505 3.107232506
notice for all practical purposes, my input is equal to my output after only about 4 "iterations" .
The closer your original guess is to the actual cube root, the less steps it will take.
my calculator says, cube root of 30 = 3.107232506
I know this is a rather tedious process, but it involves only the basic operations of addition, multiplication and division, and you did ask for a method of finding cube roots.
If you don't even have a calculator, (as in an exam, or while you're camping), you can use the following method (algorithm):
http://www.mathpath.org/Algor/cuberoot/algor.cube.root.htm
You will need pen and paper though.
To find the cube root of a number, you can follow these steps:
1. Start with the number you want to find the cube root of.
2. Make an initial guess for the cube root. This can be any number.
3. Divide the original number by this initial guess.
4. Calculate the average of the initial guess and the result of the division in step 3.
5. Use this average as a new guess and repeat steps 3 and 4.
6. Keep repeating steps 3 and 4 until you get a guess that is close enough to the actual cube root.
Here's an example to help illustrate the process:
Let's find the cube root of 125.
1. Start with the number 125.
2. Make an initial guess, say 5.
3. Divide 125 by 5: 125 / 5 = 25.
4. Calculate the average of 5 and 25: (5 + 25) / 2 = 15.
5. Use 15 as the new guess.
6. Repeat steps 3-5 using 15 as the new guess: (125 / 15) ≈ 8.33, (15 + 8.33) / 2 ≈ 11.67.
7. Repeat steps 3-5 again using 11.67 as the new guess: (125 / 11.67) ≈ 10.71, (11.67 + 10.71) / 2 ≈ 11.19.
8. Repeat this process until you reach a guess that is accurate enough, such as 11.180.
Therefore, the cube root of 125 is approximately 11.180.