So last night I was with my wife while she was shopping for clothes. Like any good husband I sat diligently in the chairs while she tried on new outfits and brought them out to remind me how little I know about fashion.
So while sitting in the chair I decided to entertain myself by calculating in my head the cubic roots of the various numbers around the store that were presented on sales signs. It was a lot of fun and kept me from going insane, but I was using a brute force approach of determining the cubes.
For the life of me, I cannot remember if I was ever taught how to perform cubic roots longhand style on paper and was wondering if in your wise old age you could tell me if their was a method and how it was performed.
Signed,
Cubically Contained in Halifax
#2
PatrThom
Can't you save time by just raising them all to 1/3 power? Seems like that would be a lot easier.
--Patrick
#3
Dave
If a is the number you want the cube root of, make a guess and call it g. The next guess is
G = (2/3)*g + (1/3)*(a/(g^2)).
Repeat this until the cube root is found to desired accuracy.
If a = 8, for example, suppose our first guess is 3. Using the above formula, here are the successive guesses:
g1 = 3
g2 = 2.2962962963
g3 = 2.03658740252
g4 = 2.00065335855
g5 = 2.00000021335
g6 = 2.00000000000 ( to the accuracy of my calculator)
