Dear Dave, a shopping question.

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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
 

Dave

Staff member
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)
 
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