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Using a method found here: https://www.wikihow.com/Calculate-Cube-Root-by-Hand, I was able to calculate cubic roots fairly quickly by hand. I did however run into something confusing. Most roots work fine but when I try to calculate the cubic root of 40, something goes wrong in the 3rd digit of the solution, I keep coming up with 9 instead of of the actual 1 I should be getting.

My math as follows:
$3^3 = 27 <=40$ Therefor first solution digit is 3.
$40-27=13$
Bringdown $000 = 13,000$
$300*3^2=2700$
$2700*4=10,800<=13,000$ Therefore next solution digit is "4".
$3*10*3*4=360$
$4^2=16$
$Sum=3076$
$13,000-3076=9924$ Bringdown $000 = 9,924,000$
This is where it goes wrong
$300*34^2=346,800$
$346,800*9=3,121,200<=9,924,000$ Therefore 3rd digit is 9 <-- WRONG (Should be 1)

Haven't gone further as that is wrong. The next two numbers are both 9, am I somehow skipping a line somewhere??

Any help would be appreciated.

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I am an idiot, theres a little chunk I missed in the explanation, wherein one multiplies their new divisor by the most recent result digit before subtracting. Whoops.

ie. $3076*4=12,304$
$13,000 - 12,304=696$ bring down "000" etc.
This gives the correct solution.

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