Also this scene was in the math in movie collection
since a while. I still don't have the Blueray and the DVD was a bit dark. Here is a color corrected version of the
Abacus scene which features the linearization of f(x) = x^{1/3}.
The task had been to take the cube root of 1729.03 which is close to 1728=12^{3}. The
linearization gives 12 + 1.03/(144*3) = 12.002384
This result 12.002384 is shown in the movie. The actual cube root is 12.002383785691718123057.