21. We want to show that a branch of the cube root function on this domain is given by: 22. There \ zeta is one of the complex cube roots of 1, as defined earlier in that section. 23. As 7 is not a Fermat prime, the 7th roots of unity are the first that require cube roots . 24. In the first section the five operations of addition, subtraction, multiplication, division, and square and cube roots are given. 25. Trigonal curves are those that correspond to taking a cube root , rather than a square root, of a polynomial. 26. This process can be extended to find cube roots that are 3 digits long, by using arithmetic modulo 11. 27. Airships and some square of the cube root of the airship volume ( volume to the two-thirds power ). 28. However, the cube root of 2 is not constructible; this is related to the impossibility of doubling the cube. 29. This solution in radicals involves the imaginary number \ sqrt and hence involves the cube roots of complex conjugate numbers. 30. A similar construction works for any cubic alternative separable algebra over a field containing a primitive cube root of unity.
