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