| 31. | Galois theory allows to prove that, if the angle is not a multiple of 3? non-real cube roots are unavoidable.
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| 32. | Let ( here i and \ omega are the imaginary unit and the primitive cube root of unity respectively ):
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| 33. | Where the cube roots expressed as radicals are defined to be any pair of cube roots whose product is } }.
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| 34. | Where the cube roots expressed as radicals are defined to be any pair of cube roots whose product is } }.
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| 35. | Thus C = M ^ 3 holds over the integers, and Eve can compute the cube root of C to obtain M.
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| 36. | There are six primitive 7th roots of unity; thus their computation involves solving a cubic polynomial, and therefore computing a cube root.
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| 37. | Both trisecting the general angle and doubling the cube require taking cube roots, which are not constructible numbers by compass and straightedge.
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| 38. | When tested by psychologists and scientists, a number was written on a blackboard, and Muhamed was asked to extract the cube root.
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| 39. | Exley has not left much in the way of mathematical legacy, but work on the extraction of cube roots did attract favourable attention.
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| 40. | Shugart developed the Shugart number, the observation that the number of members of the lower house tends towards the cube root of population.
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