The number 1 has three distinct cube roots in the complex number system. These roots are 1, (-\frac{1}{2} + \frac{\sqrt{3}}{2}i), and (-\frac{1}{2} - \frac{\sqrt{3}}{2}i). In polar form, these roots can be represented as (1), (1 \text{cis} \frac{2\pi}{3}), and (1 \text{cis} \frac{4\pi}{3}), where "cis" is shorthand for (\cos + i\sin).
4
All numbers have cube roots (not necessarily integral cube roots) so every prime has cube roots.
The real cube root of 1 is 1, since 13 = 1. There also a pair of complex cube roots.
Yes.
The number -512 has three cube roots in the complex number system. In general, any non-zero complex number has three distinct cube roots. For -512, these roots can be expressed in the form ( r^{1/3} (\cos(\theta/3) + i \sin(\theta/3)) ), where ( r ) is the magnitude and ( \theta ) is the argument of the complex number. The three cube roots are evenly distributed around the unit circle in the complex plane.
1
there is no cube roots in negative
4
All numbers have cube roots (not necessarily integral cube roots) so every prime has cube roots.
The real cube root of 1 is 1, since 13 = 1. There also a pair of complex cube roots.
Yes.
The number -512 has three cube roots in the complex number system. In general, any non-zero complex number has three distinct cube roots. For -512, these roots can be expressed in the form ( r^{1/3} (\cos(\theta/3) + i \sin(\theta/3)) ), where ( r ) is the magnitude and ( \theta ) is the argument of the complex number. The three cube roots are evenly distributed around the unit circle in the complex plane.
3√0.125 = 0.5 (there is only 1 real cube root of 0.125).
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Any real number - positive or negative - has exactly one real cube root. Any real number (except zero) has three cubic roots in the complex numbers; but only one of them is real.
-21 + 1.7320508i1 - 1.7320508i
There are 3 cube roots of 27. There are 2 square roots of 27 ( or any real number ). There are 4 fourth roots of 27 and so on:)