Cube-Roots
The mathmaticians agreed that every number has 3 cube roots.
But like 8, or 216, it seems that there's only 1 cube root.
But there is still 3, unless it is a perfect cube, in the form of
a3+3a2b+3ab2+b3,
where the roots can overlap, or be the same number. Now, having that said, find all 3 cube roots of 27 (and no, it is not a perfect cube so it has 3 cube roots).
But like 8, or 216, it seems that there's only 1 cube root.
But there is still 3, unless it is a perfect cube, in the form of
a3+3a2b+3ab2+b3,
where the roots can overlap, or be the same number. Now, having that said, find all 3 cube roots of 27 (and no, it is not a perfect cube so it has 3 cube roots).
Labels: SharedPuzzle
posted by James Yu at
6:27 PM
4 Comments:
3,-3/2+3sqrt(3)i/2,-3/2-3sqrt(3)i/2
3
-3(-1)^1/3
3(-1)^2/3
retry
-3*(-3)^(1/3)
3*3^(1/3)
3*(-1)^(2/3)*3^(1/3)
3, 3*cis(2*pi/3), 3*cis(4*pi/3). they are roots of unity. they are the same distance from 0, but differ by 2*pi/3 radians on the complex number plane.
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