How do you find the cube roots of $1000$ $1000$ ?

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Answer 1 · 2017-03-01T13:14:00

Cube roots of $1000$ $1000$ are $10$ $10$ , $(- 5 + 5 \sqrt{3} i)$ $(-5+5sqrt3i)$ and $(- 5 - 5 \sqrt{3} i)$ $(-5-5sqrt3i)$

Cube roots of $1$ $1$ are well known namely

$1$ $1$ , $- \frac{1}{2} + \frac{\sqrt{3}}{2} i$ $-1/2+sqrt3/2i$ and $- \frac{1}{2} - \frac{\sqrt{3}}{2} i$ $-1/2-sqrt3/2i$

Hence cube roots of $1000 = 10^{3}$ $1000=10^3$ are

$10 \times 1 = 10$ $10xx1=10$ ,

$10 \times (- \frac{1}{2} + \frac{\sqrt{3}}{2} i) = - 5 + 5 \sqrt{3} i$ $10xx(-1/2+sqrt3/2i)=-5+5sqrt3i$ and

$10 \times (- \frac{1}{2} - \frac{\sqrt{3}}{2} i) = - 5 - 5 \sqrt{3} i$ $10xx(-1/2-sqrt3/2i)=-5-5sqrt3i$

How do you find the cube roots of 10001000?