Problem with $x^{6} - 2 = 0$ compute roots in $\mathbb{C}$ 
I have problem with simple equation $x^{6} - 2 = $ compute roots in
  $\mathbb{C}$

I will try compute roots of $x^{6} - 2 = (x^{3}-\sqrt{2})(x^{3}+\sqrt{2})=(x-2^{1/6})(x^{2}+2^{1/6}x+2^{1/3})(x^{3}+\sqrt{2})$, but this not looks good. 
Maybe is better solution. 
Any suggestions? 

With $\sqrt[3]2z=x^2$, we have a cubic equation
$$z^3-1=0$$ which we can factor as (using a remarkable product)
$$(z-1)(z^2+z+1)=0.$$
Besides the obvious root $z=1$, we also have
$$z=\frac{-1\pm i\sqrt 3}{2}.$$
Finally, the six roots are
$$x=\pm\sqrt[6]2,\pm\sqrt[6]2\sqrt{\frac{-1\pm i\sqrt 3}{2}}.$$
Note that $(1\pm i\sqrt3)^2=2(-1\pm i\sqrt3)$ and we can unnest
$$\sqrt{\frac{-1\pm i\sqrt 3}{2}}=\frac{1\pm i\sqrt3}2.$$
