$(2)$ Let

$f(x)=x^3+2,$ and $,=\{inC|f()=0\},$ and $,L=Q().$

$($a$)$ Write the elements of $.$

$($b$)$ Find the degree $|L$:$Q|.$

$($c$)$ Is $\frac{L}{Q}$ a Galois extension?

$($d$)$ Determine the Galois group Gal$(\frac{L}{Q}).$

$($Hint: Consider the permutation representation $$:Gal$(\frac{L}{K})S_{}$ of Gal$(\frac{L}{K})$ induced by $.)$