Roots of Unity in fields Which roots of unity are contained in the fields: $\mathbb{Q}[i]$, $\mathbb{Q}[\sqrt2]$, $\mathbb{Q}[\sqrt3]$, $\mathbb{Q}[\sqrt5]$, $\mathbb{Q}[\sqrt{-2}]$ and $\mathbb{Q}[\sqrt{-3}]$? 
I know that the roots of unity in $\mathbb{Q}[i]$ are $1$, $-1$, $i$, and $-i$. I'm having a hard time finding the roots of unity in the other fields. If anyone could offer any advice, it would be greatly appreciated.

Hint: What is a big field that $\mathbb{Q}(\sqrt{2})$, $\mathbb{Q}(\sqrt{3})$, and $\mathbb{Q}(\sqrt{5})$ are all subfields of? You should know what this big field's roots of unity are, and then the roots of unity in each of these three fields will have to be among the roots of unity of this big field.
Hint: For $\mathbb{Q}(\sqrt{-3})$, you should write out what the cube root of unity $e^{2\pi i/3}$ is using Euler's identity. 
