Do $\Bbb Q (\sqrt 2)$ and $\Bbb Q [\sqrt 2]$ mean the same? Do $\Bbb Q (\sqrt 2)$ and $\Bbb Q [\sqrt 2]$ mean the same?
I'm trying to refer to the field of the real numbers of the form $a + b \sqrt 2$ where $a$ and $b$ are rationals.
E: I'm sorry, my question was unclear, I was using $\sqrt  2$ as an example number, but from what I read in the answers, if I choose a number like $\pi$ then $\Bbb Q (\pi)$ and $\Bbb Q [\pi]$ would be different, correct?

Yes, they are same, but it's because $\mathbb{Q}$ is a field, and they are not same if you replace it by an arbitrary ring, which is not a field. In general, bracket gives the meaning "smallest ring containing the element in the bracket and the given ring", while paranthesis means "smallest field containing the element in the paranthesis and the given ring." So, when the given ring is itself a field, they're basically same.
