Let $p$ and $q$ be two distinct primes. Pick the correct statements from the following:
a. $Q(\sqrt p)$ is isomorphic to $Q(\sqrt q)$ as fields.
b. $Q(\sqrt p)$ is isomorphic to $Q(\sqrt{−q})$ as vector spaces over Q.
c. $[Q(\sqrt p,\sqrt q) : Q] = 4$.
d. $Q(\sqrt p,\sqrt q) = Q(\sqrt p + \sqrt q)$.
(c) & (d) are correct. (a) is not correct for fields but correct for vector spaces. (b) not sure. i think it is correct by the same arguement of (a).am i right?