I need a hint to solve exercise 13.2.9 in Dummit and Foote. Suppose $F$ is a field of char not equal to 2. Suppose $a^2 -b$ is a square where $a,b \in F$ and $b$ is not a square. Show $\sqrt{a + \sqrt{b}} =\sqrt{m} +\sqrt{n}$ for some $m,n \in F$.
I've reduced to $(a+\sqrt{b})(a-\sqrt{b})=(\sqrt{m}+\sqrt{n})^{2}$ but dont know how to proceed