A field extension K/F is biquadratic if [K:F] = 4 and if $K$ is generated by the roots of two irreducible quadratic polynomials

Question

Artin claims that every biquadratic extension has the form $F(\alpha,\beta)$，where $\alpha^2 = a$ and $\beta^2 = b$ with $a,b\in F$.

I do not think this is true, just consider $\alpha = 1 + \sqrt {2}$, $\alpha^2$ clearly is not in $\mathbb Q$. Am I right? I think he means that $(\sqrt{2})^2$ should be in $\mathbb Q$.