Problem concerning formally real fields

Question

I'm trying to reconcile a fact I am reading in David Marker's Model Theory text. He claims on page 326 that $\mathbb{F}=\mathbb{Q}(\sqrt{2}, \sqrt{-2})$ is a formally real field. This seems like it must be false because,

$(\sqrt{-2})^2+1^2=-2+1=-1$

So it appears that $-1$ is a sum of squares in this field. It seems I must be misreading something but I can't see what it is. Any insight into this would be much appreciated.

Answer 1

Looking at Lemma B.3, I think what he means is that $\mathbb Q(\sqrt 2, \sqrt {- \sqrt 2})$ is real. Marker's book is a great book, but it is full of typos like this.