Notations fixing a unique square root of something can confuse even people who ought to know better. The Algebra II textbooks that my high school used stated in chapter 8(as an explicit, albeit unproved, theorem) that $\sqrt{ab}=\sqrt{a}\sqrt{b}$ for all real $a$ and $b$. Then in chapter 9, it introduced complex numbers, and I pointed out that the "theorem" actually only held for real $\sqrt{a}$ and $\sqrt{b}$. The teacher did not want to get into it, for fear of confusing the other students.