Modulo the square of the rational units

Question

In a book I'm reading the following modulus comes up, $$ \operatorname{mod} \: \mathbb{Q}^{*2}$$ and I'm struggling to understand what it means. I understand $\mathbb{Q}^{*} = \mathbb{Q}\backslash \{0\}$ but not the square.

Context: $\delta := \frac{a.b}{2} \: (\operatorname{mod} \: \mathbb{Q}^{*2})$ with $a,b \in \mathbb{R}$.

Answer 1

$x=y \mod \mathbb Q^{*2}$ means by definition that $\frac{x}{y}$ is the square of a rational number.