The proof that $\sqrt{q}$ is a rational number iff $q$ is a perfect square

Question

I have a proof of that if $q\in \mathbb{Q}$ then $ \sqrt{q}$ is rational if and only if $q$ is a perfect square (it can be written in the form $q={p_1}^{a_1}...{p_n}^{a_n}$ where integers $a_j$, which may be positive or negative are even). I just need an explanation why in this proof, when we squared $r$ there is $r^2=\pm p_1^{2a_1}...p_k^{2a_n}$ not just $r^2=p_1^{2a_1}...p_k^{2a_n}$? (Proof in the photo)

Answer 1

Hypothesis: the author copy-pasted the expression of $r$ and forgot about the $\pm$ symbol, because, you are correct: when you square a positive or negative integer, it should be positive.