When someone claims uncritically that the ratio of any two integers is √2, I get a little edgy. I'm also having a hard time following this simplification: A / √A = A × A / A = A Huh? This only holds if √A = A = 1. I haven't checked the rest, but this doesn't give me much confidence. Of course, knowing those Europeans, these sizes do probably make tons of sense on paper (see what I did there?), even if this isn't the…
He's written A / √A = A × A / A = A, but what he means is A / √A = √A × √A / √A = √A, which is actually true and is what he uses below
A / A^(1/2) = A^1 * A^(-1/2) = A^(1 + (-1/2)) = A^(1/2)