I never wrote that the factors were based on metric. ISO paper sizes are based off of an A0 sheet having an area of 1m². That's it.
The 1:sqrt(2) ratio has to do with subdivision. An A0 sheet subdivides into two A1 sheets, which subdivides into two A2 sheets, and so on. 1:sqrt(2) width/height ratio used in ISO pages sizes allows this, which makes dealing with paper significantly easier when it comes to slicing up pages, folding, packing, &c.
The 1:sqrt(2) ratio has to do with subdivision. An A0 sheet subdivides into two A1 sheets, which subdivides into two A2 sheets, and so on. 1:sqrt(2) width/height ratio used in ISO pages sizes allows this, which makes dealing with paper significantly easier when it comes to slicing up pages, folding, packing, &c.