I am starting to wonder if when OP writes "squared" it doesn't sometimes mean "multiplied by 2" and sometimes "squared".
in this example .436 raised to the 1/2 power is .218
0.218 is half of 0.436, not square root of 0.436 (which is 0.466)
but they show .218 raised to the 1/2 power again in the final theorem
For some reason we probably don't see what you see, but perhaps what is really happening is they multiply by a stoichiometric coefficient to calculate amount in the first stage (just applying simple stoichiometry), then use the stoichiometric coefficient in the K formula to raise the concentration to the second power. So it is not "squaring" twice, it is multiplying and then squaring in two different stages of solving the problem: follow the stoichiometry first, plug into K formula second.
not my fault they explain it like assholes. this would be raising it to the stoichiometric coefficient 2 different times.
Please calm down, blaming everyone around won't get you far.