That doesn’t mean anything. You need to revisit your grade school math. Square units just means: unit x unit. That’s ALL. You can get 12 square units with a blanket 3.46 units on every side.
First of all, I consider myself an equal opportunity integer/non-integer type of guy. I have used both of them without reservation for many years.
Alas, but 3.4641016... units per side (approximate square root of 12 actually equals 11.99999999...) will not get you 12 or 12.0 square units. Therefore, I assume you are using “new math” or “common core math”, in which case your solution would be correct.
In new math, 11.999999... is the equivalent of 12.0 because you feel it is so. Feelings really count in new math. One would not want to slight the problem solver by requiring an exact answer that could denigrate their self worth. In fact, 13 or 15 would be appropriate answers if one felt strongly. However, if one felt excessively strong a 12 or 16 answer would also be acceptible.
In common core math, the problem constraint (12.0) would be considered “socially unjust” and could be ignored if desired. The ultimate “right” answer would have to be the answer derived by “group think”. If you could convince the others in the group that 15 was the socially just answer then 15 would be declare the “correct” answer. If other groups came up with different answers, that would be considered OK.
The real problem with these two approaches, although they support social justice and individual freedoms, is that there are flaws when applied in “reality”. Consider a brain surgeon, nuclear physicist, lawyer or judge, etc. who uses that logic in their day to day business. Consider that we have observed this line of thought already in the Supreme Court’s decision on CommieCare.