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In case I'm using the wrong terminology, I mean 6 metres x 6 metres rather than sqrt(6) metres x sqrt(6) metres.



Yep, that would be 36m^2. If it helps, think of a grid of 1m by 1m tiles laid out on the floor. How many tiles could you fit?


I always thought it was "4 metres squared" means 4x4 and "4 square metres" means 2x2. Unless 4m^2 doesn't mean "4 metres squared", which would really be confusing me ...


Exponentiation usually binds more tightly than multiplication, so

  6 m² = 6 * (m²) != (6 m)²


m² is the symbol for "square metres", so 6 m² is e.g. a room 2m x 3m


6² m² = (6m)² != 6 m²




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