I'm trying to convert Fahrenheit squared $F^2$ into Celsius squared $C^2$.
I know how to convert a value $x$ in $F$ into $C$ with:
$\frac{5}{9}(x - 32)$
I also know how to convert a value $x$ in $km^2$ into $m^2$ with:
$x \cdot 1000 \cdot 1000$
I don't know though, how to convert a value $x$ in $F^2$ into $C^2$. It seems possible: WolframAlpha says that $5 F^2 = 1.543 C^2$, but I don't understand how they get there.
You might expect that just squaring the conversion leads to the correct result, but that appears to be wrong (following are two reasons why):
It doesn't return the same result as WolframAlpha:
$(\frac{5}{9}(5 - 32)) ^ 2 = 225$
It would be different from the $km^2$ conversion:
$(3km)^2 = 3^2 \cdot 1000^2 \cdot m^2 \neq 3 km^2 = 3 \cdot 1000^2 \cdot m^2$