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I was wondering why some notations can be written with square and some can't.

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    $\begingroup$ This question is unclear $\endgroup$ – Alfred Centauri Dec 1 '16 at 1:43
  • $\begingroup$ There's no reason why some units couldn't contain mass squared, see e.g. en.wikipedia.org/wiki/Gravitational_constant $\endgroup$ – Gert Dec 1 '16 at 1:59
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    $\begingroup$ I'm not sure what you're asking. Kilogram isn't written as kg^2, because it's written as kg. Meter is not written as m^2 because it's written as m. Square kilograms are written kg^2 and square meters are written m^2. $\endgroup$ – Cort Ammon Dec 1 '16 at 3:55
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There is no reason why a quantity cannot be defined in units of kg-squared.

For example, gravitational attraction depends on the product of 2 masses; this product could be given a name and quantified in units of $kg^2$. Likewise the magnetic force between two current-carrying wires depends on the product of the currents; this product would be measured in the unusual units of Amps-squared ($A^2$). This combination does in fact occur quite often within electo-magnetic units, but it has no special significance and no name.

The reason we don't do this already is that it is not useful, unlike $m^2$ for area and $m^3$ for volume, which are useful quantities.

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