Question regarding c^2

Hey,

What is the significance of squaring the speed of light? c^2 is used
so much in areas such as relativity, but what does the act of
"squaring" represent? I ask this because squaring is an operation the
results of which will be totally different depending on the
(arbitrary) units you use. Ie., I just presumed until now that
squaring c will cause a larger dilation in its value if you use a
smaller unit, such as km/h, vs. a larger unit, such as miles/h. What
if you make up a unit of speed that is equal to c? Then the speed of
light would be 1, and squaring c would then just leave you with c
again, so no need for the "^2". When scientists write "c^2", are they
implying necessarily a certain unit, such as km/h?

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Blitzen

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