A less metyphysical answer is that we normally assume we live in a Euclidean space in which distance depends on the squares of the difference on each axes v. Pythagoras and trigonometry.

Einstein's Special Theory also assumed a quasi-Euclidean space, even though the time dimension has a negative coefficient - S = (x² + y² + z² - ct²).

You can get involved with spaces in which the square doesn't appear, but not many of us do that. Not often at least.

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