Definition of ‘standard deviation’

Math help please. My teenager is learning about SD in math and i was wondering how/why the formula was developed.

Anyone got an opinion as to my hypothesis that the definition of SD relates to the mathematical ‘hack’ / trick/fact that a square of a difference from the mean (positive or negative) will always be positive. You average those up, take a square root and voila! (As long as ignore the negative answer).

Is there any other reason why square roots of squares are involved?

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