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The purpose of a square root is to enable some calculations, For example,

  • if you have a square with sides of 1 unit, then its diagonal has length sqrt(2) units,
  • the power output of a sound wave is related to the square root of its amplitude
  • the intensity of light (or magnetic force, gravity) is inversely proportional to the square of the distance from the source so you would have to change the distance by *sqrt(x) to reduce the intensity to 1/x (increase the distance to sqrt(3) times as much to reduce the intensity to 1/3.

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Q: What is the purpose of the square root?
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