The inverse square law 1/r2 shows the distance performance for sound intensity, an energy quantity.
But your ear drums are moved by the sound pressure vibrations using the inverse distance law 1/r for field quantities.
Scroll down to related links and look at "Sound pressure pand the inverse distance law 1/r".
Scroll down to related links and look at "Decreasing of Sound Intensity from a Point Source - Inverse square law of sound".
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The inverse operation of taking the square root is to calculate the square.
XX or X*X, can be written as X squared. The inverse of a function "sort of cancels it out". I know the inverse of a square is the square root. Since we need the inverse of X squared, it's inverse is the square root of X. sqrt(x)
The inverse operation is to take a square root.
a=b
A non-square matrix cannot be inverted.