The sum under quadrature of any set of numbers is equal to the square root of the sum of their squares. This results in something that should look an awful lot like the Pythagorean theorem. This is used a great deal with vector arithmetic, for computing the magnitude of vectors.
In physics, this is such a strong hint that whenever a derivation produces a sum of squares, a good theorist will look into the possibility that there is an underlying vector or set of linearly independent quantities that had not yet been noticed.