Weeks ago I was looking at ways to determine the RMS value of a sampled
waveform with the 16F876 and several suggestions were to take 256
measurements (for easy division later) and accumulate the sum of squares,
divide by number of samples, and square root to get the RMS value of the
readings.

Now I would like to know why this works....what is the mathematical
relationship between squaring the readings and obtaining the RMS in the end?

I know it's almost stupid to ask since we're talking about Root Mean Square
to begin with....but I  am indeed missing the in between steps in the
story...