The root mean square (RMS or rms) is defined as the square root of the mean square (the arithmetic mean of the squares of a set of numbers).
Note that, we only take square of the "set of numbers" but not of the "count of numbers".
But when calculating the rms value, we take the square root of the arithmetic mean of the squares of the values.
Note, we didn't take the square of the "count of numbers". Then, why take the square root of the arithmetic mean? Shouldn't we take the square root of only the square of the "set of numbers"?