How do you determine rms and .707 in electricity?

In electricity, the root mean square (RMS) value is calculated by taking the square of the instantaneous values of a waveform over a complete cycle, averaging those values, and then taking the square root of that average. For a sinusoidal waveform, the RMS value can also be determined by multiplying the peak voltage (V_peak) by 0.707 (or 1/√2). This factor represents the ratio of the RMS value to the peak value for sinusoidal signals, where the RMS value effectively represents the equivalent DC value that would produce the same power in a resistive load.