Square root of 3 billion digits. The fraction (…) for the square root of three can be used as an approximation. Despite having a denominator of only 56, it differs from the correct value by less than (approximately ). The rounded value of 1.732 is correct to within 0.01% of the actual value. Archimedes reported , accurate to (six decimal places) and (four decimal places), respectively. It can be expressed as the continued fraction , expanded on the right. It can also be expressed by generalized continued fractions such as which is evaluated at every second term. The following nested square expressions converge to
Root mean square power can also be found using the same method that in the case of a time-varying voltage, "V(t)", with RMS value "V", This equation can be used for any periodic waveform, such as a sinusoidal or sawtooth waveform, allowing us to calculate the mean power delivered into a specified load. By taking the square root of both these equations and multiplying them together, the power is found to be: Both derivations depend on voltage and current being proportional (i.e., the load, "R", is purely resistive). Reactive loads (i.e., loads capable of not just dissipating energy but also storing it) are