Whenever quadratics appear, surds are likely to be present also. One example would be in Physics to measure the time it takes an object undergoing constant acceleration (say, under the influence of gravity) to complete some distance, the time is likely to be irrational.
The mains AC voltage (e.g., 240v in Europe) is actually a sinewave which swings from a negative peak of sqrt(2) * 240 volts to a positive peak of sqrt(2) * 240 volts. This amplitude waveform, called 240 v RMS, makes an incandescent light bulb glow exactly as brightly as would a DC voltage of 240 volts.