Why the noise is representing volt per square root of frequency. why not in volts or decibels.

 

It is because there are two dimensions to the problem. Noise amplitude is only part of the picture. Frequency is the other part. If the noise covers a narrow band it can be eliminated with a filter. If it is wideband, then it can not be easily eliminated with a filter. Think of it as averaging the amplitude squared over a bandwidth to give Volts per root Hertz. The reason for using amplitude squared can be answered by thinking about the average value of a sine wave over a single period. Yup -- the answer is zero -- not a useful average when talking about AC signals.