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The brackets refer to the average, so $\left< x^2 \right>^{1/2}$ is the root-mean-square (RMS) of $x$. That is the square root of the mean (or average) of the square of multiple $x$s. The RMS average is useful when a quantity can be either negative or positive. For instance, a sine or cosine wave has an average of zero over one cycle, but its RMS ...