# Why would a quantity like the 'Hubble contrast' be squared, then have its square root taken?

From Sabine Hossenfelder's recent video, New Evidence AGAINST Standard Cosmology:

And her source....

I don't get why a graph would show a quantity that is squared, then immediately 'square-rooted'.....

Also, the lowercase delta does stand for the Hubble constant difference or contrast, correct?

• The plot she is showing averages over $\delta H$, not $H$, i.e. a fluctuation field. Sep 7 at 18:45

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.
$$\left< A\sin x \right> = 0, \quad\quad \left< (A\sin x)^2 \right>^{1/2} = \frac{A}{\sqrt{2}}.$$