deviation Definition and 402 Threads

Can someone take a look at http://wps.aw.com/wps/media/objects/500/512494/supplements/Ch21.pdf and tell me how they go from Eq. (7) to Eq. (8)? I've tried this and keep getting additional terms.

We know that the standard deviation [sig] for a random walk, represented by a net distance d, to be approximately the square root of the total number of steps N, each of length L, from the origin. I. e., d~N1/2L~[sig]L. Does the angle attained after these steps also have a significant...