The reason for the square root of the lens' is purely to do with SNR increase. To use a real world example, let's say I collect 5 hours of Ha data with my 130mm F/5 refractor. I would do that in 30x600s Ha subs. As I combine the subs together the SNR of the image increases by the square root of the number of subs, this equates to about 550% (5.5x) increase in signal over a single image.
Now to get the same sort of SNR from a single 600s exposure I would need a 12" F/2.1 telescope. So the benefit of having 30 telescopes collecting data is that it would be the equivalent of having a 12" F/2.1 telescope collecting that data. What would take me to collect five hours of data, it would do every 10 minutes.
Another added benefit of having 30 telescopes is that you can increase its resolving power FAR beyond what a 5.1" or even a 12" telescope can achieve. If I placed each telescope 3 metres from the next, all in a line, it would have the resolving power of a 90m telescope. Think that's for fetched? It's what SKA (Square Kilometre Array) does in WA but with radio telescopes. It's not complete yet but eventually they're going to work in conjunction with South Africa so that we can use the Earth as a base line to have the resolving power of an approximate 6000m telescope
Don't get me wrong, it would be pointless having 30x5.1" telescopes for resolving power as the atmosphere makes anything over the 8-10" range redundant.
Want an incredibly deep all sky survey telescope? An AP3600 with a hundred QSI690 cameras, Nikon F Mounted with Samyang 135mm F/2 lens. It would effectively be a 213mm F/0.64 lens with a 36.8mp camera and resolution of 2.82"/pixel.
Of course if you want to study planetary nebula, nothing beats a good ol' 10m mirror