I don't have room for quarter length radials for my Hustler 6 band vertical (10through 80 meters). Can I use 20 foot radials? If so, how many?
The hustler is a Hustler 6-BTV 6 band HF vertical antenna
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20-foot (6.1 m) radials are certainly better than nothing; your Hustler would work with 20' radials, just not as well as it would with longer radials. 20 feet is longer than a quarter-wavelength for 20m, so your antenna would perform reasonably well at frequencies of 14 MHz and higher (10m through 20m), and not as well at lower frequencies (30m through 80m). The conventional advice is that more radials are better; I'd suggest at least 16 radials.
For limited-space antenna installations, the 6-BTV manual suggests bending the radials to increase the amount of wire on the ground further from the antenna; see the graphic below, which I have borrowed from the manual. This would improve the antenna's performance at the higher frequencies, but wouldn't do much for the lower frequencies. Still, it's probably worth doing.
There are many questions tagged radial with more information. I've linked to a couple.
The mentioned antenna is designed for specific radial lengths to cover the ham bands. Each tuned section depends on the radial system for tuning in the mid of that band. Deviation from the advised radial system will detune the antenna (each band different) and also the SWR as function of the frequency will alter: matching deviates from the center frequency of the band. In some ham bands it will be more difficult to match the antenna. And probably the losses will be higher with shorter radials.
Not for this specific antenna, but for the whole range of short verticals: missing so far in this discussion is that a short vertical above ground with short radial system, or radial system above ground, is a vertical dipole, not relying on ground. The radiation in vertical direction (elevation up to 90 degrees) is affected by nearby ground. Without serious grounding or a radial screen you will not have a ground wave, not at all a problem, but your elevation of the radiation will be higher above the horizon. For serious DX this is a disadvantage.
As long as you can match an antenna with less radials it is very well usable and not that world of difference. Depending on the method of feeding (tap on coil or inductive coupling) it is very well possible that the coax screen will conduct an RF voltage to the tuner or even up to your shack.