We're not in a good location for root vegetables. I keep running across cheerful pieces about how easy radishes, carrots, and beets are to grow. Not in the Piedmont (of the Southern US), they're not. The best-looking radishes I've seen 'locally" came from raised beds full of organic potting mix.
Turnips are an exception, and a southern favorite, but I suspect they're most productive down in the sandy Coastal Plain parts of the Southern U.S, and we favor the green tops, in any case.
Here in the Piedmont, our heavy clay soils, even greatly amended with compost and other organic matter, is still not exactly "loamy soil" - hmmm. And we have warm springs and long summers, and root vegetables are cool weather crops. There's a photo of Joan Gussow accompanying her book, This Organic Life: Confessions of an Urban Homesteader, that shows her harvesting huge fat carrots and beets in her NY garden. Hmrph, great for her (and it's a remarkable book, too).
Regardless, I was quite pleased to harvest a bunch of a short, compact variety of carrot this afternoon; they became roasted 'baby carrots' for dinner. They were quite acceptable and certainly attractive.