I bet you have a heavy clay soil. Working organics (grass clippings, leaves, shredded news print, veg. scrapes, etc) or mulch into the soil over time will improve the soil so you can grow root crops.

I bet you should have a soil test. Every year, I take a soil sample to my county agricultural agent and get it tested for a small fee. I get a report that includes recommendations for soil improvement and PH adjustment techniques, and fertilizer needed for planting and side-dressing the garden this year.

Overall, I think I save money by not applying fertilizer when none is needed. Also, if I followed suggestions often made here from other users, I could be led to do exactly the wrong thing.

For example, many here seem to always suggest NPK fertilizer in the same ratio to everyone. My soil naturally has enough K (potassium) for the rest of my life, and if I add any more, I will only reduce production.

Likewise, many (apparently from the eastern US) will encourage anyone and everyone to apply additives to increase the PH of their acidic soil. My soil, and our groundwater has a natural PH of about 8.6 or 8.7. My soil test report tells me how much sulfur to add to bring the PH down to an acceptable level.

My neighbor cuts his soil with sand. It seems to work, but I still prefer compost and other goodies.

I have found the same problem in my garden down here in Georgia. I tilled some fresh manure in the soil and it seemed to soften it up a bit for them to grow.

Zgardennut, what problems are you seeing? Stunted roots, malformed roots, yellow leaves, not a lot of leaves... etc.? How far apart are you growing them (for each type ~ ie how far apart turnips, how far apart carrots, etc.)?

While we're at it, what's your soil like (clay, sand, rocky, lots of organic matter or not, raised bed or not, etc.)? And what are you fertilizing with and how much?

Having this info will greatly help us figure out how to help you.