Gisette has done some great radishes, I don't want to copy her completely so have done it a little differently.
I'm growing mine in a mixture of perlite and vermiculite, ratio mix of 3:1 The pot stands in a constant container of water, the water will be sucked up by the per/ver mix which will keep the radishes watered, see here for more details on how to grow using this method.
The seeds are a popular variety, French Breakfast 3 from Thompson & Morgan. They take 30 days to crop.
Weekly Pictures
Looking forward to this! It's funny, how some seedlings have such bright red stems, and some are green, huh?
It can't be worse than the carrots?
They're still potted, I've not had a look yet...
Eh, they're brassicas. They do fine in growrocks, they should love perlite. 
Park Seed's weekly Know-before-you-grow newsletter features root veggies this week. Though radishes look like a stem veggie, not a root... Same diff.
Nice.
It's funny how far they go with those seed leaves, huh?
Week 3
What a difference a week makes, the plants now look sickly and pale (not shown too much on the picture)... In desperation I fed them some Miracle Grow I used to use in the pre-hydro days. My new grow light is up and they are now under this instead of the AG, only time will tell.
The green algae is new, it's from the Miracle Grow, it's loving the light!
Quote from post 3 "It can't be worse than the carrots?" 
Gisette, I marvel at your radishes - tell me the secret. Or tell me to stick to water in future. 
Persnickety aren't they? 
Mm, compared to mine, yours look like they've been stretching. Need more light. The falling-over thing, though, mine do, too. Shortly before splitting their stems.
I googled around about that, and saw claims that it was due to uneven watering. But I suspect its uneven growth from all possible causes (maybe water, maybe light, maybe cold or heat...)
My latest aren't doing too well. Their 25 days are up, and not a one is ready to eat. They got evicted from the heat mat this time around, in favor of summer flower seedlings. Not your problem, of course - I'm sure your kitchen is much warmer than my garage.
The problem may be with the AG bulbs, I've been running mine for 10 months now without being changed - hopefully the new CFL will sort things out...
I'll should really get round to ordering some more bulbs.
LOL! Well, having the same bulbs for 10 months must have seemed such a major improvement! 
125 watts of new CFL light in the kitchen now, I need
before I venture in there.
Oh, plus 4 ten month old 25w AG ones, heck, 225w! Pass the sun cream. 






Week 0 - Starting Week
Plastic cling film placed over the pot to aid germination, all the light will be provided by the AeroGarden.
Week 1
One week into the grow, seedlings have been thinned out - doing well so far.