Okay, I'm guessing because guessing is fun.
Second one looks very weedish to me.
First one looks brassica-ish -- like turnip or as you mentioned radish. Test: taste the leaves. If they are mild, it's turnip (baby ones good in salad, cooked larger ones terrific while weather still cool. Don't know your zone.) If they're very peppery, radish. Also, taste the root! Turnip is milder.

What do I get if I guessed right? :)

First one looks like a radish to me big time!

Second one is less clear to me. It looks minty or something though. Have you ripped open a leaf and smelled it?

1st looks like turnip. 2nd may be Amaranthus, Pigweed.

not sure on the first one, kind of looks radish/turnip. The second one is "red rooted pigweed", amaranth, edible leaves and seeds, more nutritious than spinach. Can get5-6ft. tall and can drive a root 18in. into the ground.There is a lot of info on it. A google search can do it more justice than I can.

Thank you so much everyone, I really appreciate your responses. I just got back from the garden where I did have a nibble on the leaves of the first one. Not peppery at all so I'm thinking that perhaps it is a turnip.
I'm in Chicago btw, so zone 5a.
A bit of a bummer to know the pigweed was edible, almost the entire 5x10 plot was full of it...and unfortunately now the trash can is full of it. Oh well, next time I'll know.

Elisa, you get a gold star ;) Thanks again!

sandgroper your killing me. Not in the trash can. compost, compost, compost

myluck, I know I know I know...but I live in an apartment and due to strict regulations regarding compost bins by the city, neither of the gardens that I rent plots from compost

sandgroper, now you know why I don't live by Chicago anymore. Do yourself a favor--- RUN AWAY---RUN FAST---DON'T LOOK BACK!!! Oh, also on the first picture, upper left above the radish is a tiny four leaf plant. I think it is a tiny purslane, edible, good in salads, you might let one grow and give it a try.

Yay! Very pleased with my gold star :)

But isn't pigweed an invasive? You'll probably have more popping up to taste -- but I don't think you have to feel bad about clearing it out of your plot. Of course, you DO need to feel bad about not composting it :)

Actually, my niece lives and gardens in Chicago, and I know that rats are a problem, so no compost heaps for sure. What about using the limp leaves for mulch? Or digging them under (sheet composting)? Then they'll rot in, improve your soil, and not attract Templeton and/or Reepicheep.

First one might be a radish, as others have suggested. It's hard to tell "scale" of size though.

I have some mustard plants in my garden that look a lot like that first one.

Given that this is a community garden, though, the volunteer plant would more likely be radish than mustard. Lots of people grow radishes. Mustard, not so much.

sandgroper1968 -that is just bizarre that your plots don't compost. On my allotment (community garden) composting is practically compulsory. Would 'they' be able to tell the difference between a compost heap and a pile of material you were 'waiting to put in the trash'? Oh, oops - it seems to have turned into compost before I got round to throwing it out. Or maybe bury the compost materials? Trench composting? How would 'they' ever know?

Are you allowed to dig a trench about twelve inches deep, put in your wilted plant material, cover it with a layer of earth - 2-3" deep, and a light sprinkle of blood and bone or alfalfa meal, then repeat until the trench is full and a little bit mounded? You could add some 'carbon' by way of raw sawdust or soaked plain cardboard in pieces, or similar.

Your ground needs to be free-draining for this to work without tears.

Not all compost making needs to be above ground...:-)

Thanks for the composting suggestion, folks!
flora_uk --unfortunately that wouldn't work for either of the gardens I'm with, we must keep the area around our beds weed-free and neat at all times. I have started digging my inedible leaves and roots back into the soil though and have started researching a bit more about the subject--vetivert8 --you had some great suggestion, thank you.

So......*drum roll*, I just harvested my big white mystery vegetable!!
Aaaaaaaaaaaand, I still have no clue what the heck it is.
Here are some pics though.
I sliced a piece off and it tasted dreadful :( Hopefully it improves with cooking. It weighs TWO POUNDS!

Here's another pic of my mystery monster

Pic 2

after seeing that, I think your to close to the Zion Nuke Plant

LOL :D

White lady turnip?

Looks like a dag-gummed sugar beet.

calliope, you win the Golden Tomato award!!! I checked out other pictures of sugar beets and that's exactly what it is!
Thank you.
Now what the heck does one do with a sugarbeet? :-\