Hi...I just put a bunch of rooted cuttings out in the sun.  All have pretty good root growth and most have green growth up top.  They are all in clear plastic containers.  My question is....will the sun burn the roots?  should I protect the roots from the sun?

Thanks :)

You need to protect both the roots and top. Neither will take full sun for more than a few minutes. Set them in the shade and even there I'd protect the top to some extent.

It is the heat that does the roots in.  The clear plastic container will allow the root zone to get hotter (and very quickly into the danger zone) than an opaque container.

So when is it safe to put them in the sun?

When they are are ready you have to introduce them to the sun gradually or you will burn the leaves, it is called "hardening off".  If you have a spot where they will get dappled morning sun that is ideal.  You can then every few days move them out so they get more and more sun.  You don't want to let those clear cups get sun at all.  If they have no leaves or just buds they can have sun and the leaves that open will already be hardened off.  

Hi hicrystalfan,
It all depends on the size of the cup, the amount of warm and the amount of sunlight.
So if you are full sun in the desert, well ok, they'll last 30 minutes and you can toss them.

If the warmth is mild 15°c/20°c they should be able to take it except for the weakest.
Clear cups should be shaded for young roots don't like light.

Depending on your climate zone, you can do it, but start first with a shaded spot, and progressively move them to more light.
You should check on each day's conditions, as in a cloudy day, you could set them "Full sun", but on a bright day, I would keep them half shaded.

Because of gnats, I've been putting for a week 3 pots of rooted cuttings on the outside windowsill for the day - in the evening I bring them in as we still get 4°c in the night and that would be bad for the trees.