At what stage do you want to do this?

I did the radishes today and plan to do the beetroot tomorrow carrots too small to move as yet.

Welcome, Dredlocks!
Sorry to bear bad news, but it's hard to do, in my experience, without stunting or distorting the roots. Radishes are the most forgiving, but also the least likely to need starting in pots.

Radishes take a very short time to grow. Sow where you want them to grow and be harvest. Neither beetroot nor carrots will take kindly to being transplanted.

Carrots in particular produce a long tap root, once this is disturbed they will branch instead of growing one root - hence they are grown commercially on light, sandy soil to encourage the long single root to develop. In addition any moving of carrots will only attract the dreaded carrot rot fly.

In spite of being more or less round beetroot also have a tap root and again are not at al happy to be transplanted.

With al roots the rule is to sow where they will grow and thin out as the plants grow - being careful to think no a windy day for carrots to, hopefully, deter the root fly.