Q.Crape myrtle tap root
I went to repot a crape myrtle and found the main root has gone into a crack in cement. Can I cut this root without killing the tree?

The Crepe Myrtle does not really send down deep roots. You can cut this root with likely no issue or stress to the tree.
Repotting into a larger container sounds like the best plant!
https://www.gardeningknowhow.com/ornamental/trees/crepe-myrtle/tips-to-grow-crepe-myrtles-in-containers.htm
https://www.gardeningknowhow.com/ornamental/trees/crepe-myrtle/crepe-myrtle-root-system.htm