About how long does it take for teeth roots to straighten?

It depends on the bracket system being utilized. With conventional braces and round archwires the crowns of teeth move into place in roughly a year average time and then another year for the roots to move into place.There is a newer system (called Fastbraces) with triangular brackets and square archwires that move the crown of the teeth and the roots at the same time. The treatment time is therefore half as long or less (triangular bracket design also moves teeth faster than square brackets).Good luck!