How do i know if a tooth that has had root canal is cracked?( there is no pain)?

See your dentist: Best to have a dentist check it if you are concerned. Without pain, the way you might know is mobility of all or part of the tooth or a gum infection.

Examination: Your dentist can check to see if there is a crack using various methods. They are sometimes difficult to detect.

Fancy 3-D x-ray: If you can't see a crack, and it is pain free, then it probably isn't cracked. There are 3-d panorex type xRay units now that could show images of the tooth, from different angles and at different levels. If there is a fracture, these things would show it.