Lye will "dissolve" organic matter. Copper sulfate will kill, at least temporarily, the roots. But the roots are drawn to leaking moisture from the pipe. So sealing the pipe is the real answer. Pipes can be lined while in place, not inexpensively.

go to the hardware and look for root killer. There are a number of different products. It will take a while for the wood to rot though.

Also have you tried a power snake, alot of them have root cutter blades that can be attached.

Lye and sulphuric acid both eat wood but not PVC or ABS.
The problem with using a lot of either is that the heat they can generate can softenthe pipe enough to cause ot to deform.
A root cutter on a power snake will usually do the job, but it will be back.
Once the roots enter they will continue to grow backeven qafter being cut.
There are a number of copper containing compounds that can be used to kill back roots, but roots often come in from the top if the line and the solution is not going to touch them there - it runs in the bottom of the pipe like all the waste.

Thanks, I'll try your suggestions. The root in question was from a holly foundation shrub that I tore out. There will be no more plantings in the immediate area of the pipe as I'm putting in a patio butting against the wall. So I can use some herbicides also.

Fix the problem, not the symptom of the problem. Your problem is a broken drainage pipe that is very likely leaking waste into it's surroundings, which can cause moisture problems for your home and is a health hazard as well. If the pipe weren't broken, a root couldn't infiltrate. Fix the broken pipe. I dertainly wouldn't to frequent a patio built above a broken sewage pipe!