Depends on the tree and the timing. You can be very drastic with both root and tree pruning on deciduous trees just before they break dormancy. Bare-rooting these and pruning back severly is usually quite safe. Evergreens or trees not in dormancy require much more care and much less pruning. Rule of thumb is if you take a third of the foliage take a third of the root mass.

I'll admit that personally it's a feel thing. I've killed my share to aquire the feel but that's what I go on now. I recently found I had lots of great feeder roots very close in on a spruce. I felt it was safe to remove all the long roots and got it in a pot much smaller than I thought I would the first year in training. It's a mame so I felt good about that. I've had pleanty of other trees however that only had feeders at the end of long root runs it seemed. Namely my new pines and junipers always seem to come that way. Those got a very light and selective root-pruning and take several years to down size into apropriate sized pots.

If you don't have a lot of fine roots close in to the trunk you may wish to cut only one or two of the long roots back at a time(depending upon how many long roots there are). The long roots will continue to feed the plant while the one--or ones--you cut will start to branch close in. When you repot again you can take off another long root or two. This way you can cut the individual roots way back and the plant will still have a lot of healthy feeder roots.
Turtle.

Neal,

It's a good question.

I find on Bonsai I buy, that the untouched soil near the trunk ends up going very hard in which no roots can grow. I always blast off all the soil with a hose when I'm repotting. It seems harsh at the time, but the tree will grow much healthier throughout the following season

Advanced root pruning is a subject that requires a lot more space than we have here. For example, this is me holding a large trident maple prepared for repotting. You can see the gray areas under the trunk which are wounds that we shaved down to make the rootball thinner and covered with cut paste. Notice how little large root and how much feeder root we have left.
{{gwi:6756}}

I have other photos of repotting showing rootwork, but they seem to large to post here.

Good luck!
Chris

Here is a link that might be useful: Japanese Black Pine repotting

Chris- The Coastal Redwood that I pruned back has nowhere near the thick root pad that your Trident has. It has a couple large thick roots that I have pruned back lightly to ensure that I do not remove too much sustaining root mass at one time. The amount of fine feeder roots that have grown out has astounded me but I still think that I have a few years left of work on them before I get a full healthy root mass like that. Once I do then I will begin work on styling the tree. Thanks for your comments and photo.

For what it's worth, I wouldn't use trident as an example of typical root pruning. They can take an extraordinary amount of root removal with no problem. Dramatic root reduction (up to 90 percent) is almost necessary with them, as they grow like weeds and push themselves out of pots in a growing season. Taking off the same amount of root from a pine, or a beech, or some hornbeams could kill them. They are not as quick to regenerate root tissue.

The amount of root removed at repotting is a kind of learned, species to species and even individual to individual thing. In repotting, you're walking a line between taking enough roots to make the tree look good in a pot, while also trying not to take enough to kill the tree.

Did you notice the article showing the repotting of the Japanese black pine?

Chris