How good is your root?
Some facts from the 4th edition of Arboriculture (Richard Harris, James Clark and Nelda Matheny) can make it easier to predict where roots might be:
Roots are opportunistic. There will be more roots when conditions are favorable. Fertile, moist, uncompacted soils will have more fibrous roots.
In dry, compacted soils with no organic matter, roots are fewer but larger and able to grow further distances from the plant.
Open-grown trees often have a wider root system than trees closely planted together. Some species, such as Coast redwood (Sequoia sempervirens) can root-graft with others of their kind, sharing nutrients, stabilizing each other and reducing the stress on each individual tree.
Root systems may grow wider when downward growth is restricted, such as by a high water table or perhaps bedrock.
However, roots can always surprise you, and direct inspection is always required to be sure where roots are.