We have a very large, healthy river birch. The problem is that some of the roots are pushing up brick in our patio. Is it acceptable to cut out a few roots to solve this problem? These roots are approximately 15 feet away from the base of the tree. Thanks.

Cutting the roots of trees will most likely result in damage to the topgrowth. Root damage also provides an opportunity for disease causing fungi and bacteria to invade the tree leading to the tree's demise. That said, it sounds like your choice is between the tree and your patio.