Digging fence post holes is not a fun job, and it is worse when there is a root directly in the path of a post. Post hole diggers are not capable of cutting through large roots, and it is time consuming to try and chop the root out by hand. The most effective method of installing a post through a root is to drill through it. There is a power tool available known as an auger that will drill through the root, and allow you to put the post right where you need it.
Dig the post hole with a post hole digger, or a spade approximately six inches deep before using the auger. Digging a starter hole will create a stable spot to set the drill tip into while you are starting the auger.
Ask for help before using the auger to drill through the tree root. An auger resembles a large drill, but it is heavy, and it will throw you when it hits the root.
Stand on one side of the auger, and ask the helper to stand on the other side of the auger. Place the tip of the auger drill bit into the pre-dug hole.
Ask the helper to grasp the handles and hold the auger steady while you start it. A gas-powered auger has two handles located on each side of the motor. Start the motor of the auger according to the manufacturer's instructions. The starting instructions will be clearly written on the top of the auger. Grasp the handles on the opposite side of the auger. You should be standing on one side of the auger, while your helper is standing on the other. Both of you should be holding onto the handles.
Keep the auger in an upright position while the auger bit is spinning, and do not let go of the auger while it is drilling. It will not take long for the bit to connect with the root. Hold the auger steady and with a firm grip until the auger has cut through the tree root.