There are a couple of things you can do to improve rooting and balance during your Tai Chi training.
One of those things is the practice of "Hugging the Tree" posture. This practice will increase rootedness and balance both in life and in your Tai Chi Practice.
First, stand with feet shoulder width apart. Relax your shoulders and sink. That means bend your knees one or two inches if you are a beginner at this type of training. Your body position should be similar to that of somebody who is about to sit on a bar stool. Your knees should be bent in such a way that, if you look over any of your knees, you should be able to see the tip of your big toe. Your neck and shoulder muscles shoud be relaxed. Your arms should be in the shape of the arms of somebody who is about to hug somebody else, or just imagine you are hugging a wide tree trunk. Your body weight should be distributed evenly between your legs concentrating the bulk of it on the center point right behind the ball of your feet. This point is known in the practice of Chi Gung as the "Bubbling Spring."
If you are a beginner, you will hold this posture for one minute trying to increase your time every day. A good Tai Chi Practitioner will hold this posture for a Solid Hour!!!
This exercise will increase the strenght of your legs and arms muscles, joints and tendons around ankles, knees, hips, shoulder, elbows, wrists, and fingers. You will increase your ability to withstand a push (rooting), and your balance, specially during form performance, will be solid!
Ush! Chen! Sifu Pedro