Key idea An inversion keeps the same three chord notes but changes which is lowest. Root position: root at the bottom. First inversion: the third at the bottom. Second inversion: the fifth at the bottom.
To find the root of an inversion, rearrange the notes into stacked thirds. The bottom note of that stack is the root. For E-G-C, move C down to get C-E-G: the root is C.
Why inversions matter
Playing C, F, and G all in root position makes the right hand jump around. With inversions, fingers move only a key or two, which sounds smoother and is much easier.
All root position
Using inversions
Press C in first inversion: E at the bottom.
Press F in second inversion starting on middle C.
Quick check
Question 1/5E G C is which position of the C chord?