Let's say you had the two numbers 12 and 3. They multiply to 12*3 = 36. Applying the square root leads to sqrt(36) = 6.
Therefore, the geometric mean of 12 and 3 is 6.
In general, the geometric mean between two numbers x and y is sqrt(x*y). You multiply first, then apply the square root.
If you are working with 3 numbers, you multiply them out like before, but you instead apply the cube root. With 4 numbers you multiply like normal, but this time you would use a fourth root, and so on. With n numbers, you'll apply the nth root.