The geometric mean of 3 and 48 is 12. Option (a) 12 is the correct answer, as it corresponds to the square root of the product of these two numbers.
Thus, the correct option is A.
The geometric mean of two numbers is the square root of their product. For the numbers 3 and 48, their product is 144 (3 * 48). The square root of 144 is 12. Therefore, the geometric mean of 3 and 48 is 12.
Now, let's evaluate the options
a) 12: This is the correct answer, as calculated above.
b) 25.5: This is not the geometric mean of 3 and 48.
c) square root 51: The square root of 51 is approximately 7.141, which is not the geometric mean of 3 and 48.
d) 22.5: This is not the geometric mean of 3 and 48.
In conclusion, option (a) 12 is the correct answer, as it corresponds to the geometric mean of 3 and 48. The other options do not represent the geometric mean of these two numbers.
So, the correct option is A: 12.