The correct answer is (a) 8.
A perfect square is a number that can be obtained by squaring an integer. For example, 16 is a perfect square because it is equal to $4^2$.
To find the last number that must be added to 7912 to make it a perfect square, we can start by finding the square root of 7912. The square root of 7912 is approximately 88.83. This means that 7912 is very close to $88.83^2$, which is 7793.24.
To make 7912 a perfect square, we need to add a number that is close to 7793.24 – 7912 = -120.76. The only answer choice that is close to -120.76 is 8.
Therefore, the last number that must be added to 7912 to make it a perfect square is 8.
Here is a brief explanation of each option:
(a) 8: This is the correct answer. 8 is the only answer choice that is close to -120.76, which is the difference between 7793.24 and 7912.
(b) 9: 9 is not close to -120.76. Therefore, it is not the correct answer.
(c) 12: 12 is not close to -120.76. Therefore, it is not the correct answer.
(d) 16: 16 is not close to -120.76. Therefore, it is not the correct answer.