The greatest three-digit perfect square is 961.

To determine the greatest three-digit perfect square, we need to check the perfect squares of three-digit numbers.

Finding the perfect squares of three-digit numbers:
To find the perfect squares of three-digit numbers, we can start by finding the square root of the largest three-digit number, which is 999.

Taking the square root of 999, we get:
√999 ≈ 31.63

Since the square root of 999 is not a whole number, we can conclude that 999 is not a perfect square.

Next, we need to calculate the square root of the largest three-digit number that is less than 999, which is 961.

Taking the square root of 961, we get:
√961 = 31

Since the square root of 961 is a whole number, we can conclude that 961 is a perfect square.

Comparing the perfect squares:
Now that we have found the perfect square of 961, we can compare it to the other options given in the question.

Option a) 999: As we have already determined, 999 is not a perfect square.
Option c) 962: We can quickly see that 962 is not a perfect square as it does not end with a perfect square digit.
Option d) 970: Similarly, 970 does not end with a perfect square digit, so it is not a perfect square.

Therefore, the only option that is a perfect square is option b) 961.

Conclusion:
The greatest three-digit perfect square is 961.