The question asks which lists contain only rational numbers, and here are the groups of numbers provided:

1. 25, 36, 49, 144, 81
   All of these are perfect squares, meaning their square roots are integers. Therefore, all numbers in this list are rational.

2. √25, √36, √144, √100, √81
   These square roots evaluate to 5, 6, 12, 10, and 9, respectively. All are integers, so they are rational numbers.

3. 81/36, 64/25, 100/36, 81/49, 64/9
   Each of these fractions simplifies to a ratio of integers:

   • $81/36 = 9/4$
   • $64/25 = 64/25$ (already in simplest form)
   • $100/36 = 25/9$
   • $81/49 = 81/49$ (already in simplest form)
   • $64/9 = 64/9$ (already in simplest form)
     Since all are fractions of integers, they are all rational.

4. 0.25, 0.36, 0.9, 0.4, 0.16
   These are finite decimals, and finite decimals are always rational numbers.

5. 0.4̅, 0.36̅, 0.64̅, 0.81̅, 0.9̅
   Each of these numbers has a repeating decimal (e.g., 0.4̅ = 0.4444..., 0.36̅ = 0.363636...). Repeating decimals are also rational numbers.

Conclusion:

All five lists contain only rational numbers, and all the boxes marked are correct.

Would you like more details on any of these solutions, or do you have any further questions?

Here are some related questions:

1. What makes a number rational?
2. How can you simplify fractions to check if they are rational?
3. What is the difference between repeating and non-repeating decimals?
4. How do you determine if a square root is rational?
5. What are some examples of irrational numbers?

Tip: Rational numbers are any numbers that can be expressed as the ratio of two integers, including both finite and repeating decimals.