The image you've uploaded appears to be a multiple-choice question asking you to classify each number as either a rational or irrational number. Let's go through each expression one by one:

1. 2.75:

   • Rational or Irrational?
   • Answer: Rational.
     • Reason: This is a terminating decimal, which can be expressed as a fraction (e.g., $\frac{11}{4}$).

2. $-\frac{7}{2}$:

   • Rational or Irrational?
   • Answer: Rational.
     • Reason: This is already a fraction of two integers.

3. $\sqrt{16}$:

   • Rational or Irrational?
   • Answer: Rational.
     • Reason: The square root of 16 is 4, which is an integer.

4. $\sqrt{20}$:

   • Rational or Irrational?
   • Answer: Irrational.
     • Reason: $\sqrt{20}$ simplifies to $2\sqrt{5}$, and $\sqrt{5}$ is an irrational number.

5. $\sqrt[3]{8}$:

   • Rational or Irrational?
   • Answer: Rational.
     • Reason: The cube root of 8 is 2, which is an integer.

Based on these explanations, you should now be able to correctly identify each number as rational or irrational.

Would you like any more details or have further questions?

Here are 5 related questions that can expand your understanding:

1. What are the key characteristics that differentiate rational numbers from irrational numbers?
2. Can a repeating decimal be considered a rational number?
3. How can you prove whether a square root is rational or irrational?
4. What happens when you multiply a rational number with an irrational number?
5. How can cube roots be simplified to determine if they are rational or irrational?

Tip: Always remember that any number that can be expressed as a fraction of two integers is a rational number, while numbers that cannot be expressed as such, especially non-repeating, non-terminating decimals, are irrational.