This image contains a question asking the user to select all the irrational numbers. Let’s analyze the options provided:

1. 1.5 - This is a rational number because it can be expressed as the fraction $\frac{3}{2}$.

2. $\sqrt{3}$ - This is an irrational number because the square root of 3 cannot be expressed as a fraction, and its decimal expansion is non-terminating and non-repeating.

3. $3\sqrt{2}$ - This is also an irrational number because it involves the product of a rational number (3) and an irrational number ($\sqrt{2}$), which results in an irrational number.

4. $\pi$ - This is an irrational number. Its decimal expansion is non-terminating and non-repeating.

5. $\frac{1}{9}$ - This is a rational number because it can be expressed as a fraction.

Correct Selection:

• $\sqrt{3}$
• $3\sqrt{2}$
• $\pi$

Would you like me to provide further explanations or a deeper dive into the concept of irrational numbers?

Here are 5 related questions to explore further:

1. What is the formal definition of an irrational number?
2. How can you determine if the square root of a number is irrational?
3. Are all non-repeating decimals considered irrational numbers?
4. Can the product of two irrational numbers be rational? Provide an example.
5. Why is $\pi$ classified as irrational, and how was this determined?

Tip: An irrational number is not just non-terminating but must also be non-repeating in its decimal form!