Q1. Consider the set . Identify which of its elements are irrational numbers.

Background

Topic: Rational and Irrational Numbers

This question tests your understanding of the difference between rational and irrational numbers, and your ability to classify numbers accordingly.

Key Terms and Concepts:

• Rational Numbers: Numbers that can be expressed as a fraction where and are integers and .

• Irrational Numbers: Numbers that cannot be written as a simple fraction. Their decimal expansions are non-terminating and non-repeating (e.g., , ).

• Examples: is irrational if is not a perfect square; is always irrational.

Step-by-Step Guidance

1. Examine each element in the set and determine if it can be written as a fraction of two integers (rational) or not (irrational).

2. For numbers like , , , $0, and $11$, check if they are integers or fractions of integers.

3. For , consider whether 24 is a perfect square. If not, $\sqrt{24}$ is irrational.

4. For , recall that multiplying a rational number by an irrational number (like ) results in an irrational number.

5. List out which numbers from the set are irrational based on your analysis above, but do not select the final answer yet.

Try solving on your own before revealing the answer!