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

Background

Topic: Real Numbers – 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 Formulas

• Rational Numbers: Numbers that can be written 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. Review each element in the set and determine if it can be written as a fraction of two integers (rational) or not (irrational).

2. Check the numbers involving square roots and carefully. For example, is not a perfect square, and is a multiple of an irrational number.

3. For each element, ask: Can this number be written as with integers and ? If not, it is irrational.

4. List the elements that are irrational, but do not select the final answer yet. Review the answer choices to see which one matches your list.

Try solving on your own before revealing the answer!