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., , ).

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. Recall that integers (like 0, $11-2050/5$, $-3/25) are rational numbers.

3. Examine and :

   • is not a perfect square, so it is irrational.

   • is a product of a rational number and an irrational number, which is also irrational.

4. List all elements from that are irrational based on your analysis above.

Try solving on your own before revealing the answer!