Irrational Numbers Worksheet

Name:

Date:

Mathematical symbols and numbers illustration

🎯 WALT: We Are Learning To identify and classify irrational numbers

Success Criteria:

✓ I can define what makes a number irrational
✓ I can distinguish between rational and irrational numbers
✓ I can approximate irrational numbers using decimals

Key Facts: Irrational numbers cannot be written as fractions and have decimal expansions that never end or repeat. Examples include √2, π, and √3.

Part 1: Multiple Choice

1. Which of the following is an irrational number?

0.5

√9

√7

3/4

2. The decimal expansion of an irrational number:

Always terminates

Never terminates and never repeats

Repeats in a pattern

Has exactly 3 decimal places

3. Which of these statements are true? (Select all that apply)

π is approximately 3.14159

√16 is irrational

√2 is irrational

All square roots are irrational

Part 2: Classification and Approximation

4. Classify each number as rational (R) or irrational (I). Write R or I in each box.

a) √25 ____ b) √15 ____ c) 0.333... ____ d) π ____ e) 7/8 ____ f) √50 ____

5. Use a calculator to find decimal approximations (to 3 decimal places):

a) √3 ≈ __________ b) √10 ≈ __________ c) √20 ≈ __________

6. Explain why √8 is irrational.

Sentence starter: √8 is irrational because...

7. Between which two consecutive whole numbers does √30 lie? Show your working.

Part 3: Extension Activities

8. Advanced: Explain why the sum of a rational number and an irrational number is always irrational.

Sentence starter: When we add a rational and irrational number, the result is irrational because...

9. Real Life Connection: Name two real-life situations where irrational numbers occur naturally.

Hint: Think about circles, architecture, or nature

10. Challenge: If you know that √2 ≈ 1.414, estimate √8 without using a calculator. Explain your method.

Sentence starter: I can find √8 by recognising that √8 = √(4×2) = ...

Differentiation Support:
• Use larger font or coloured paper if needed
• Work with a partner for discussion questions
• Use a calculator for all decimal approximations
• Focus on questions 1-7 for core understanding