8th Grade Math Worksheet: Approximating Irrational Numbers (Square Roots & Pi)

Aligned to CCSS 8.NS.A.2

This no-prep 8th grade math worksheet is designed to help students develop a strong understanding of approximating irrational numbers through decimal expansions. Students will practice estimating square roots, working with pi, and using rational numbers to approximate irrational values, all aligned to key middle school standards.

This resource fits seamlessly into Chapter 1: Rational and Irrational Numbers and is ideal for classwork, homework, review, or assessment.

What’s Included:

• Warm-Up section with key vocabulary and pre-requisite skills
• 6 structured parts (A–F) that build understanding progressively
• A variety of problems focused on:
• Bounding irrational numbers between integers
• Approximating square roots to tenths and hundredths
• Truncating vs. rounding decimal expansions
• Comparing and ordering irrational numbers
• Estimating expressions involving square roots and pi

• Complete Answer Key

Detailed Worksheet Breakdown:

Warm-Up

• Key terms with definitions
• Pre-requisite skill review (perfect squares, rational vs. irrational numbers)

Part A: Bounding Irrational Numbers

• Identify consecutive integers between which square roots fall

Part B: Decimal Approximations

• Determine tenths and hundredths bounds for irrational numbers

Part C: Truncating and Rounding

• Practice truncating and rounding square roots and pi

Part D: Comparing Irrational Numbers

• Use inequalities to compare values

Part E: Ordering Numbers

• Order rational and irrational numbers from least to greatest

Part F: Estimating Values

• Evaluate expressions involving square roots and pi
  

Skills Covered:

• Approximating irrational numbers using rational numbers
• Estimating square roots between integers
• Understanding non-terminating, non-repeating decimals
• Rounding and truncating decimal expansions
• Comparing and ordering irrational numbers
• Evaluating expressions with square roots and pi

Standards Alignment:

CCSS 8.NS.A.2
Understand that irrational numbers have non-terminating, non-repeating decimal expansions, and approximate them by rational numbers.

Why Teachers Choose This Resource:

• No prep required
• 100% editable to fit your classroom needs
• Clear progression from basic to more advanced problems
• Supports both practice and assessment
• Includes a complete answer key for easy grading
  

Ideal For:

• 8th Grade Math
• Algebra Readiness
• Homework and Independent Practice
• Test Prep and Review
• Sub Plans or Math Centers
  

This worksheet provides meaningful, standards-aligned practice that helps students confidently work with irrational numbers, square roots, and decimal approximations while saving teachers valuable planning time.