MAKE IT YOURS

A world for every learner

Choose a grade to discover its colours and creative world.

Grade 8 Rational & Irrational Numbers Worksheet with Answers

Grade 8 (US) · Year 9 (UK) · Class 8 (India) · Math

Unit 1: Real Numbers & ExponentsRational & Irrational NumbersCCSS 8.NS.A.1

Telling rational and irrational numbers apart and estimating irrational numbers like √30. This free middle school worksheet has 12 questions and a full answer key. Print it or save it as a PDF — every answer is checked by code, not guessed.

Save to PinterestJump to answer key
  • Answer keys checked by code
  • No ads, ever
  • No student accounts needed
  • Safety & privacy
Practice Sheetaethelsystems.com

Rational & Irrational Numbers

Grade 8 · Math

Score___ / 12

Name

Class

Date

Learning goal: Rational & Irrational Numbers · CCSS 8.NS.A.1

Directions: Solve each problem. Show your work, then write your answer in the box.

Example

Is -39 rational or irrational?

Answer: rational

RememberNumber sets, squares and roots

Real numbersRational: −2, ½, 0.75Integers: −3, 0, 4Whole: 0, 1, 2Irrational√2, πnever ends,never repeatsPerfect squares:1, 4, 9, 16, 25, 36, 49, 64, 81, 100Perfect cubes:1, 8, 27, 64, 125√50 = √(25 × 2) = 5√2
  1. 1

    Is √2 rational or irrational?

    RationalIrrational
  2. 2

    Estimate √83 to the nearest whole number.

    Answer
  3. 3

    Estimate √116 to the nearest whole number.

    Answer
  4. 4

    Is 0.333... (the 3 repeats forever) rational or irrational?

    RationalIrrational
  5. 5

    Is -21 rational or irrational?

    RationalIrrational
  6. 6

    Estimate √52 to the nearest whole number.

    Answer
  7. 7

    Is -32 rational or irrational?

    RationalIrrational
  8. 8

    Estimate √62 to the nearest whole number.

    Answer
  9. 9

    Is 0.431 rational or irrational?

    RationalIrrational
  10. 10

    Is 0.1010010001... (the pattern never repeats) rational or irrational?

    RationalIrrational
  11. 11

    Estimate √50 to the nearest whole number.

    Answer
  12. 12

    Estimate √126 to the nearest whole number.

    Answer

★ Challenge corner for fast finishers

Each scale balances. Scale 1: circle + square = 8; scale 2: square + triangle = 11; scale 3: circle + circle = 4. What is one triangle worth?

8Scale 111Scale 24Scale 3

How did I do?

Teacher's comments

Free printable worksheets with answer keys · aethelsystems.com/worksheets/math/8/irrational_numbers

Answer key (click to show)
  1. 1.irrational
  2. 2.9
  3. 3.11
  4. 4.rational
  5. 5.rational
  6. 6.7
  7. 7.rational
  8. 8.8
  9. 9.rational
  10. 10.irrational
  11. 11.7
  12. 12.11
  13. ★5 (challenge corner)

Need another Rational & Irrational Numbers worksheet?

Generate unlimited fresh versions at easy, medium or hard difficulty, each with its own answer key. Free during our launch — no card needed.

Create a free account

How to use this worksheet

  • Works well as a bell-ringer, exit ticket, homework set or quick quiz.
  • Have students self-check with the answer key, then correct their own mistakes before you review.
  • Generate a new version of the same topic for a re-test, so students can't just memorise the answers.

Related worksheets

More Grade 8 Math worksheets

Grade 8 Square & Cube RootsGrade 8 ExponentsGrade 8 Scientific NotationGrade 8 Linear EquationsGrade 8 Equations with Variables on Both SidesGrade 8 Systems of EquationsGrade 8 Introduction to FunctionsGrade 8 Proportions

Guides for teaching Rational & Irrational Numbers

What Are the Common Core and NGSS Standards? A Parent's GuideWhat learning standards are, how to read a code like 3.NF.A.1 or MS-PS1-2, what each grade covers in Math, English and Science, and how to use them at home.

Can't find what you need? Tell us which worksheet to make next.

Frequently asked questions

Does this Grade 8 Rational & Irrational Numbers worksheet come with answers?

Yes. The full answer key is on this page, and it prints on its own page after the questions. Every answer is calculated or checked by code rather than written by an AI model, so the key is always correct.

How do I print it or save it as a PDF?

Click "Download PDF" to save a ready-to-print PDF with the answer key on the last page, or click "Print" to send the worksheet and answer key straight to your printer.

Can I get a different Rational & Irrational Numbers worksheet?

Yes. Create a free account to generate as many fresh Grade 8 Rational & Irrational Numbers worksheets as you like, at easy, medium or hard difficulty, each with its own answer key.

Is this worksheet free?

Yes. This worksheet is free to print, and Practice Sheet is free to use during our launch with no card needed.