MyMathKidK-8 Curriculum

Grade 8 Irrational Numbers Worksheets

Master irrational numbers step by step, from basic concepts to advanced problem solving

Common Core: 8.NS

Watch & Learn

Learning Path

Start with Lesson 1 and work your way through!

1

Rational vs Irrational

Easy

Classify numbers as rational or irrational

Define irrational numbersClassify numbers
2

Approximating Irrationals

Easy

Estimate irrational numbers

Estimate square rootsRound to decimal places
3

Comparing Numbers

Easy

Compare rational and irrational numbers

Compare different formsOrder numbers
4

Number Line

Easy

Place irrationals on a number line

Locate irrationalsUnderstand density
5

Unit Review

Easy

Review all irrational number concepts

Review all conceptsPrepare for assessment

How to solve Grade 8 irrational numbers problems

Real problems from these worksheets, solved one step at a time — the same explanations your child sees when practicing online.

  1. Example 1

    Write the repeating decimal 0.484848… (the 48 repeats) as a fraction in simplest form.

    1. Let x = 0.484848…; the block "48" has 2 digits, so multiply by 100: 100x = 48.4848…
    2. Subtract x from 100x — the repeating parts cancel: 100x − x = 48.4848… − 0.4848…, so 99x = 48.
    3. Divide by 99: x = 48/99.
    4. Simplify by dividing the top and bottom by 3: 48/99 = 16/33.
    5. So 0.484848… = 16/33.

    Answer: 16/33

  2. Example 2

    Which number is the greatest? Choices: √27 · √30 · √34 · 4.2

    1. Write each number as a decimal so they are easy to compare: √27 ≈ 5.20, √30 ≈ 5.48, √34 ≈ 5.83, 4.2.
    2. From least to greatest: 4.2 < √27 < √30 < √34.
    3. The greatest is √34.

    Answer: √34

  3. Example 3

    How many of these numbers are irrational? √82 · 7/10 · √144 · 7.25 · √13

    1. A rational number can be written as a fraction of two integers; its decimal ends or repeats. An irrational number cannot — its decimal goes on forever without repeating.
    2. 82 is not a perfect square (9² = 81, 10² = 100), so √82 is irrational.
    3. 7/10 is a fraction of two integers — rational.
    4. √144 = 12 (12 × 12 = 144) — rational.
    5. 7.25 is a decimal that ends — rational.
    6. 13 is not a perfect square (3² = 9, 4² = 16), so √13 is irrational.
    7. The irrational ones are √82, √13 — that is 2 numbers.

    Answer: 2

Frequently Asked Questions

Are these Grade 8 Irrational Numbers worksheets free?
All printable Irrational Numbers worksheets on MyMathKid are free to download and print. Answer keys are a premium feature available with a subscription.
How many Irrational Numbers worksheets are available for Grade 8?
There are 5 progressive Irrational Numbers lessons with worksheets for Grade 8, covering skills from foundational concepts to advanced problem solving.
Are these Irrational Numbers worksheets aligned to Common Core?
Yes — Grade 8 Irrational Numbers aligns with Common Core 8.NS (The Number System).
What will my child practice with these Irrational Numbers worksheets?
Your child will practice: Rational vs Irrational, Approximating Irrationals, Comparing Numbers, Number Line, and more.