Math With Mr DJ

Grade 8 · The Number System · 8.NS.A.2

Locating Irrational Numbers Worksheets

Free, printable, and ready to teach: a practice worksheet, homework, an exit ticket, and an answer key with step-by-step solutions — plus lesson slides you can edit. No sign-up needed.

First page of the locating irrational numbers practice worksheet Open the practice worksheet

Download free

PDFs print on US Letter paper. Free for classroom and home use.

Watch: Simplifying Square Roots — Step by Step Guide
Key idea

25 < 30 < 36, so 5 < √30 < 6. To compare, square both sides.

Sample problems

  1. List the perfect squares from 1 to 100.
  2. Bracket √12 and √40 between consecutive whole numbers.
  3. Which is bigger, √20 or 4.5? Show your working.
  4. Is √30 nearer 5 or nearer 6? Justify it without a calculator.

Common mistakes to watch for

  • Answered between 25 and 26 by halving, or gave 7 and 8 with no squares shown — the squares are what makes it a method rather than a recollection.
  • Chose √2 because the root sign looks like it should be larger, or compared decimals from memory without squaring. Squaring is the reliable move and the one being assessed.
  • Answered nearer 2, splitting the gap evenly. The squares are not evenly spaced, so the midpoint of the bracket is not the midpoint of the numbers.

The answer key explains each one, so you can tell what a wrong answer means.

How to use this set

  1. Teach with the slides (about 15 minutes), or watch the video together.
  2. Practice with the worksheet. Questions climb from fluency to application to reasoning.
  3. Check understanding with the exit ticket, and send the homework home.
  4. Mark with the answer key — each answer shows the steps and the most likely mistake.

More Grade 8 worksheets

All Grade 8 →
Rational and Irrational Numbers8.NS.A.1 · Practice · Homework · Exit ticket · Answer key · SlidesInteger Exponents8.EE.A.1 · Practice · Homework · Exit ticket · Answer key · SlidesSquare and Cube Roots8.EE.A.2 · Practice · Homework · Exit ticket · Answer key · Slides▶ Video lessonScientific Notation8.EE.A.3 · Practice · Homework · Exit ticket · Answer key · SlidesSlope as a Unit Rate8.EE.B.5 · Practice · Homework · Exit ticket · Answer key · SlidesWhy Slope Is Constant8.EE.B.6 · Practice · Homework · Exit ticket · Answer key · Slides
Daily math puzzlesThree new puzzles every day, mild to spicy. Great as a warm-up. Step-by-step videosFree math lessons on YouTube from Mr DJ.

Get new worksheets first

New worksheets, videos, and free resources from Mr DJ — about once a month. No spam, ever.