Worksheets · Algebra 1

Algebra 1 classifying real numbers worksheet

The sets nest: every natural number is whole, every whole number is an integer, every integer is rational. The most specific name is the innermost one that fits. A number is irrational when it cannot be written as a fraction of integers, and a square root is rational only when the number under it is a perfect square.

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Pick more than one for a sheet that mixes them.

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Classifying Real Numbers

Date Period

Name the most specific set each number belongs to: natural, whole, integer, rational or irrational. For a root, say whether it is rational.

  1. 144
  2. Is 114 rational or irrational?
  3. 139
  4. Is 16 rational or irrational?
  5. 20
  6. Is 81 rational or irrational?
  7. 2
  8. Is 169 rational or irrational?
  9. 27
  10. Is 304 rational or irrational?
  11. 34
  12. Is 63 rational or irrational?
  13. 7
  14. Is 231 rational or irrational?
  15. 25
  16. Is 97 rational or irrational?
  17. 94
  18. Is 370 rational or irrational?
  19. 9.33
  20. Is 4 rational or irrational?

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Classifying Real NumbersAnswer keyVersion 1

Date Period

Name the most specific set each number belongs to: natural, whole, integer, rational or irrational. For a root, say whether it is rational.

  1. 144Natural
  2. Is 114 rational or irrational?Irrational
  3. 139Rational
  4. Is 16 rational or irrational?Rational, 16=4
  5. 20Natural
  6. Is 81 rational or irrational?Rational, 81=9
  7. 2Natural
  8. Is 169 rational or irrational?Rational, 169=13
  9. 27Natural
  10. Is 304 rational or irrational?Irrational
  11. 34Rational
  12. Is 63 rational or irrational?Irrational
  13. 7Integer
  14. Is 231 rational or irrational?Irrational
  15. 25Natural
  16. Is 97 rational or irrational?Irrational
  17. 94Rational
  18. Is 370 rational or irrational?Irrational
  19. 9.33Rational
  20. Is 4 rational or irrational?Rational, 4=2

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

How to do these

25

  1. The root of 25 is 5, so this is -5.
  2. -5 is an integer, and not whole or natural, because it is negative.

The answer is Integer.

Where students go wrong

Calling every root irrational. The root of 25 is 5, a perfectly good natural number; only roots of non-squares are irrational.

Also called number sets, rational and irrational numbers, real number system or classifying numbers.

What you can put on this worksheet

The most specific set
4 Integer
Is the square root rational
Is 57 rational or irrational? Irrational

Questions about these worksheets

Yes. Every classifying real numbers sheet is free to print and free to download as a PDF. There is no account to make, no email to hand over and no limit on how many you take.

Yes. The answer key prints on a second page, and you can choose whether it shows each question beside its answer or just the answers in a list.

Yes. Print straight from the page, or download the PDF and print that. The sheet is laid out for paper rather than squeezed off a screen, so there is room to work under each question, and the answer key comes out on its own page.

Algebra 1 is usually taken around 8th or 9th grade, though schools vary and plenty of students meet it earlier or later. Pick the difficulty rather than the grade: the easy level suits a first lesson on it, the hard level suits review before a test.

Yes, as many as you like. The questions are built fresh each time rather than picked from a fixed set of files, so pressing Generate gives a new sheet. That is what you want for a second class, a retake, or two students sitting next to each other.

That is the closest comparison, and Kuta Software is good software. It is also paid software you install on a computer. These worksheets run in a browser tab for free, with no account and nothing to install. Like Kuta, the classifying real numbers questions are generated when you ask for them rather than pulled from a fixed set of files, so two classes never get the same sheet, and the answer key comes with it.

Yes. There are three levels, and you can tick more than one for a sheet that mixes them, in which case the questions come out easiest first. The harder levels are not just larger numbers: they ask for something the easy ones do not.

You pick from 2: the most specific set and is the square root rational. Tick as many as you want and set how many of each, or let it spread them evenly.

Calling every root irrational. The root of 25 is 5, a perfectly good natural number; only roots of non-squares are irrational.