Grade 8 · Math

8th grade Kinds of real numbers: rational and irrational worksheet

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Kinds of real numbers: rational and irrational

Grade 8 Math Worksheet

NameDate

Circle the best answer.

1.
Esme sorts number cards before a game. What is the smallest group that holds √81?
- irrational numbers
- rational numbers
- whole numbers
- integers
2.
Kira draws √45 from a pile of cards. What is the smallest group that holds √45?
- rational numbers
- whole numbers
- irrational numbers
- integers
Read this first
Use this
Number line from 0 to 2, ticks every 1. Green marks are whole numbers, blue marks the other integers, orange marks the other rational numbers, and purple marks irrational numbers.
3.
Milo reads a repeating decimal on a calculator. What is the smallest group that holds 0.7272…, where the block 72 repeats forever?
- integers
- irrational numbers
- whole numbers
- rational numbers
4.
Noah's square window has an area of 10 square feet, so each side is √10 feet long. What is the smallest group that holds the side length?
- irrational numbers
- integers
- whole numbers
- rational numbers
5.
Pia's square sticky note has an area of 25 square centimeters, so each side is √25 cm long. What is the smallest group that holds the side length?
- irrational numbers
- integers
- rational numbers
- whole numbers
Use this
Number line from 0 to 5, ticks every 1. Green marks are whole numbers, blue marks the other integers, orange marks the other rational numbers, and purple marks irrational numbers.
6.
Ren's round pizza is 1 foot across. The distance around its crust is exactly π feet. What is the smallest group that holds the distance around the crust?
- integers
- rational numbers
- irrational numbers
- whole numbers
7.
Tala reads four numbers on a quiz card. Which of these numbers is irrational?
- 22/7
- √36
- √28
- 0.75
8.
Ari finds four numbers in a puzzle book. Which of these numbers is irrational?
- √60
- 0.1666…
- 7/9
- −√100
9.
Bo marks four points on a number line for a poster. Which point is an irrational number?
- Point A
- Point C
- Point D
- Point B
10.
Esme plots four numbers for a math club. Which point is an irrational number?
- Point B
- Point D
- Point C
- Point A

8th grade Kinds of real numbers: rational and irrational worksheet – printable — Print: 1 2 3 4 5 6

About this worksheet

Kinds of real numbers: rational and irrational. Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

I can tell whether a number is rational or irrational and say why: its decimal stops or repeats, or it never ends and never repeats.
I can name the smallest group that holds a number, or a whole list of numbers, and I know the rational and irrational numbers together make up the real numbers.

Standard: 8.NS.A.1 (irrational numbers)

Words to know

rational number: A number you can write as a fraction. Its decimal stops or repeats.

irrational number: A number with a decimal that never ends and never repeats, like π.

real number: Any number that has a mark on the number line.

perfect square: A number you get by multiplying a whole number by itself: 49 = 7 × 7.

square root (√): The number that, multiplied by itself, gives the number under the sign.

repeating decimal: A decimal with a block of digits that repeats forever, like 0.4545….

Common mistakes

Your child treated every square root as irrational.

Your child read a calculator's short decimal for a square root as if it ended.

Your child rounded a square root to a whole number and called it whole.

What to say

Ask: what is the square root of 49? Does it come out exactly?

Ask: do the digits of the square root of 2 stop, or do they keep going with no pattern?

Ask: is the square root of 20 exactly 4 or exactly 5?

Questions parents ask

What is the most common mistake with kinds of real numbers: rational and irrational?

Your child treated every square root as irrational.

How can I help my child with kinds of real numbers: rational and irrational?

Ask: what is the square root of 49? Does it come out exactly?

Are these 8th grade math worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

More grade 8 math

See all grade 8 math

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