Kinds of real numbers: rational and irrational
Grade 8 Math Worksheet

Circle the best answer.
Esme sorts number cards before a game. What is the smallest group that holds √81?
- rational numbers
- integers
- irrational numbers
- whole numbers
Jun gets a card with a minus sign in front of a root. What is the smallest group that holds −√64?
Number line from -10 to 0, ticks every 1. Green marks are whole numbers, blue marks the other integers, orange marks the other rational numbers, and purple marks irrational numbers. Number line from -10 to 0, ticks every 1. Green marks are whole numbers, blue marks the other integers, orange marks the other rational numbers, and purple marks irrational numbers. −10 −9 −8 −7 −6 −5 −4 −3 −2 −1 0 Green marks are whole numbers, blue marks the other integers, orange marks the other rational numbers, and purple marks irrational numbers. - irrational numbers
- integers
- whole numbers
- rational numbers
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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.
Luz traces a circle and wonders about the number π. What is the smallest group that holds π?
- rational numbers
- integers
- whole numbers
- irrational numbers
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?
Number line from 0 to 8, ticks every 1. Green marks are whole numbers, blue marks the other integers, orange marks the other rational numbers, and purple marks irrational numbers. Number line from 0 to 8, ticks every 1. Green marks are whole numbers, blue marks the other integers, orange marks the other rational numbers, and purple marks irrational numbers. 0 1 2 3 4 5 6 7 8 Green marks are whole numbers, blue marks the other integers, orange marks the other rational numbers, and purple marks irrational numbers. - whole numbers
- integers
- irrational numbers
- rational 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.
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?
- irrational numbers
- rational numbers
- integers
- whole numbers
Tala reads four numbers on a quiz card. Which of these numbers is irrational?
Number line from 0 to 8, ticks every 1. Green marks are whole numbers, blue marks the other integers, orange marks the other rational numbers, and purple marks irrational numbers. Number line from 0 to 8, ticks every 1. Green marks are whole numbers, blue marks the other integers, orange marks the other rational numbers, and purple marks irrational numbers. 0 1 2 3 4 5 6 7 8 Green marks are whole numbers, blue marks the other integers, orange marks the other rational numbers, and purple marks irrational numbers. - √28
- 22/7
- 0.75
- √36
Zee sorts four number cards into two piles. Which of these numbers is irrational?
Number line from 0 to 14, ticks every 1. Green marks are whole numbers, blue marks the other integers, orange marks the other rational numbers, and purple marks irrational numbers. Number line from 0 to 14, ticks every 1. Green marks are whole numbers, blue marks the other integers, orange marks the other rational numbers, and purple marks irrational numbers. 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Green marks are whole numbers, blue marks the other integers, orange marks the other rational numbers, and purple marks irrational numbers. - √26
- 3.14
- √169
- 0.3636…
Ari finds four numbers in a puzzle book. Which of these numbers is irrational?
Number line from -12 to 10, ticks every 2. Green marks are whole numbers, blue marks the other integers, orange marks the other rational numbers, and purple marks irrational numbers. Number line from -12 to 10, ticks every 2. Green marks are whole numbers, blue marks the other integers, orange marks the other rational numbers, and purple marks irrational numbers. −12 −8 −4 0 4 8 Green marks are whole numbers, blue marks the other integers, orange marks the other rational numbers, and purple marks irrational numbers. - −√100
- √60
- 0.1666…
- 7/9
Esme plots four numbers for a math club. Which point is an irrational number?
Number line from -1 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. Point A is 1/2, point B is √9, point C is √11, and point D is -0.6. Number line from -1 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. Point A is 1/2, point B is √9, point C is √11, and point D is -0.6. −1 0 1 2 3 4 5 A B C D Green marks are whole numbers, blue marks the other integers, orange marks the other rational numbers, and purple marks irrational numbers. Point A is 1/2, point B is √9, point C is √11, and point D is -0.6. - Point A
- Point B
- Point D
- Point C
Jun labels four points on a number line. Which point is an irrational number?
Number line from -2 to 6, ticks every 1. Green marks are whole numbers, blue marks the other integers, orange marks the other rational numbers, and purple marks irrational numbers. Point A is 0.1212…, point B is -√2, point C is 5, and point D is 3.8. Number line from -2 to 6, ticks every 1. Green marks are whole numbers, blue marks the other integers, orange marks the other rational numbers, and purple marks irrational numbers. Point A is 0.1212…, point B is -√2, point C is 5, and point D is 3.8. −2 −1 0 1 2 3 4 5 6 A B C D Green marks are whole numbers, blue marks the other integers, orange marks the other rational numbers, and purple marks irrational numbers. Point A is 0.1212..., point B is -√2, point C is 5, and point D is 3.8. - Point A
- Point B
- Point C
- Point D