Kinds of real numbers: rational and irrational

Grade 8 Math Worksheet

Circle the best answer.

1. 1.

   Jun gets a card with a minus sign in front of a root. What is the smallest group that holds −√64?

   • rational numbers
   • integers
   • irrational numbers
   • whole numbers
2. 2.

   Kira draws √45 from a pile of cards. What is the smallest group that holds √45?

   • integers
   • rational numbers
   • irrational numbers
   • whole numbers

3. Read this first

   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.

4. 3.

   Luz traces a circle and wonders about the number π. What is the smallest group that holds π?

   • irrational numbers
   • whole numbers
   • rational numbers
   • integers

5. 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.

6. 4.

   Milo reads a repeating decimal on a calculator. What is the smallest group that holds 0.7272…, where the block 72 repeats forever?

   • integers
   • rational numbers
   • whole numbers
   • irrational numbers
7. 5.

   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?

   • integers
   • rational numbers
   • irrational numbers
   • whole numbers
8. 6.

   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?

   • integers
   • irrational numbers
   • whole numbers
   • rational numbers

9. 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.

10. 7.

    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?

    • rational numbers
    • whole numbers
    • integers
    • irrational numbers
11. 8.

    Tala reads four numbers on a quiz card. Which of these numbers is irrational?

    • √36
    • 22/7
    • 0.75
    • √28
12. 9.

    Zee sorts four number cards into two piles. Which of these numbers is irrational?

    • √169
    • 3.14
    • 0.3636…
    • √26
13. 10.

    Bo marks four points on a number line for a poster. Which point is an irrational number?

    • Point D
    • Point B
    • Point A
    • Point C