Kinds of real numbers: rational and irrational

Answer Key - Grade 8 Math Worksheet - Challenge Me

Circle the best answer, or write your answer on the line.

1. 1.

   Luz deals seven cards from a number deck: √225, √56, √91, √95, √78, 0.9, 0.7272…. How many of the cards show an irrational number?

   4
2. 2.

   Milo deals six cards from a number deck: π, √324, √65, 0.6, 0.4545…, 7/8. How many of the cards show an irrational number?

   2
3. 3.

   Ren picks cards √17, 9, π and 0.5. What is the smallest group that holds all of these numbers?

   • rational numbers
   • irrational numbers
   • integers
   • real numbers
4. 4.

   Tala gets two clues about a mystery number: it is irrational, and it is between 5 and 6. Which number fits both clues?

   • √70
   • √25
   • 5.5
   • √30
5. 5.

   Zee gets two clues about a mystery number: it is rational, and it is not an integer. Which number fits both clues?

   • √13
   • −1.75
   • √121
   • −20
6. 6.

   Ari gets two clues about a mystery number: it is a real number, and it is not rational. Which number fits both clues?

   • 0.1818…
   • √64
   • 6.4
   • √48

7. Read this first

   Use this

   Number line from -4 to 4, ticks every 1. Green marks are whole numbers, blue marks the other integers, orange marks the other rational numbers, and purple marks irrational numbers. The real numbers are every mark on the line.

8. 7.

   Bo reads four claims about number groups on a sticky note. Which claim is true?

   • Every integer is a real number.
   • Every square root is an irrational number.
   • Every real number is an integer.
   • Irrational numbers have no place on the number line.
9. 8.

   Esme reads four claims about number groups on a sticky note. Which claim is true?

   • Some numbers are both rational and irrational.
   • Every real number is rational.
   • No number is both rational and irrational.
   • Irrational numbers are not real numbers.
10. 9.

    Jun reads four claims about number groups on a sticky note. Which claim is true?

    • Rational and irrational numbers together make up all the real numbers.
    • Rational numbers make up all the real numbers.
    • Whole numbers, integers and rational numbers make up the irrational numbers.
    • Irrational numbers make up all the real numbers.
11. 10.

    Noah says √60 is irrational. Which reason is best?

    • Every number under a root sign is irrational.
    • 60 is even, so its root is irrational.
    • 60 is not a perfect square, so the decimal never ends or repeats.
    • √60 is about 7.75, which is a short decimal, so it is rational.