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.

   Kira deals six cards from a number deck: √196, √77, π, 0.8, 0.3636…, √88. How many of the cards show an irrational number?

   3
2. 2.

   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
3. 3.

   Noah picks cards −15, 7/10 and 22/7. What is the smallest group that holds all of these numbers?

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

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

   • integers
   • irrational numbers
   • rational numbers
   • real numbers
5. 5.

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

   • √30
   • √25
   • √70
   • 5.5
6. 6.

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

   • −20
   • √121
   • −1.75
   • √13
7. 7.

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

   • √64
   • 6.4
   • 0.1818…
   • √48

8. 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.

9. 8.

   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.
   • Irrational numbers have no place on the number line.
   • Every real number is an integer.
10. 9.

    Kira says √26 is irrational. Which reason is best?

    • √26 has a root sign, and every square root is irrational.
    • 26 is a big number, so √26 must be irrational.
    • 26 is not a perfect square, so the decimal stops after a few digits.
    • 26 is not a perfect square, so the decimal never ends or repeats.
11. 10.

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

    • 60 is even, so its root is irrational.
    • Every number under a root sign 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.