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.

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

   • √13
   • −20
   • −1.75
   • √121
4. 4.

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

   • 6.4
   • √48
   • √64
   • 0.1818…

5. 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.

6. 5.

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

   • Irrational numbers have no place on the number line.
   • Every square root is an irrational number.
   • Every real number is an integer.
   • Every integer is a real number.
7. 6.

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

   • Every real number is rational.
   • No number is both rational and irrational.
   • Irrational numbers are not real numbers.
   • Some numbers are both rational and irrational.
8. 7.

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

   • Whole numbers, integers and rational numbers make up the irrational numbers.
   • Irrational numbers make up all the real numbers.
   • Rational and irrational numbers together make up all the real numbers.
   • Rational numbers make up all the real numbers.
9. 8.

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

   • 26 is not a perfect square, so the decimal never ends or repeats.
   • 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 has a root sign, and every square root is irrational.

10. 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.

11. 9.

    Luz says 0.2727… is rational. Which reason is best?

    • It is less than 1, so it is rational.
    • All decimals are rational.
    • The block 27 repeats, so it can be written as a fraction.
    • Its digits go on forever, so it cannot be a fraction.
12. 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 about 7.75, which is a short decimal, so it is rational.
    • 60 is not a perfect square, so the decimal never ends or repeats.