Is the sum or product rational or irrational?

Answer Key - Grade 9 Math Worksheet - Challenge Me

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

1. 1.

   Esme reads a claim on a card: "The sum of a rational number and an irrational number is irrational." Is the claim always, sometimes or never true?

   • Never true
   • Always true
   • Sometimes true
2. 2.

   In math club, Kira tests a claim: "The product of two irrational numbers is rational." Is the claim always, sometimes or never true?

   • Never true
   • Always true, since one pair of numbers works
   • Sometimes true
3. 3.

   Noah reads a claim in a puzzle app: "The product of two irrational numbers is irrational." Is the claim always, sometimes or never true?

   • Never true
   • Always true
   • Sometimes true
4. 4.

   Pia writes a claim on the board: "π times a rational number is irrational." Is the claim always, sometimes or never true?

   • Never true
   • Always true
   • Sometimes true
5. 5.

   Ren wants √3 × √n = 6, a rational answer. Both roots are irrational. What whole number is n?

   12
6. 6.

   In math club, Zee finds n so that √5 × √n = 10. Both roots are irrational. What whole number is n?

   20
7. 7.

   Ari's padlock opens when √6 × √n = 12 (it likes whole numbers). Both roots are irrational. What whole number is n?

   24
8. 8.

   Bo wants an example for a poster. Which example shows that the sum of two irrational numbers can be rational?

   • 0.5 + 0.5 = 1
   • (3 + √2) + (1 − √2) = 4
   • √4 + √9 = 5
   • √2 + √3
9. 9.

   In math club, Jun looks for an example. Which example shows that a rational number times an irrational number can be rational?

   • 0 × √5 = 0
   • √9 × √5 = 3√5
   • 2 × √5 = 2√5
   • 1/2 × 4 = 2
10. 10.

    Kira's padlock opens only for the right example (it is a picky padlock). Which example shows that a rational number times an irrational number can be rational?

    • 2/3 × 6 = 4
    • 5 × √11 = 5√11
    • 0 × √11 = 0
    • √25 × √11 = 5√11