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?

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

   Jun's robot makes a claim: "The sum of two irrational numbers is irrational." Is the claim always, sometimes or never true?

   • Sometimes true
   • Always true, for any two irrational numbers
   • Never true
3. 3.

   Luz's padlock only opens for the right verdict on a claim: "A rational number times an irrational number is irrational." Is the claim always, sometimes or never true?

   • Sometimes true
   • Always true, whichever rational number is used
   • Never true
4. 4.

   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
   • Sometimes true
   • Always true
5. 5.

   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
6. 6.

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

   12
7. 7.

   Tala's robot looks for a partner root so that √2 × √n = 10. Both roots are irrational. What whole number is n?

   50
8. 8.

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

   24
9. 9.

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

   • (3 + √2) + (1 − √2) = 4
   • √4 + √9 = 5
   • √2 + √3
   • 0.5 + 0.5 = 1
10. 10.

    Esme's robot collects examples (it has a whole folder of them). Which example shows that the product of two irrational numbers can be rational?

    • √3 × √5 = √15
    • 3 × √3 = 3√3
    • √3 × √12 = 6
    • √4 × √9 = 6