Is the sum or product rational or irrational?
Grade 9 Math Worksheet - Challenge Me
Circle the best answer, or write your answer on the line.
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
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
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
- Never true
- Always true, whichever rational number is used
Noah reads a claim in a puzzle app: "The product of two irrational numbers is irrational." Is the claim always, sometimes or never true?
- Sometimes true
- Never true
- Always true
Pia writes a claim on the board: "π times a rational number is irrational." Is the claim always, sometimes or never true?
- Always true
- Never true
- Sometimes true
In math club, Zee finds n so that √5 × √n = 10. Both roots are irrational. What whole number is n?
Ari's padlock opens when √6 × √n = 12 (it likes whole numbers). Both roots are irrational. What whole number is n?
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
- √2 + √3
- (3 + √2) + (1 − √2) = 4
- √4 + √9 = 5
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?
- √4 × √9 = 6
- 3 × √3 = 3√3
- √3 × √12 = 6
- √3 × √5 = √15
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