Math 9 · Unit 1: Number and calculation · Cambridge Lower Secondary Maths Stage 9

Questions

1. 1. Which 2 of these numbers are rational?

   Tick all the right answers.

   • ☐ √36
   • ☐ √48
   • ☐ √64
   • ☐ √84
   • ☐ ∛100
   Check

2. 2. Look at these numbers: 12.77, −36, √27, √500, 61/12, −∛8. Which are the irrational numbers?

   • √500 only
   • 12.77 and 61/12
   • √27, √500 and −∛8
   • √27 and √500
   Check

3. 3. Look at these numbers: 12.77, −36, √27, √500, 61/12, −∛8. Which are the integers?

   • −36 and −∛8
   • −36, √27 and −∛8
   • −36 only
   • 12.77 and −36
   Check

4. 4. Is √25 an integer or a surd?

   • an integer
   • a surd
   Check

5. 5. Is ∛25 an integer or a surd?

   • an integer
   • a surd
   Check

6. 6. Is √125 an integer or a surd?

   • an integer
   • a surd
   Check

7. 7. Is ∛125 an integer or a surd?

   • an integer
   • a surd
   Check

8. 8. Is √225 an integer or a surd?

   • an integer
   • a surd
   Check

9. 9. Is ∛225 an integer or a surd?

   • an integer
   • a surd
   Check

10. 10. Is √3 + 6 rational or irrational?

    • rational
    • irrational
    Check

11. 11. Is √(3 + 6) rational or irrational?

    • rational, because it equals 9
    • irrational, because it is a square root
    • irrational, because √3 is irrational
    • rational, because it equals 3
    Check

12. 12. Is √64 + ∛64 rational or irrational?

    • rational, because it equals 16
    • irrational, because 64 isn't prime
    • rational, because it equals 12
    • irrational, because it has roots in it
    Check

13. 13. Is ∛8 + ∛19 rational or irrational?

    • rational, because ∛8 = 2
    • rational, because it equals ∛27 = 3
    • irrational, because ∛19 is irrational
    • irrational, because ∛8 is irrational
    Check

14. 14. Find 1.5²

    • 2.25
    • 3
    • 22.5
    • 1.25
    Check

15. 15. True or false? √2.25 is a rational number.

    • True
    • False
    Check

16. 16. Is √20.25 a rational number?

    • Yes
    • No
    Check

17. 17. Is ∛1.331 a rational number?

    • Yes
    • No
    Check

18. 18. Without a calculator: true or false? 3 < ∛41 < 4

    • True
    • False
    Check

19. 19. Without a calculator: true or false? 9 < ∛800 < 10

    • True
    • False
    Check

20. 20. Without a calculator: true or false? 1.1 < √1.36 < 1.2

    • True
    • False
    Check