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Ignition Learning — Activity Sheet

Squares, square roots & index notation

Mathematics · Year 7

Name: ______________________Date: ____________

A square number is the result of multiplying a whole number by itself — 4² (four squared) = 4 × 4 = 16. The square root of a number is the reverse: it asks "what number, multiplied by itself, gives this?" So √16 = 4. Index (or exponent) notation is a shorthand for repeated multiplication: 2³ means 2 × 2 × 2 = 8. Every whole number greater than 1 can be broken down into a unique set of prime factors, often written using index notation — e.g. 12 = 2² × 3.

Example

A square garden bed has an area of 25m². Since 25 = 5², each side must be 5m long — finding the square root tells you the side length directly.

Key terms

Square number:
The result of multiplying a whole number by itself.
Square root:
The number which, multiplied by itself, gives a given number.
Index notation:
A shorthand for repeated multiplication, e.g. 2³ = 2×2×2.

Questions

  1. 1. What is 4 squared (4²)?

    • 8
    • 16
    • 12
    • 44

  2. 2. What is 5²?

    • 10
    • 20
    • 25
    • 55

  3. 3. What is √16?

    • 2
    • 4
    • 8
    • 16

  4. 4. What is √25?

    • 4
    • 5
    • 6
    • 25

  5. 5. 2³ means:

    • 2 × 3
    • 2 × 2 × 2
    • 3 × 3
    • 2 + 2 + 2

  6. 6. What is 2³?

    • 4
    • 6
    • 8
    • 9

  7. 7. What is 3²?

    • 6
    • 9
    • 12
    • 27

  8. 8. What is 6²?

    • 12
    • 26
    • 36
    • 66

  9. 9. What is √36?

    • 4
    • 5
    • 6
    • 9

  10. 10. What is 10²?

    • 20
    • 100
    • 1000
    • 10

  11. 11. What is 3³?

    • 9
    • 27
    • 6
    • 33

  12. 12. What is the square root of 49?

    • 6
    • 7
    • 8
    • 9

  13. 13. 12 written as a product of prime factors using index notation is:

    • 2 × 6
    • 2² × 3
    • 2 × 3 × 3
    • 4 × 3

  14. 14. What is √64?

    • 6
    • 7
    • 8
    • 9

  15. 15. What is 7² + 3²?

    • 52
    • 58
    • 64
    • 70

  16. 16. Using index laws, 2² × 2³ simplifies to:

    • 16
    • 32
    • 64
    • 25

  17. 17. A square has an area of 81m². What is its side length?

    • 8m
    • 9m
    • 81m
    • 18m

  18. 18. Which number is NOT a perfect square?

    • 16
    • 25
    • 32
    • 36

  19. 19. 18 written as a product of prime factors using index notation is:

    • 2 × 3²
    • 2² × 3
    • 3 × 6
    • 2 × 9

  20. 20. What is √100 + √9?

    • 12
    • 13
    • 19
    • 109

Answer key (parent copy)

  1. 1. 16
  2. 2. 25
  3. 3. 4
  4. 4. 5
  5. 5. 2 × 2 × 2
  6. 6. 8
  7. 7. 9
  8. 8. 36
  9. 9. 6
  10. 10. 100
  11. 11. 27
  12. 12. 7
  13. 13. 2² × 3
  14. 14. 8
  15. 15. 58
  16. 16. 32
  17. 17. 9m
  18. 18. 32
  19. 19. 2 × 3²
  20. 20. 13