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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 423 · 40 sums
TalentJR

The method (Pairs make squares): Square: n × n. Quick way: (a + b)² = a² + 2ab + b², e.g. 42² = 1600 + 160 + 4. Square root: the number that times itself gives the square; a square ending in 4 has a root ending in 2 or 8. Make a perfect square: break into primes; multiply (or divide) by the prime left without a partner. 1 + 3 + 5 + … (n odd numbers) = n². Between n² and (n + 1)² there are 2n whole numbers.

NameDateTime takenScore ___ / 40
  1. 1.How many whole numbers lie between 8² and 9²?
  2. 2.What is √6724? =
  3. 3.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)?
  4. 4.What is √121? =
  5. 5.A square garden has an area of 169 square m. How long is each side (in m)?
  6. 6.Which of these is a perfect square? (a) 729 (b) 742 (c) 749
  7. 7.What is the smallest whole number by which 960 must be multiplied to get a perfect square?
  8. 8.How many whole numbers lie between 31² and 32²?
  9. 9.How many whole numbers lie between 10² and 11²?
  10. 10.What is the smallest whole number by which 20 must be multiplied to get a perfect square?
  11. 11.A square garden has an area of 36 square m. How long is each side (in m)?
  12. 12.What is the smallest whole number by which 48 must be multiplied to get a perfect square?
  13. 13.What is √256? =
  14. 14.What is 62²? =
  15. 15.What is the smallest whole number by which 490 must be multiplied to get a perfect square?
  16. 16.What is √2500? =
  17. 17.What is 88²? =
  18. 18.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)?
  19. 19.How many whole numbers lie between 6² and 7²?
  20. 20.What is √1521? =
  21. 21.What is √4096? =
  22. 22.What is √1089? =
  23. 23.A square garden has an area of 3025 square m. How long is each side (in m)?
  24. 24.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
  25. 25.What is √5776? =
  26. 26.What is 99²? =
  27. 27.What is the smallest whole number by which 125 must be multiplied to get a perfect square?
  28. 28.What is 30²? =
  29. 29.What is √7744? =
  30. 30.What is the smallest whole number by which 147 must be multiplied to get a perfect square?
  31. 31.How many whole numbers lie between 38² and 39²?
  32. 32.What is the smallest whole number by which 216 must be multiplied to get a perfect square?
  33. 33.How many whole numbers lie between 17² and 18²?
  34. 34.A square garden has an area of 144 square m. How long is each side (in m)?
  35. 35.What is 65²? =
  36. 36.What is 21²? =
  37. 37.A square garden has an area of 3136 square m. How long is each side (in m)?
  38. 38.What is the smallest whole number by which 24 must be multiplied to get a perfect square?
  39. 39.What is √1024? =
  40. 40.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?

Answer key

  1. 16
  2. 82
  3. 441
  4. 11
  5. 13
  6. 729
  7. 15
  8. 62
  9. 20
  10. 5
  11. 6
  12. 3
  13. 16
  14. 3844
  15. 10
  16. 50
  17. 7744
  18. 361
  19. 12
  20. 39
  21. 64
  22. 33
  23. 55
  24. 49
  25. 76
  26. 9801
  27. 5
  28. 900
  29. 88
  30. 3
  31. 76
  32. 6
  33. 34
  34. 12
  35. 4225
  36. 441
  37. 56
  38. 6
  39. 32
  40. 64

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