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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 615 · 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.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)?
  2. 2.What is √4225? =
  3. 3.What is the smallest whole number by which 539 must be multiplied to get a perfect square?
  4. 4.Which of these is a perfect square? (a) 256 (b) 257 (c) 258
  5. 5.A square garden has an area of 144 square m. How long is each side (in m)?
  6. 6.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
  7. 7.What is the smallest whole number by which 147 must be divided to get a perfect square?
  8. 8.What is 48²? =
  9. 9.What is √1849? =
  10. 10.What is the smallest whole number by which 224 must be divided to get a perfect square?
  11. 11.How many whole numbers lie between 5² and 6²?
  12. 12.A square garden has an area of 49 square m. How long is each side (in m)?
  13. 13.Which of these is a perfect square? (a) 484 (b) 492 (c) 520
  14. 14.How many whole numbers lie between 8² and 9²?
  15. 15.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)?
  16. 16.Which of these is a perfect square? (a) 729 (b) 768 (c) 743
  17. 17.What is the smallest whole number by which 567 must be multiplied to get a perfect square?
  18. 18.How many whole numbers lie between 10² and 11²?
  19. 19.How many whole numbers lie between 37² and 38²?
  20. 20.What is 22²? =
  21. 21.What is the smallest whole number by which 112 must be multiplied to get a perfect square?
  22. 22.Which of these is a perfect square? (a) 1138 (b) 1111 (c) 1089
  23. 23.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?
  24. 24.How many whole numbers lie between 32² and 33²?
  25. 25.How many whole numbers lie between 39² and 40²?
  26. 26.What is 93²? =
  27. 27.How many whole numbers lie between 15² and 16²?
  28. 28.What is the smallest whole number by which 56 must be divided to get a perfect square?
  29. 29.What is √9025? =
  30. 30.A square garden has an area of 196 square m. How long is each side (in m)?
  31. 31.How many whole numbers lie between 35² and 36²?
  32. 32.How many whole numbers lie between 31² and 32²?
  33. 33.How many whole numbers lie between 21² and 22²?
  34. 34.Which of these is a perfect square? (a) 293 (b) 289 (c) 323
  35. 35.How many whole numbers lie between 13² and 14²?
  36. 36.What is √729? =
  37. 37.What is the smallest whole number by which 56 must be multiplied to get a perfect square?
  38. 38.What is √7225? =
  39. 39.How many whole numbers lie between 6² and 7²?
  40. 40.What is 31²? =

Answer key

  1. 225
  2. 65
  3. 11
  4. 256
  5. 12
  6. 64
  7. 3
  8. 2304
  9. 43
  10. 14
  11. 10
  12. 7
  13. 484
  14. 16
  15. 169
  16. 729
  17. 7
  18. 20
  19. 74
  20. 484
  21. 7
  22. 1089
  23. 289
  24. 64
  25. 78
  26. 8649
  27. 30
  28. 14
  29. 95
  30. 14
  31. 70
  32. 62
  33. 42
  34. 289
  35. 26
  36. 27
  37. 14
  38. 85
  39. 12
  40. 961

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