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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 490 · 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 28 odd numbers (1 + 3 + 5 + …)?
  2. 2.How many whole numbers lie between 32² and 33²?
  3. 3.What is the smallest whole number by which 24 must be divided to get a perfect square?
  4. 4.How many whole numbers lie between 22² and 23²?
  5. 5.What is 36²? =
  6. 6.How many whole numbers lie between 16² and 17²?
  7. 7.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)?
  8. 8.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)?
  9. 9.Which of these is a perfect square? (a) 224 (b) 196 (c) 209
  10. 10.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?
  11. 11.What is 64²? =
  12. 12.Which of these is a perfect square? (a) 100 (b) 106 (c) 103
  13. 13.What is 12²? =
  14. 14.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)?
  15. 15.How many whole numbers lie between 10² and 11²?
  16. 16.How many whole numbers lie between 20² and 21²?
  17. 17.Which of these is a perfect square? (a) 900 (b) 934 (c) 912
  18. 18.A square garden has an area of 784 square m. How long is each side (in m)?
  19. 19.What is 43²? =
  20. 20.How many whole numbers lie between 26² and 27²?
  21. 21.How many whole numbers lie between 9² and 10²?
  22. 22.A square garden has an area of 100 square m. How long is each side (in m)?
  23. 23.How many whole numbers lie between 27² and 28²?
  24. 24.What is 44²? =
  25. 25.What is 14²? =
  26. 26.What is the smallest whole number by which 250 must be divided to get a perfect square?
  27. 27.What is 87²? =
  28. 28.Which of these is a perfect square? (a) 169 (b) 192 (c) 179
  29. 29.What is 95²? =
  30. 30.How many whole numbers lie between 40² and 41²?
  31. 31.Which of these is a perfect square? (a) 245 (b) 225 (c) 231
  32. 32.How many whole numbers lie between 37² and 38²?
  33. 33.What is 56²? =
  34. 34.A square garden has an area of 1681 square m. How long is each side (in m)?
  35. 35.What is √9409? =
  36. 36.What is 91²? =
  37. 37.What is the smallest whole number by which 810 must be multiplied to get a perfect square?
  38. 38.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)?
  39. 39.What is √1089? =
  40. 40.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)?

Answer key

  1. 784
  2. 64
  3. 6
  4. 44
  5. 1296
  6. 32
  7. 529
  8. 225
  9. 196
  10. 289
  11. 4096
  12. 100
  13. 144
  14. 576
  15. 20
  16. 40
  17. 900
  18. 28
  19. 1849
  20. 52
  21. 18
  22. 10
  23. 54
  24. 1936
  25. 196
  26. 10
  27. 7569
  28. 169
  29. 9025
  30. 80
  31. 225
  32. 74
  33. 3136
  34. 41
  35. 97
  36. 8281
  37. 10
  38. 81
  39. 33
  40. 484

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