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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 202 · 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 26² and 27²?
  2. 2.What is the smallest whole number by which 112 must be multiplied to get a perfect square?
  3. 3.A square garden has an area of 1681 square m. How long is each side (in m)?
  4. 4.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
  5. 5.What is √8464? =
  6. 6.What is √2809? =
  7. 7.What is 35²? =
  8. 8.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)?
  9. 9.How many whole numbers lie between 8² and 9²?
  10. 10.A square garden has an area of 2116 square m. How long is each side (in m)?
  11. 11.What is √4624? =
  12. 12.How many whole numbers lie between 14² and 15²?
  13. 13.A square garden has an area of 841 square m. How long is each side (in m)?
  14. 14.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
  15. 15.What is the smallest whole number by which 1053 must be divided to get a perfect square?
  16. 16.What is 19²? =
  17. 17.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
  18. 18.How many whole numbers lie between 40² and 41²?
  19. 19.What is √4761? =
  20. 20.Which of these is a perfect square? (a) 353 (b) 354 (c) 324
  21. 21.What is the smallest whole number by which 405 must be divided to get a perfect square?
  22. 22.Which of these is a perfect square? (a) 1089 (b) 1117 (c) 1147
  23. 23.What is √5329? =
  24. 24.A square garden has an area of 484 square m. How long is each side (in m)?
  25. 25.Which of these is a perfect square? (a) 180 (b) 169 (c) 187
  26. 26.Which of these is a perfect square? (a) 904 (b) 927 (c) 900
  27. 27.Which of these is a perfect square? (a) 1622 (b) 1600 (c) 1630
  28. 28.Which of these is a perfect square? (a) 1056 (b) 1040 (c) 1024
  29. 29.Which of these is a perfect square? (a) 121 (b) 137 (c) 141
  30. 30.A square garden has an area of 400 square m. How long is each side (in m)?
  31. 31.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)?
  32. 32.What is 61²? =
  33. 33.What is the smallest whole number by which 80 must be multiplied to get a perfect square?
  34. 34.A square garden has an area of 441 square m. How long is each side (in m)?
  35. 35.What is 45²? =
  36. 36.What is √5041? =
  37. 37.Which of these is a perfect square? (a) 635 (b) 625 (c) 646
  38. 38.How many whole numbers lie between 25² and 26²?
  39. 39.What is the smallest whole number by which 384 must be divided to get a perfect square?
  40. 40.Which of these is a perfect square? (a) 227 (b) 225 (c) 237

Answer key

  1. 52
  2. 7
  3. 41
  4. 36
  5. 92
  6. 53
  7. 1225
  8. 361
  9. 16
  10. 46
  11. 68
  12. 28
  13. 29
  14. 121
  15. 13
  16. 361
  17. 49
  18. 80
  19. 69
  20. 324
  21. 5
  22. 1089
  23. 73
  24. 22
  25. 169
  26. 900
  27. 1600
  28. 1024
  29. 121
  30. 20
  31. 576
  32. 3721
  33. 5
  34. 21
  35. 2025
  36. 71
  37. 625
  38. 50
  39. 6
  40. 225

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