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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 705 · 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 48²? =
  2. 2.What is the smallest whole number by which 180 must be multiplied to get a perfect square?
  3. 3.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)?
  4. 4.What is 17²? =
  5. 5.How many whole numbers lie between 22² and 23²?
  6. 6.What is √1849? =
  7. 7.What is the smallest whole number by which 243 must be multiplied to get a perfect square?
  8. 8.Which of these is a perfect square? (a) 747 (b) 729 (c) 771
  9. 9.Which of these is a perfect square? (a) 260 (b) 274 (c) 256
  10. 10.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)?
  11. 11.What is 30²? =
  12. 12.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)?
  13. 13.How many whole numbers lie between 38² and 39²?
  14. 14.What is √1764? =
  15. 15.A square garden has an area of 2704 square m. How long is each side (in m)?
  16. 16.What is √2116? =
  17. 17.A square garden has an area of 64 square m. How long is each side (in m)?
  18. 18.What is √9409? =
  19. 19.A square garden has an area of 361 square m. How long is each side (in m)?
  20. 20.Which of these is a perfect square? (a) 1021 (b) 961 (c) 1008
  21. 21.What is 66²? =
  22. 22.Which of these is a perfect square? (a) 119 (b) 100 (c) 105
  23. 23.What is 18²? =
  24. 24.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
  25. 25.Which of these is a perfect square? (a) 232 (b) 229 (c) 225
  26. 26.What is 43²? =
  27. 27.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)?
  28. 28.What is 40²? =
  29. 29.What is 71²? =
  30. 30.How many whole numbers lie between 45² and 46²?
  31. 31.What is √676? =
  32. 32.What is √9801? =
  33. 33.How many whole numbers lie between 20² and 21²?
  34. 34.What is √7396? =
  35. 35.How many whole numbers lie between 47² and 48²?
  36. 36.How many whole numbers lie between 14² and 15²?
  37. 37.What is 86²? =
  38. 38.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)?
  39. 39.How many whole numbers lie between 8² and 9²?
  40. 40.Which of these is a perfect square? (a) 447 (b) 444 (c) 441

Answer key

  1. 2304
  2. 5
  3. 100
  4. 289
  5. 44
  6. 43
  7. 3
  8. 729
  9. 256
  10. 529
  11. 900
  12. 625
  13. 76
  14. 42
  15. 52
  16. 46
  17. 8
  18. 97
  19. 19
  20. 961
  21. 4356
  22. 100
  23. 324
  24. 36
  25. 225
  26. 1849
  27. 900
  28. 1600
  29. 5041
  30. 90
  31. 26
  32. 99
  33. 40
  34. 86
  35. 94
  36. 28
  37. 7396
  38. 441
  39. 16
  40. 441

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