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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 175 · 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 21 odd numbers (1 + 3 + 5 + …)?
  2. 2.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)?
  3. 3.What is the smallest whole number by which 28 must be divided to get a perfect square?
  4. 4.What is 71²? =
  5. 5.A square garden has an area of 1764 square m. How long is each side (in m)?
  6. 6.A square garden has an area of 1296 square m. How long is each side (in m)?
  7. 7.Which of these is a perfect square? (a) 517 (b) 503 (c) 484
  8. 8.What is √484? =
  9. 9.A square garden has an area of 3249 square m. How long is each side (in m)?
  10. 10.What is √7225? =
  11. 11.A square garden has an area of 81 square m. How long is each side (in m)?
  12. 12.What is the smallest whole number by which 243 must be divided to get a perfect square?
  13. 13.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)?
  14. 14.What is 63²? =
  15. 15.Which of these is a perfect square? (a) 252 (b) 225 (c) 240
  16. 16.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)?
  17. 17.How many whole numbers lie between 8² and 9²?
  18. 18.What is the smallest whole number by which 832 must be divided to get a perfect square?
  19. 19.What is 33²? =
  20. 20.A square garden has an area of 64 square m. How long is each side (in m)?
  21. 21.How many whole numbers lie between 9² and 10²?
  22. 22.What is 23²? =
  23. 23.A square garden has an area of 121 square m. How long is each side (in m)?
  24. 24.Which of these is a perfect square? (a) 968 (b) 996 (c) 961
  25. 25.A square garden has an area of 196 square m. How long is each side (in m)?
  26. 26.What is 51²? =
  27. 27.What is the smallest whole number by which 125 must be divided to get a perfect square?
  28. 28.What is 26²? =
  29. 29.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?
  30. 30.How many whole numbers lie between 31² and 32²?
  31. 31.A square garden has an area of 1521 square m. How long is each side (in m)?
  32. 32.How many whole numbers lie between 17² and 18²?
  33. 33.What is √3600? =
  34. 34.How many whole numbers lie between 12² and 13²?
  35. 35.Which of these is a perfect square? (a) 645 (b) 625 (c) 629
  36. 36.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)?
  37. 37.What is the smallest whole number by which 96 must be divided to get a perfect square?
  38. 38.How many whole numbers lie between 23² and 24²?
  39. 39.What is 35²? =
  40. 40.Which of these is a perfect square? (a) 214 (b) 199 (c) 196

Answer key

  1. 441
  2. 729
  3. 7
  4. 5041
  5. 42
  6. 36
  7. 484
  8. 22
  9. 57
  10. 85
  11. 9
  12. 3
  13. 841
  14. 3969
  15. 225
  16. 900
  17. 16
  18. 13
  19. 1089
  20. 8
  21. 18
  22. 529
  23. 11
  24. 961
  25. 14
  26. 2601
  27. 5
  28. 676
  29. 289
  30. 62
  31. 39
  32. 34
  33. 60
  34. 24
  35. 625
  36. 100
  37. 6
  38. 46
  39. 1225
  40. 196

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