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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 601 · 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 26 odd numbers (1 + 3 + 5 + …)?
  2. 2.Which of these is a perfect square? (a) 176 (b) 178 (c) 169
  3. 3.Which of these is a perfect square? (a) 223 (b) 196 (c) 205
  4. 4.What is √6561? =
  5. 5.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)?
  6. 6.What is √2500? =
  7. 7.How many whole numbers lie between 26² and 27²?
  8. 8.Which of these is a perfect square? (a) 225 (b) 239 (c) 242
  9. 9.What is 34²? =
  10. 10.What is √4225? =
  11. 11.What is the smallest whole number by which 56 must be divided to get a perfect square?
  12. 12.What is 91²? =
  13. 13.What is the smallest whole number by which 27 must be multiplied to get a perfect square?
  14. 14.What is the smallest whole number by which 112 must be multiplied to get a perfect square?
  15. 15.A square garden has an area of 1444 square m. How long is each side (in m)?
  16. 16.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)?
  17. 17.A square garden has an area of 900 square m. How long is each side (in m)?
  18. 18.What is 68²? =
  19. 19.Which of these is a perfect square? (a) 640 (b) 646 (c) 625
  20. 20.A square garden has an area of 961 square m. How long is each side (in m)?
  21. 21.How many whole numbers lie between 47² and 48²?
  22. 22.What is √7921? =
  23. 23.What is √2116? =
  24. 24.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)?
  25. 25.What is √1521? =
  26. 26.What is the smallest whole number by which 108 must be divided to get a perfect square?
  27. 27.Which of these is a perfect square? (a) 1102 (b) 1104 (c) 1089
  28. 28.Which of these is a perfect square? (a) 121 (b) 137 (c) 128
  29. 29.What is 17²? =
  30. 30.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)?
  31. 31.How many whole numbers lie between 41² and 42²?
  32. 32.How many whole numbers lie between 13² and 14²?
  33. 33.How many whole numbers lie between 31² and 32²?
  34. 34.What is 13²? =
  35. 35.What is √784? =
  36. 36.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)?
  37. 37.What is 31²? =
  38. 38.What is √9409? =
  39. 39.Which of these is a perfect square? (a) 269 (b) 267 (c) 256
  40. 40.What is 94²? =

Answer key

  1. 676
  2. 169
  3. 196
  4. 81
  5. 361
  6. 50
  7. 52
  8. 225
  9. 1156
  10. 65
  11. 14
  12. 8281
  13. 3
  14. 7
  15. 38
  16. 225
  17. 30
  18. 4624
  19. 625
  20. 31
  21. 94
  22. 89
  23. 46
  24. 625
  25. 39
  26. 3
  27. 1089
  28. 121
  29. 289
  30. 900
  31. 82
  32. 26
  33. 62
  34. 169
  35. 28
  36. 196
  37. 961
  38. 97
  39. 256
  40. 8836

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