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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 285 · 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 smallest whole number by which 294 must be multiplied to get a perfect square?
  2. 2.What is √7921? =
  3. 3.Which of these is a perfect square? (a) 169 (b) 172 (c) 191
  4. 4.What is √5776? =
  5. 5.A square garden has an area of 784 square m. How long is each side (in m)?
  6. 6.A square garden has an area of 1024 square m. How long is each side (in m)?
  7. 7.A square garden has an area of 81 square m. How long is each side (in m)?
  8. 8.What is the smallest whole number by which 117 must be multiplied to get a perfect square?
  9. 9.A square garden has an area of 1849 square m. How long is each side (in m)?
  10. 10.What is 53²? =
  11. 11.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)?
  12. 12.What is the smallest whole number by which 294 must be divided to get a perfect square?
  13. 13.Which of these is a perfect square? (a) 729 (b) 777 (c) 771
  14. 14.A square garden has an area of 144 square m. How long is each side (in m)?
  15. 15.A square garden has an area of 324 square m. How long is each side (in m)?
  16. 16.What is the smallest whole number by which 686 must be multiplied to get a perfect square?
  17. 17.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)?
  18. 18.Which of these is a perfect square? (a) 237 (b) 231 (c) 225
  19. 19.How many whole numbers lie between 7² and 8²?
  20. 20.What is 20²? =
  21. 21.What is √6889? =
  22. 22.How many whole numbers lie between 11² and 12²?
  23. 23.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)?
  24. 24.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
  25. 25.How many whole numbers lie between 16² and 17²?
  26. 26.What is √1681? =
  27. 27.What is √4761? =
  28. 28.What is the smallest whole number by which 243 must be multiplied to get a perfect square?
  29. 29.Which of these is a perfect square? (a) 841 (b) 871 (c) 894
  30. 30.How many whole numbers lie between 50² and 51²?
  31. 31.Which of these is a perfect square? (a) 342 (b) 324 (c) 331
  32. 32.How many whole numbers lie between 49² and 50²?
  33. 33.What is √1444? =
  34. 34.Which of these is a perfect square? (a) 1233 (b) 1225 (c) 1246
  35. 35.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)?
  36. 36.What is the smallest whole number by which 112 must be multiplied to get a perfect square?
  37. 37.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
  38. 38.What is √4225? =
  39. 39.How many whole numbers lie between 43² and 44²?
  40. 40.Which of these is a perfect square? (a) 1118 (b) 1099 (c) 1089

Answer key

  1. 6
  2. 89
  3. 169
  4. 76
  5. 28
  6. 32
  7. 9
  8. 13
  9. 43
  10. 2809
  11. 841
  12. 6
  13. 729
  14. 12
  15. 18
  16. 14
  17. 676
  18. 225
  19. 14
  20. 400
  21. 83
  22. 22
  23. 256
  24. 64
  25. 32
  26. 41
  27. 69
  28. 3
  29. 841
  30. 100
  31. 324
  32. 98
  33. 38
  34. 1225
  35. 400
  36. 7
  37. 49
  38. 65
  39. 86
  40. 1089

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