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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 104 · 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 6² and 7²?
  2. 2.What is 41²? =
  3. 3.Which of these is a perfect square? (a) 172 (b) 169 (c) 186
  4. 4.A square garden has an area of 3364 square m. How long is each side (in m)?
  5. 5.How many whole numbers lie between 44² and 45²?
  6. 6.Which of these is a perfect square? (a) 592 (b) 594 (c) 576
  7. 7.What is √5041? =
  8. 8.Which of these is a perfect square? (a) 100 (b) 108 (c) 115
  9. 9.Which of these is a perfect square? (a) 377 (b) 361 (c) 391
  10. 10.What is the smallest whole number by which 99 must be multiplied to get a perfect square?
  11. 11.A square garden has an area of 3249 square m. How long is each side (in m)?
  12. 12.A square garden has an area of 81 square m. How long is each side (in m)?
  13. 13.How many whole numbers lie between 19² and 20²?
  14. 14.What is 53²? =
  15. 15.What is 59²? =
  16. 16.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)?
  17. 17.What is 66²? =
  18. 18.What is √256? =
  19. 19.Which of these is a perfect square? (a) 414 (b) 400 (c) 430
  20. 20.Which of these is a perfect square? (a) 256 (b) 264 (c) 276
  21. 21.What is √2916? =
  22. 22.What is 15²? =
  23. 23.What is √4624? =
  24. 24.Which of these is a perfect square? (a) 289 (b) 306 (c) 318
  25. 25.What is the smallest whole number by which 135 must be divided to get a perfect square?
  26. 26.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)?
  27. 27.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)?
  28. 28.What is √4225? =
  29. 29.What is 63²? =
  30. 30.What is √4489? =
  31. 31.How many whole numbers lie between 26² and 27²?
  32. 32.How many whole numbers lie between 24² and 25²?
  33. 33.What is the smallest whole number by which 45 must be divided 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 √3600? =
  36. 36.What is 39²? =
  37. 37.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?
  38. 38.What is √1600? =
  39. 39.How many whole numbers lie between 5² and 6²?
  40. 40.Which of these is a perfect square? (a) 1260 (b) 1226 (c) 1225

Answer key

  1. 12
  2. 1681
  3. 169
  4. 58
  5. 88
  6. 576
  7. 71
  8. 100
  9. 361
  10. 11
  11. 57
  12. 9
  13. 38
  14. 2809
  15. 3481
  16. 81
  17. 4356
  18. 16
  19. 400
  20. 256
  21. 54
  22. 225
  23. 68
  24. 289
  25. 15
  26. 841
  27. 196
  28. 65
  29. 3969
  30. 67
  31. 52
  32. 48
  33. 5
  34. 21
  35. 60
  36. 1521
  37. 289
  38. 40
  39. 10
  40. 1225

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