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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 383 · 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 31² and 32²?
  2. 2.How many whole numbers lie between 6² and 7²?
  3. 3.How many whole numbers lie between 42² and 43²?
  4. 4.What is √841? =
  5. 5.What is 71²? =
  6. 6.What is 60²? =
  7. 7.Which of these is a perfect square? (a) 1111 (b) 1089 (c) 1090
  8. 8.What is the smallest whole number by which 72 must be divided to get a perfect square?
  9. 9.A square garden has an area of 729 square m. How long is each side (in m)?
  10. 10.What is √484? =
  11. 11.What is 76²? =
  12. 12.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
  13. 13.What is the smallest whole number by which 125 must be multiplied to get a perfect square?
  14. 14.Which of these is a perfect square? (a) 635 (b) 644 (c) 625
  15. 15.What is √4225? =
  16. 16.Which of these is a perfect square? (a) 609 (b) 618 (c) 576
  17. 17.Which of these is a perfect square? (a) 134 (b) 140 (c) 121
  18. 18.Which of these is a perfect square? (a) 119 (b) 100 (c) 115
  19. 19.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)?
  20. 20.Which of these is a perfect square? (a) 266 (b) 268 (c) 256
  21. 21.What is 21²? =
  22. 22.Which of these is a perfect square? (a) 196 (b) 223 (c) 199
  23. 23.How many whole numbers lie between 10² and 11²?
  24. 24.What is √2500? =
  25. 25.Which of these is a perfect square? (a) 379 (b) 397 (c) 361
  26. 26.What is 37²? =
  27. 27.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
  28. 28.What is 23²? =
  29. 29.Which of these is a perfect square? (a) 1197 (b) 1156 (c) 1176
  30. 30.What is the smallest whole number by which 28 must be multiplied to get a perfect square?
  31. 31.How many whole numbers lie between 12² and 13²?
  32. 32.How many whole numbers lie between 27² and 28²?
  33. 33.What is the smallest whole number by which 44 must be divided to get a perfect square?
  34. 34.A square garden has an area of 484 square m. How long is each side (in m)?
  35. 35.What is 55²? =
  36. 36.What is √4489? =
  37. 37.What is √576? =
  38. 38.Which of these is a perfect square? (a) 455 (b) 441 (c) 478
  39. 39.What is the smallest whole number by which 686 must be multiplied to get a perfect square?
  40. 40.How many whole numbers lie between 25² and 26²?

Answer key

  1. 62
  2. 12
  3. 84
  4. 29
  5. 5041
  6. 3600
  7. 1089
  8. 2
  9. 27
  10. 22
  11. 5776
  12. 36
  13. 5
  14. 625
  15. 65
  16. 576
  17. 121
  18. 100
  19. 441
  20. 256
  21. 441
  22. 196
  23. 20
  24. 50
  25. 361
  26. 1369
  27. 121
  28. 529
  29. 1156
  30. 7
  31. 24
  32. 54
  33. 11
  34. 22
  35. 3025
  36. 67
  37. 24
  38. 441
  39. 14
  40. 50

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