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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 12 · 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 11 odd numbers (1 + 3 + 5 + …)?
  2. 2.Which of these is a perfect square? (a) 1593 (b) 1528 (c) 1521
  3. 3.What is √7569? =
  4. 4.A square garden has an area of 729 square m. How long is each side (in m)?
  5. 5.Which of these is a perfect square? (a) 218 (b) 196 (c) 217
  6. 6.What is √900? =
  7. 7.How many whole numbers lie between 11² and 12²?
  8. 8.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)?
  9. 9.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)?
  10. 10.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)?
  11. 11.A square garden has an area of 3025 square m. How long is each side (in m)?
  12. 12.A square garden has an area of 1296 square m. How long is each side (in m)?
  13. 13.What is the smallest whole number by which 448 must be divided to get a perfect square?
  14. 14.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)?
  15. 15.Which of these is a perfect square? (a) 251 (b) 249 (c) 225
  16. 16.What is the smallest whole number by which 98 must be divided to get a perfect square?
  17. 17.How many whole numbers lie between 42² and 43²?
  18. 18.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)?
  19. 19.Which of these is a perfect square? (a) 121 (b) 127 (c) 141
  20. 20.Which of these is a perfect square? (a) 102 (b) 105 (c) 100
  21. 21.A square garden has an area of 169 square m. How long is each side (in m)?
  22. 22.What is √289? =
  23. 23.What is 19²? =
  24. 24.How many whole numbers lie between 16² and 17²?
  25. 25.What is √2916? =
  26. 26.What is 35²? =
  27. 27.What is the smallest whole number by which 735 must be multiplied to get a perfect square?
  28. 28.What is the smallest whole number by which 44 must be divided to get a perfect square?
  29. 29.How many whole numbers lie between 26² and 27²?
  30. 30.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)?
  31. 31.Which of these is a perfect square? (a) 1198 (b) 1156 (c) 1161
  32. 32.What is the smallest whole number by which 112 must be multiplied to get a perfect square?
  33. 33.Which of these is a perfect square? (a) 729 (b) 761 (c) 736
  34. 34.What is √3600? =
  35. 35.How many whole numbers lie between 31² and 32²?
  36. 36.How many whole numbers lie between 9² and 10²?
  37. 37.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)?
  38. 38.What is √4624? =
  39. 39.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)?
  40. 40.What is the smallest whole number by which 40 must be divided to get a perfect square?

Answer key

  1. 121
  2. 1521
  3. 87
  4. 27
  5. 196
  6. 30
  7. 22
  8. 625
  9. 100
  10. 81
  11. 55
  12. 36
  13. 7
  14. 225
  15. 225
  16. 2
  17. 84
  18. 576
  19. 121
  20. 100
  21. 13
  22. 17
  23. 361
  24. 32
  25. 54
  26. 1225
  27. 15
  28. 11
  29. 52
  30. 144
  31. 1156
  32. 7
  33. 729
  34. 60
  35. 62
  36. 18
  37. 900
  38. 68
  39. 529
  40. 10

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