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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 558 · 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 23² and 24²?
  2. 2.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)?
  3. 3.What is the smallest whole number by which 490 must be multiplied to get a perfect square?
  4. 4.What is the smallest whole number by which 96 must be divided to get a perfect square?
  5. 5.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
  6. 6.A square garden has an area of 81 square m. How long is each side (in m)?
  7. 7.What is 54²? =
  8. 8.What is the smallest whole number by which 135 must be multiplied to get a perfect square?
  9. 9.What is the smallest whole number by which 637 must be divided to get a perfect square?
  10. 10.A square garden has an area of 1444 square m. How long is each side (in m)?
  11. 11.What is √8836? =
  12. 12.How many whole numbers lie between 48² and 49²?
  13. 13.How many whole numbers lie between 35² and 36²?
  14. 14.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)?
  15. 15.How many whole numbers lie between 33² and 34²?
  16. 16.What is the smallest whole number by which 320 must be divided to get a perfect square?
  17. 17.How many whole numbers lie between 39² and 40²?
  18. 18.What is 47²? =
  19. 19.Which of these is a perfect square? (a) 100 (b) 112 (c) 118
  20. 20.A square garden has an area of 3136 square m. How long is each side (in m)?
  21. 21.What is √1369? =
  22. 22.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)?
  23. 23.What is the smallest whole number by which 20 must be multiplied to get a perfect square?
  24. 24.What is √5929? =
  25. 25.What is √1444? =
  26. 26.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)?
  27. 27.A square garden has an area of 1296 square m. How long is each side (in m)?
  28. 28.What is √8464? =
  29. 29.How many whole numbers lie between 12² and 13²?
  30. 30.Which of these is a perfect square? (a) 1156 (b) 1175 (c) 1212
  31. 31.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)?
  32. 32.What is √484? =
  33. 33.What is 12²? =
  34. 34.How many whole numbers lie between 31² and 32²?
  35. 35.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
  36. 36.What is √3025? =
  37. 37.What is √441? =
  38. 38.A square garden has an area of 2401 square m. How long is each side (in m)?
  39. 39.A square garden has an area of 169 square m. How long is each side (in m)?
  40. 40.What is the smallest whole number by which 504 must be multiplied to get a perfect square?

Answer key

  1. 46
  2. 144
  3. 10
  4. 6
  5. 121
  6. 9
  7. 2916
  8. 15
  9. 13
  10. 38
  11. 94
  12. 96
  13. 70
  14. 196
  15. 66
  16. 5
  17. 78
  18. 2209
  19. 100
  20. 56
  21. 37
  22. 441
  23. 5
  24. 77
  25. 38
  26. 625
  27. 36
  28. 92
  29. 24
  30. 1156
  31. 841
  32. 22
  33. 144
  34. 62
  35. 64
  36. 55
  37. 21
  38. 49
  39. 13
  40. 14

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