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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 660 · 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.Which of these is a perfect square? (a) 126 (b) 121 (c) 138
  2. 2.How many whole numbers lie between 28² and 29²?
  3. 3.What is 13²? =
  4. 4.A square garden has an area of 2025 square m. How long is each side (in m)?
  5. 5.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)?
  6. 6.How many whole numbers lie between 17² and 18²?
  7. 7.What is 49²? =
  8. 8.How many whole numbers lie between 30² and 31²?
  9. 9.How many whole numbers lie between 35² and 36²?
  10. 10.What is 33²? =
  11. 11.What is the smallest whole number by which 343 must be multiplied to get a perfect square?
  12. 12.A square garden has an area of 1225 square m. How long is each side (in m)?
  13. 13.What is 46²? =
  14. 14.Which of these is a perfect square? (a) 995 (b) 1020 (c) 961
  15. 15.What is √9801? =
  16. 16.What is 16²? =
  17. 17.What is √8649? =
  18. 18.What is 24²? =
  19. 19.How many whole numbers lie between 12² and 13²?
  20. 20.What is 87²? =
  21. 21.What is the smallest whole number by which 250 must be multiplied to get a perfect square?
  22. 22.What is √3969? =
  23. 23.What is √784? =
  24. 24.What is √4356? =
  25. 25.What is the smallest whole number by which 240 must be multiplied to get a perfect square?
  26. 26.What is √3364? =
  27. 27.A square garden has an area of 2401 square m. How long is each side (in m)?
  28. 28.What is √1600? =
  29. 29.What is √196? =
  30. 30.What is the smallest whole number by which 98 must be multiplied to get a perfect square?
  31. 31.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
  32. 32.What is 58²? =
  33. 33.What is √3721? =
  34. 34.How many whole numbers lie between 23² and 24²?
  35. 35.Which of these is a perfect square? (a) 873 (b) 841 (c) 883
  36. 36.What is √2500? =
  37. 37.Which of these is a perfect square? (a) 554 (b) 530 (c) 529
  38. 38.A square garden has an area of 64 square m. How long is each side (in m)?
  39. 39.Which of these is a perfect square? (a) 1662 (b) 1658 (c) 1600
  40. 40.Which of these is a perfect square? (a) 1332 (b) 1296 (c) 1320

Answer key

  1. 121
  2. 56
  3. 169
  4. 45
  5. 144
  6. 34
  7. 2401
  8. 60
  9. 70
  10. 1089
  11. 7
  12. 35
  13. 2116
  14. 961
  15. 99
  16. 256
  17. 93
  18. 576
  19. 24
  20. 7569
  21. 10
  22. 63
  23. 28
  24. 66
  25. 15
  26. 58
  27. 49
  28. 40
  29. 14
  30. 2
  31. 49
  32. 3364
  33. 61
  34. 46
  35. 841
  36. 50
  37. 529
  38. 8
  39. 1600
  40. 1296

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