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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 56 · 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 84²? =
  2. 2.What is 39²? =
  3. 3.Which of these is a perfect square? (a) 824 (b) 784 (c) 835
  4. 4.How many whole numbers lie between 15² and 16²?
  5. 5.What is √1600? =
  6. 6.What is 66²? =
  7. 7.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)?
  8. 8.What is 34²? =
  9. 9.How many whole numbers lie between 8² and 9²?
  10. 10.What is √2304? =
  11. 11.How many whole numbers lie between 42² and 43²?
  12. 12.What is √9801? =
  13. 13.How many whole numbers lie between 9² and 10²?
  14. 14.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)?
  15. 15.What is √1225? =
  16. 16.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
  17. 17.What is 71²? =
  18. 18.Which of these is a perfect square? (a) 183 (b) 179 (c) 169
  19. 19.What is √8649? =
  20. 20.A square garden has an area of 289 square m. How long is each side (in m)?
  21. 21.What is the smallest whole number by which 128 must be multiplied to get a perfect square?
  22. 22.What is √9025? =
  23. 23.What is 50²? =
  24. 24.What is 99²? =
  25. 25.What is the smallest whole number by which 162 must be divided to get a perfect square?
  26. 26.What is 27²? =
  27. 27.Which of these is a perfect square? (a) 287 (b) 256 (c) 274
  28. 28.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)?
  29. 29.What is √1369? =
  30. 30.Which of these is a perfect square? (a) 1534 (b) 1521 (c) 1564
  31. 31.What is √8464? =
  32. 32.What is √8100? =
  33. 33.A square garden has an area of 900 square m. How long is each side (in m)?
  34. 34.What is 53²? =
  35. 35.Which of these is a perfect square? (a) 900 (b) 927 (c) 901
  36. 36.A square garden has an area of 2025 square m. How long is each side (in m)?
  37. 37.How many whole numbers lie between 6² and 7²?
  38. 38.Which of these is a perfect square? (a) 1156 (b) 1199 (c) 1207
  39. 39.How many whole numbers lie between 36² and 37²?
  40. 40.Which of these is a perfect square? (a) 681 (b) 698 (c) 676

Answer key

  1. 7056
  2. 1521
  3. 784
  4. 30
  5. 40
  6. 4356
  7. 784
  8. 1156
  9. 16
  10. 48
  11. 84
  12. 99
  13. 18
  14. 529
  15. 35
  16. 121
  17. 5041
  18. 169
  19. 93
  20. 17
  21. 2
  22. 95
  23. 2500
  24. 9801
  25. 2
  26. 729
  27. 256
  28. 144
  29. 37
  30. 1521
  31. 92
  32. 90
  33. 30
  34. 2809
  35. 900
  36. 45
  37. 12
  38. 1156
  39. 72
  40. 676

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