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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 389 · 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.How many whole numbers lie between 36² and 37²?
  3. 3.What is 25²? =
  4. 4.What is 68²? =
  5. 5.What is √3136? =
  6. 6.How many whole numbers lie between 49² and 50²?
  7. 7.What is the smallest whole number by which 176 must be divided to get a perfect square?
  8. 8.What is the smallest whole number by which 960 must be divided to get a perfect square?
  9. 9.How many whole numbers lie between 34² and 35²?
  10. 10.What is √784? =
  11. 11.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)?
  12. 12.Which of these is a perfect square? (a) 698 (b) 676 (c) 709
  13. 13.What is 21²? =
  14. 14.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)?
  15. 15.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
  16. 16.Which of these is a perfect square? (a) 1225 (b) 1241 (c) 1230
  17. 17.How many whole numbers lie between 21² and 22²?
  18. 18.What is 33²? =
  19. 19.What is the smallest whole number by which 240 must be multiplied to get a perfect square?
  20. 20.Which of these is a perfect square? (a) 1521 (b) 1575 (c) 1589
  21. 21.What is the smallest whole number by which 125 must be multiplied to get a perfect square?
  22. 22.What is 88²? =
  23. 23.What is 22²? =
  24. 24.Which of these is a perfect square? (a) 324 (b) 340 (c) 348
  25. 25.What is the smallest whole number by which 704 must be multiplied to get a perfect square?
  26. 26.How many whole numbers lie between 39² and 40²?
  27. 27.What is √7744? =
  28. 28.What is 84²? =
  29. 29.Which of these is a perfect square? (a) 1205 (b) 1156 (c) 1203
  30. 30.What is 74²? =
  31. 31.How many whole numbers lie between 16² and 17²?
  32. 32.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)?
  33. 33.Which of these is a perfect square? (a) 264 (b) 278 (c) 256
  34. 34.How many whole numbers lie between 8² and 9²?
  35. 35.What is √841? =
  36. 36.Which of these is a perfect square? (a) 403 (b) 413 (c) 400
  37. 37.Which of these is a perfect square? (a) 1600 (b) 1611 (c) 1612
  38. 38.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)?
  39. 39.Which of these is a perfect square? (a) 114 (b) 100 (c) 115
  40. 40.What is √2025? =

Answer key

  1. 121
  2. 72
  3. 625
  4. 4624
  5. 56
  6. 98
  7. 11
  8. 15
  9. 68
  10. 28
  11. 169
  12. 676
  13. 441
  14. 144
  15. 25
  16. 1225
  17. 42
  18. 1089
  19. 15
  20. 1521
  21. 5
  22. 7744
  23. 484
  24. 324
  25. 11
  26. 78
  27. 88
  28. 7056
  29. 1156
  30. 5476
  31. 32
  32. 441
  33. 256
  34. 16
  35. 29
  36. 400
  37. 1600
  38. 361
  39. 100
  40. 45

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