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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 508 · 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.A square garden has an area of 2116 square m. How long is each side (in m)?
  2. 2.Which of these is a perfect square? (a) 479 (b) 483 (c) 441
  3. 3.Which of these is a perfect square? (a) 343 (b) 324 (c) 354
  4. 4.What is the smallest whole number by which 128 must be divided to get a perfect square?
  5. 5.How many whole numbers lie between 44² and 45²?
  6. 6.What is the smallest whole number by which 44 must be multiplied to get a perfect square?
  7. 7.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)?
  8. 8.How many whole numbers lie between 33² and 34²?
  9. 9.Which of these is a perfect square? (a) 225 (b) 230 (c) 231
  10. 10.What is 55²? =
  11. 11.What is the smallest whole number by which 32 must be multiplied to get a perfect square?
  12. 12.What is 88²? =
  13. 13.What is the smallest whole number by which 540 must be divided to get a perfect square?
  14. 14.Which of these is a perfect square? (a) 293 (b) 289 (c) 310
  15. 15.What is the smallest whole number by which 20 must be multiplied to get a perfect square?
  16. 16.How many whole numbers lie between 43² and 44²?
  17. 17.How many whole numbers lie between 25² and 26²?
  18. 18.How many whole numbers lie between 10² and 11²?
  19. 19.How many whole numbers lie between 12² and 13²?
  20. 20.What is √4225? =
  21. 21.What is 74²? =
  22. 22.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)?
  23. 23.A square garden has an area of 3136 square m. How long is each side (in m)?
  24. 24.What is 77²? =
  25. 25.A square garden has an area of 1849 square m. How long is each side (in m)?
  26. 26.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)?
  27. 27.A square garden has an area of 1600 square m. How long is each side (in m)?
  28. 28.What is √3969? =
  29. 29.Which of these is a perfect square? (a) 1241 (b) 1225 (c) 1228
  30. 30.How many whole numbers lie between 30² and 31²?
  31. 31.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?
  32. 32.What is √5625? =
  33. 33.How many whole numbers lie between 19² and 20²?
  34. 34.What is √625? =
  35. 35.Which of these is a perfect square? (a) 121 (b) 125 (c) 122
  36. 36.What is 23²? =
  37. 37.How many whole numbers lie between 41² and 42²?
  38. 38.What is √144? =
  39. 39.What is 51²? =
  40. 40.How many whole numbers lie between 37² and 38²?

Answer key

  1. 46
  2. 441
  3. 324
  4. 2
  5. 88
  6. 11
  7. 225
  8. 66
  9. 225
  10. 3025
  11. 2
  12. 7744
  13. 15
  14. 289
  15. 5
  16. 86
  17. 50
  18. 20
  19. 24
  20. 65
  21. 5476
  22. 841
  23. 56
  24. 5929
  25. 43
  26. 144
  27. 40
  28. 63
  29. 1225
  30. 60
  31. 289
  32. 75
  33. 38
  34. 25
  35. 121
  36. 529
  37. 82
  38. 12
  39. 2601
  40. 74

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