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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 569 · 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 16² and 17²?
  2. 2.Which of these is a perfect square? (a) 293 (b) 289 (c) 294
  3. 3.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)?
  4. 4.How many whole numbers lie between 39² and 40²?
  5. 5.What is the smallest whole number by which 350 must be divided to get a perfect square?
  6. 6.A square garden has an area of 484 square m. How long is each side (in m)?
  7. 7.How many whole numbers lie between 32² and 33²?
  8. 8.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)?
  9. 9.What is √5041? =
  10. 10.What is √8649? =
  11. 11.A square garden has an area of 1225 square m. How long is each side (in m)?
  12. 12.A square garden has an area of 289 square m. How long is each side (in m)?
  13. 13.What is √1936? =
  14. 14.Which of these is a perfect square? (a) 539 (b) 529 (c) 537
  15. 15.How many whole numbers lie between 31² and 32²?
  16. 16.What is 42²? =
  17. 17.How many whole numbers lie between 40² and 41²?
  18. 18.What is √1521? =
  19. 19.A square garden has an area of 1764 square m. How long is each side (in m)?
  20. 20.How many whole numbers lie between 46² and 47²?
  21. 21.What is 71²? =
  22. 22.How many whole numbers lie between 50² and 51²?
  23. 23.How many whole numbers lie between 7² and 8²?
  24. 24.A square garden has an area of 441 square m. How long is each side (in m)?
  25. 25.What is √1764? =
  26. 26.What is 63²? =
  27. 27.What is √1089? =
  28. 28.A square garden has an area of 1849 square m. How long is each side (in m)?
  29. 29.Which of these is a perfect square? (a) 256 (b) 285 (c) 258
  30. 30.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)?
  31. 31.Which of these is a perfect square? (a) 1157 (b) 1156 (c) 1178
  32. 32.A square garden has an area of 2209 square m. How long is each side (in m)?
  33. 33.Which of these is a perfect square? (a) 1340 (b) 1296 (c) 1333
  34. 34.A square garden has an area of 841 square m. How long is each side (in m)?
  35. 35.Which of these is a perfect square? (a) 1102 (b) 1089 (c) 1104
  36. 36.Which of these is a perfect square? (a) 576 (b) 592 (c) 599
  37. 37.A square garden has an area of 2025 square m. How long is each side (in m)?
  38. 38.What is 36²? =
  39. 39.What is √7921? =
  40. 40.How many whole numbers lie between 13² and 14²?

Answer key

  1. 32
  2. 289
  3. 625
  4. 78
  5. 14
  6. 22
  7. 64
  8. 100
  9. 71
  10. 93
  11. 35
  12. 17
  13. 44
  14. 529
  15. 62
  16. 1764
  17. 80
  18. 39
  19. 42
  20. 92
  21. 5041
  22. 100
  23. 14
  24. 21
  25. 42
  26. 3969
  27. 33
  28. 43
  29. 256
  30. 484
  31. 1156
  32. 47
  33. 1296
  34. 29
  35. 1089
  36. 576
  37. 45
  38. 1296
  39. 89
  40. 26

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