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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 137 · 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 400 square m. How long is each side (in m)?
  2. 2.Which of these is a perfect square? (a) 199 (b) 196 (c) 203
  3. 3.What is √5625? =
  4. 4.What is √2704? =
  5. 5.How many whole numbers lie between 49² and 50²?
  6. 6.Which of these is a perfect square? (a) 1156 (b) 1167 (c) 1210
  7. 7.Which of these is a perfect square? (a) 1539 (b) 1587 (c) 1521
  8. 8.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)?
  9. 9.A square garden has an area of 2209 square m. How long is each side (in m)?
  10. 10.What is √576? =
  11. 11.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)?
  12. 12.How many whole numbers lie between 21² and 22²?
  13. 13.What is √5929? =
  14. 14.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)?
  15. 15.What is 43²? =
  16. 16.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
  17. 17.How many whole numbers lie between 20² and 21²?
  18. 18.A square garden has an area of 25 square m. How long is each side (in m)?
  19. 19.What is the smallest whole number by which 12 must be multiplied to get a perfect square?
  20. 20.What is 32²? =
  21. 21.How many whole numbers lie between 19² and 20²?
  22. 22.How many whole numbers lie between 31² and 32²?
  23. 23.What is √3600? =
  24. 24.Which of these is a perfect square? (a) 387 (b) 390 (c) 361
  25. 25.What is 62²? =
  26. 26.Which of these is a perfect square? (a) 132 (b) 121 (c) 127
  27. 27.What is the smallest whole number by which 208 must be divided to get a perfect square?
  28. 28.What is 20²? =
  29. 29.How many whole numbers lie between 5² and 6²?
  30. 30.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)?
  31. 31.A square garden has an area of 3025 square m. How long is each side (in m)?
  32. 32.A square garden has an area of 1681 square m. How long is each side (in m)?
  33. 33.A square garden has an area of 784 square m. How long is each side (in m)?
  34. 34.What is 30²? =
  35. 35.How many whole numbers lie between 44² and 45²?
  36. 36.Which of these is a perfect square? (a) 484 (b) 486 (c) 525
  37. 37.A square garden has an area of 225 square m. How long is each side (in m)?
  38. 38.How many whole numbers lie between 50² and 51²?
  39. 39.How many whole numbers lie between 27² and 28²?
  40. 40.What is 94²? =

Answer key

  1. 20
  2. 196
  3. 75
  4. 52
  5. 98
  6. 1156
  7. 1521
  8. 100
  9. 47
  10. 24
  11. 529
  12. 42
  13. 77
  14. 900
  15. 1849
  16. 64
  17. 40
  18. 5
  19. 3
  20. 1024
  21. 38
  22. 62
  23. 60
  24. 361
  25. 3844
  26. 121
  27. 13
  28. 400
  29. 10
  30. 81
  31. 55
  32. 41
  33. 28
  34. 900
  35. 88
  36. 484
  37. 15
  38. 100
  39. 54
  40. 8836

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