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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 539 · 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 49 square m. How long is each side (in m)?
  2. 2.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)?
  3. 3.What is the smallest whole number by which 350 must be divided to get a perfect square?
  4. 4.What is 65²? =
  5. 5.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
  6. 6.How many whole numbers lie between 19² and 20²?
  7. 7.What is the smallest whole number by which 275 must be multiplied to get a perfect square?
  8. 8.A square garden has an area of 1024 square m. How long is each side (in m)?
  9. 9.Which of these is a perfect square? (a) 676 (b) 689 (c) 713
  10. 10.What is √3969? =
  11. 11.Which of these is a perfect square? (a) 187 (b) 180 (c) 169
  12. 12.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)?
  13. 13.What is √8836? =
  14. 14.How many whole numbers lie between 5² and 6²?
  15. 15.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)?
  16. 16.What is √3600? =
  17. 17.How many whole numbers lie between 43² and 44²?
  18. 18.What is √4900? =
  19. 19.What is the smallest whole number by which 490 must be multiplied to get a perfect square?
  20. 20.What is √1024? =
  21. 21.What is 18²? =
  22. 22.A square garden has an area of 484 square m. How long is each side (in m)?
  23. 23.What is 35²? =
  24. 24.A square garden has an area of 1936 square m. How long is each side (in m)?
  25. 25.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
  26. 26.A square garden has an area of 81 square m. How long is each side (in m)?
  27. 27.How many whole numbers lie between 23² and 24²?
  28. 28.What is 11²? =
  29. 29.Which of these is a perfect square? (a) 961 (b) 981 (c) 971
  30. 30.What is √400? =
  31. 31.A square garden has an area of 2304 square m. How long is each side (in m)?
  32. 32.How many whole numbers lie between 35² and 36²?
  33. 33.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
  34. 34.What is the smallest whole number by which 180 must be multiplied to get a perfect square?
  35. 35.What is √2601? =
  36. 36.How many whole numbers lie between 20² and 21²?
  37. 37.What is the smallest whole number by which 50 must be multiplied to get a perfect square?
  38. 38.Which of these is a perfect square? (a) 1089 (b) 1153 (c) 1091
  39. 39.What is √2809? =
  40. 40.How many whole numbers lie between 27² and 28²?

Answer key

  1. 7
  2. 225
  3. 14
  4. 4225
  5. 36
  6. 38
  7. 11
  8. 32
  9. 676
  10. 63
  11. 169
  12. 361
  13. 94
  14. 10
  15. 100
  16. 60
  17. 86
  18. 70
  19. 10
  20. 32
  21. 324
  22. 22
  23. 1225
  24. 44
  25. 49
  26. 9
  27. 46
  28. 121
  29. 961
  30. 20
  31. 48
  32. 70
  33. 64
  34. 5
  35. 51
  36. 40
  37. 2
  38. 1089
  39. 53
  40. 54

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