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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 624 · 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 smallest whole number by which 1134 must be divided to get a perfect square?
  2. 2.What is 22²? =
  3. 3.How many whole numbers lie between 26² and 27²?
  4. 4.A square garden has an area of 25 square m. How long is each side (in m)?
  5. 5.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)?
  6. 6.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)?
  7. 7.What is 86²? =
  8. 8.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
  9. 9.Which of these is a perfect square? (a) 1089 (b) 1120 (c) 1098
  10. 10.A square garden has an area of 1849 square m. How long is each side (in m)?
  11. 11.What is √5041? =
  12. 12.Which of these is a perfect square? (a) 884 (b) 841 (c) 850
  13. 13.How many whole numbers lie between 14² and 15²?
  14. 14.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)?
  15. 15.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)?
  16. 16.A square garden has an area of 49 square m. How long is each side (in m)?
  17. 17.What is 93²? =
  18. 18.A square garden has an area of 2209 square m. How long is each side (in m)?
  19. 19.What is 90²? =
  20. 20.What is the smallest whole number by which 12 must be multiplied to get a perfect square?
  21. 21.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
  22. 22.What is 56²? =
  23. 23.What is √2601? =
  24. 24.What is √1521? =
  25. 25.A square garden has an area of 676 square m. How long is each side (in m)?
  26. 26.What is the smallest whole number by which 216 must be divided to get a perfect square?
  27. 27.Which of these is a perfect square? (a) 125 (b) 127 (c) 121
  28. 28.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
  29. 29.A square garden has an area of 361 square m. How long is each side (in m)?
  30. 30.What is the smallest whole number by which 32 must be divided to get a perfect square?
  31. 31.What is √1089? =
  32. 32.How many whole numbers lie between 45² and 46²?
  33. 33.What is the smallest whole number by which 75 must be multiplied to get a perfect square?
  34. 34.What is the smallest whole number by which 224 must be divided to get a perfect square?
  35. 35.What is 55²? =
  36. 36.How many whole numbers lie between 42² and 43²?
  37. 37.How many whole numbers lie between 49² and 50²?
  38. 38.A square garden has an area of 3481 square m. How long is each side (in m)?
  39. 39.What is the smallest whole number by which 891 must be multiplied to get a perfect square?
  40. 40.What is the smallest whole number by which 24 must be multiplied to get a perfect square?

Answer key

  1. 14
  2. 484
  3. 52
  4. 5
  5. 169
  6. 81
  7. 7396
  8. 64
  9. 1089
  10. 43
  11. 71
  12. 841
  13. 28
  14. 144
  15. 256
  16. 7
  17. 8649
  18. 47
  19. 8100
  20. 3
  21. 36
  22. 3136
  23. 51
  24. 39
  25. 26
  26. 6
  27. 121
  28. 25
  29. 19
  30. 2
  31. 33
  32. 90
  33. 3
  34. 14
  35. 3025
  36. 84
  37. 98
  38. 59
  39. 11
  40. 6

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