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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 111 · 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.Which of these is a perfect square? (a) 1048 (b) 1024 (c) 1084
  2. 2.What is √121? =
  3. 3.What is the smallest whole number by which 250 must be multiplied to get a perfect square?
  4. 4.What is 27²? =
  5. 5.What is the smallest whole number by which 99 must be divided to get a perfect square?
  6. 6.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
  7. 7.How many whole numbers lie between 32² and 33²?
  8. 8.A square garden has an area of 441 square m. How long is each side (in m)?
  9. 9.How many whole numbers lie between 20² and 21²?
  10. 10.What is √3136? =
  11. 11.How many whole numbers lie between 37² and 38²?
  12. 12.What is 76²? =
  13. 13.Which of these is a perfect square? (a) 713 (b) 715 (c) 676
  14. 14.How many whole numbers lie between 48² and 49²?
  15. 15.What is 35²? =
  16. 16.How many whole numbers lie between 13² and 14²?
  17. 17.Which of these is a perfect square? (a) 900 (b) 948 (c) 908
  18. 18.What is √256? =
  19. 19.What is 28²? =
  20. 20.A square garden has an area of 400 square m. How long is each side (in m)?
  21. 21.Which of these is a perfect square? (a) 169 (b) 170 (c) 179
  22. 22.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)?
  23. 23.What is 26²? =
  24. 24.What is the smallest whole number by which 125 must be divided to get a perfect square?
  25. 25.Which of these is a perfect square? (a) 118 (b) 100 (c) 119
  26. 26.What is the smallest whole number by which 216 must be divided to get a perfect square?
  27. 27.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)?
  28. 28.What is √529? =
  29. 29.What is 17²? =
  30. 30.What is 94²? =
  31. 31.What is the smallest whole number by which 126 must be divided to get a perfect square?
  32. 32.What is the smallest whole number by which 243 must be divided to get a perfect square?
  33. 33.What is √3481? =
  34. 34.What is the smallest whole number by which 90 must be divided to get a perfect square?
  35. 35.How many whole numbers lie between 12² and 13²?
  36. 36.How many whole numbers lie between 43² and 44²?
  37. 37.What is the smallest whole number by which 375 must be multiplied to get a perfect square?
  38. 38.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)?
  39. 39.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)?
  40. 40.A square garden has an area of 784 square m. How long is each side (in m)?

Answer key

  1. 1024
  2. 11
  3. 10
  4. 729
  5. 11
  6. 121
  7. 64
  8. 21
  9. 40
  10. 56
  11. 74
  12. 5776
  13. 676
  14. 96
  15. 1225
  16. 26
  17. 900
  18. 16
  19. 784
  20. 20
  21. 169
  22. 841
  23. 676
  24. 5
  25. 100
  26. 6
  27. 100
  28. 23
  29. 289
  30. 8836
  31. 14
  32. 3
  33. 59
  34. 10
  35. 24
  36. 86
  37. 15
  38. 784
  39. 529
  40. 28

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