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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 75 · 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 √9604? =
  2. 2.What is √9409? =
  3. 3.What is √8649? =
  4. 4.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)?
  5. 5.How many whole numbers lie between 10² and 11²?
  6. 6.What is √1681? =
  7. 7.What is the smallest whole number by which 18 must be multiplied to get a perfect square?
  8. 8.What is √1764? =
  9. 9.A square garden has an area of 2916 square m. How long is each side (in m)?
  10. 10.Which of these is a perfect square? (a) 848 (b) 893 (c) 841
  11. 11.What is the smallest whole number by which 40 must be divided to get a perfect square?
  12. 12.A square garden has an area of 324 square m. How long is each side (in m)?
  13. 13.What is the smallest whole number by which 180 must be multiplied to get a perfect square?
  14. 14.What is √2209? =
  15. 15.What is 63²? =
  16. 16.What is 16²? =
  17. 17.How many whole numbers lie between 20² and 21²?
  18. 18.What is the smallest whole number by which 80 must be multiplied to get a perfect square?
  19. 19.A square garden has an area of 81 square m. How long is each side (in m)?
  20. 20.A square garden has an area of 121 square m. How long is each side (in m)?
  21. 21.What is the smallest whole number by which 45 must be divided to get a perfect square?
  22. 22.What is the smallest whole number by which 294 must be divided to get a perfect square?
  23. 23.What is the smallest whole number by which 54 must be divided to get a perfect square?
  24. 24.How many whole numbers lie between 16² and 17²?
  25. 25.What is √2704? =
  26. 26.Which of these is a perfect square? (a) 1004 (b) 1020 (c) 961
  27. 27.Which of these is a perfect square? (a) 827 (b) 786 (c) 784
  28. 28.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)?
  29. 29.How many whole numbers lie between 21² and 22²?
  30. 30.How many whole numbers lie between 50² and 51²?
  31. 31.A square garden has an area of 961 square m. How long is each side (in m)?
  32. 32.How many whole numbers lie between 8² and 9²?
  33. 33.A square garden has an area of 49 square m. How long is each side (in m)?
  34. 34.Which of these is a perfect square? (a) 601 (b) 576 (c) 609
  35. 35.Which of these is a perfect square? (a) 178 (b) 182 (c) 169
  36. 36.A square garden has an area of 1600 square m. How long is each side (in m)?
  37. 37.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
  38. 38.What is the smallest whole number by which 96 must be divided to get a perfect square?
  39. 39.How many whole numbers lie between 12² and 13²?
  40. 40.How many whole numbers lie between 28² and 29²?

Answer key

  1. 98
  2. 97
  3. 93
  4. 484
  5. 20
  6. 41
  7. 2
  8. 42
  9. 54
  10. 841
  11. 10
  12. 18
  13. 5
  14. 47
  15. 3969
  16. 256
  17. 40
  18. 5
  19. 9
  20. 11
  21. 5
  22. 6
  23. 6
  24. 32
  25. 52
  26. 961
  27. 784
  28. 729
  29. 42
  30. 100
  31. 31
  32. 16
  33. 7
  34. 576
  35. 169
  36. 40
  37. 64
  38. 6
  39. 24
  40. 56

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