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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 709 · 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 69²? =
  2. 2.What is the smallest whole number by which 99 must be multiplied to get a perfect square?
  3. 3.Which of these is a perfect square? (a) 156 (b) 148 (c) 144
  4. 4.How many whole numbers lie between 40² and 41²?
  5. 5.What is 91²? =
  6. 6.How many whole numbers lie between 49² and 50²?
  7. 7.Which of these is a perfect square? (a) 1156 (b) 1166 (c) 1158
  8. 8.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)?
  9. 9.What is 15²? =
  10. 10.What is √961? =
  11. 11.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)?
  12. 12.Which of these is a perfect square? (a) 246 (b) 225 (c) 254
  13. 13.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)?
  14. 14.A square garden has an area of 2025 square m. How long is each side (in m)?
  15. 15.What is √121? =
  16. 16.What is √784? =
  17. 17.How many whole numbers lie between 22² and 23²?
  18. 18.What is √5184? =
  19. 19.What is 74²? =
  20. 20.What is 39²? =
  21. 21.Which of these is a perfect square? (a) 116 (b) 100 (c) 108
  22. 22.What is √6889? =
  23. 23.A square garden has an area of 841 square m. How long is each side (in m)?
  24. 24.A square garden has an area of 1296 square m. How long is each side (in m)?
  25. 25.What is the smallest whole number by which 405 must be multiplied to get a perfect square?
  26. 26.A square garden has an area of 1024 square m. How long is each side (in m)?
  27. 27.What is the smallest whole number by which 1053 must be multiplied to get a perfect square?
  28. 28.How many whole numbers lie between 47² and 48²?
  29. 29.A square garden has an area of 3600 square m. How long is each side (in m)?
  30. 30.What is 48²? =
  31. 31.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
  32. 32.What is √6400? =
  33. 33.A square garden has an area of 441 square m. How long is each side (in m)?
  34. 34.How many whole numbers lie between 27² and 28²?
  35. 35.What is 71²? =
  36. 36.A square garden has an area of 1849 square m. How long is each side (in m)?
  37. 37.How many whole numbers lie between 29² and 30²?
  38. 38.A square garden has an area of 400 square m. How long is each side (in m)?
  39. 39.A square garden has an area of 144 square m. How long is each side (in m)?
  40. 40.What is the smallest whole number by which 448 must be divided to get a perfect square?

Answer key

  1. 4761
  2. 11
  3. 144
  4. 80
  5. 8281
  6. 98
  7. 1156
  8. 169
  9. 225
  10. 31
  11. 576
  12. 225
  13. 676
  14. 45
  15. 11
  16. 28
  17. 44
  18. 72
  19. 5476
  20. 1521
  21. 100
  22. 83
  23. 29
  24. 36
  25. 5
  26. 32
  27. 13
  28. 94
  29. 60
  30. 2304
  31. 49
  32. 80
  33. 21
  34. 54
  35. 5041
  36. 43
  37. 58
  38. 20
  39. 12
  40. 7

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