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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 668 · 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) 288 (b) 256 (c) 270
  2. 2.Which of these is a perfect square? (a) 289 (b) 319 (c) 295
  3. 3.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)?
  4. 4.How many whole numbers lie between 30² and 31²?
  5. 5.A square garden has an area of 784 square m. How long is each side (in m)?
  6. 6.Which of these is a perfect square? (a) 1079 (b) 1024 (c) 1075
  7. 7.What is 69²? =
  8. 8.Which of these is a perfect square? (a) 196 (b) 222 (c) 212
  9. 9.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)?
  10. 10.What is √6561? =
  11. 11.What is 61²? =
  12. 12.What is √7921? =
  13. 13.What is the smallest whole number by which 126 must be multiplied to get a perfect square?
  14. 14.What is 85²? =
  15. 15.How many whole numbers lie between 7² and 8²?
  16. 16.What is the smallest whole number by which 72 must be multiplied to get a perfect square?
  17. 17.What is √2601? =
  18. 18.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)?
  19. 19.What is 31²? =
  20. 20.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)?
  21. 21.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
  22. 22.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)?
  23. 23.What is √2025? =
  24. 24.How many whole numbers lie between 44² and 45²?
  25. 25.A square garden has an area of 3136 square m. How long is each side (in m)?
  26. 26.What is the smallest whole number by which 44 must be multiplied to get a perfect square?
  27. 27.How many whole numbers lie between 15² and 16²?
  28. 28.How many whole numbers lie between 49² and 50²?
  29. 29.A square garden has an area of 900 square m. How long is each side (in m)?
  30. 30.Which of these is a perfect square? (a) 160 (b) 144 (c) 148
  31. 31.What is √256? =
  32. 32.Which of these is a perfect square? (a) 126 (b) 121 (c) 143
  33. 33.What is the smallest whole number by which 224 must be divided to get a perfect square?
  34. 34.What is √3025? =
  35. 35.A square garden has an area of 1681 square m. How long is each side (in m)?
  36. 36.How many whole numbers lie between 9² and 10²?
  37. 37.What is 87²? =
  38. 38.What is √6724? =
  39. 39.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)?
  40. 40.A square garden has an area of 676 square m. How long is each side (in m)?

Answer key

  1. 256
  2. 289
  3. 676
  4. 60
  5. 28
  6. 1024
  7. 4761
  8. 196
  9. 841
  10. 81
  11. 3721
  12. 89
  13. 14
  14. 7225
  15. 14
  16. 2
  17. 51
  18. 900
  19. 961
  20. 144
  21. 121
  22. 100
  23. 45
  24. 88
  25. 56
  26. 11
  27. 30
  28. 98
  29. 30
  30. 144
  31. 16
  32. 121
  33. 14
  34. 55
  35. 41
  36. 18
  37. 7569
  38. 82
  39. 169
  40. 26

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