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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 322 · 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 sum of the first 9 odd numbers (1 + 3 + 5 + …)?
  2. 2.What is √2209? =
  3. 3.Which of these is a perfect square? (a) 1156 (b) 1182 (c) 1174
  4. 4.What is the smallest whole number by which 12 must be divided to get a perfect square?
  5. 5.How many whole numbers lie between 17² and 18²?
  6. 6.How many whole numbers lie between 39² and 40²?
  7. 7.A square garden has an area of 1444 square m. How long is each side (in m)?
  8. 8.What is the smallest whole number by which 117 must be divided to get a perfect square?
  9. 9.How many whole numbers lie between 9² and 10²?
  10. 10.What is √4356? =
  11. 11.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
  12. 12.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)?
  13. 13.What is √4096? =
  14. 14.Which of these is a perfect square? (a) 663 (b) 660 (c) 625
  15. 15.Which of these is a perfect square? (a) 190 (b) 169 (c) 189
  16. 16.What is the smallest whole number by which 80 must be divided to get a perfect square?
  17. 17.A square garden has an area of 49 square m. How long is each side (in m)?
  18. 18.What is √8649? =
  19. 19.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)?
  20. 20.A square garden has an area of 1296 square m. How long is each side (in m)?
  21. 21.What is the smallest whole number by which 162 must be divided to get a perfect square?
  22. 22.Which of these is a perfect square? (a) 471 (b) 476 (c) 441
  23. 23.How many whole numbers lie between 47² and 48²?
  24. 24.What is √2601? =
  25. 25.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)?
  26. 26.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)?
  27. 27.Which of these is a perfect square? (a) 249 (b) 235 (c) 225
  28. 28.What is the smallest whole number by which 192 must be multiplied to get a perfect square?
  29. 29.How many whole numbers lie between 18² and 19²?
  30. 30.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)?
  31. 31.How many whole numbers lie between 26² and 27²?
  32. 32.How many whole numbers lie between 10² and 11²?
  33. 33.What is 12²? =
  34. 34.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)?
  35. 35.A square garden has an area of 64 square m. How long is each side (in m)?
  36. 36.What is √8464? =
  37. 37.What is 37²? =
  38. 38.How many whole numbers lie between 35² and 36²?
  39. 39.What is √3025? =
  40. 40.How many whole numbers lie between 38² and 39²?

Answer key

  1. 81
  2. 47
  3. 1156
  4. 3
  5. 34
  6. 78
  7. 38
  8. 13
  9. 18
  10. 66
  11. 36
  12. 196
  13. 64
  14. 625
  15. 169
  16. 5
  17. 7
  18. 93
  19. 361
  20. 36
  21. 2
  22. 441
  23. 94
  24. 51
  25. 625
  26. 144
  27. 225
  28. 3
  29. 36
  30. 100
  31. 52
  32. 20
  33. 144
  34. 400
  35. 8
  36. 92
  37. 1369
  38. 70
  39. 55
  40. 76

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