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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 582 · 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 √6400? =
  2. 2.How many whole numbers lie between 38² and 39²?
  3. 3.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?
  4. 4.A square garden has an area of 2116 square m. How long is each side (in m)?
  5. 5.What is 41²? =
  6. 6.What is 13²? =
  7. 7.What is √5041? =
  8. 8.Which of these is a perfect square? (a) 1251 (b) 1255 (c) 1225
  9. 9.A square garden has an area of 100 square m. How long is each side (in m)?
  10. 10.What is the smallest whole number by which 54 must be multiplied to get a perfect square?
  11. 11.What is the smallest whole number by which 160 must be multiplied to get a perfect square?
  12. 12.How many whole numbers lie between 37² and 38²?
  13. 13.What is 25²? =
  14. 14.What is √9216? =
  15. 15.A square garden has an area of 3364 square m. How long is each side (in m)?
  16. 16.A square garden has an area of 289 square m. How long is each side (in m)?
  17. 17.How many whole numbers lie between 27² and 28²?
  18. 18.How many whole numbers lie between 8² and 9²?
  19. 19.Which of these is a perfect square? (a) 789 (b) 784 (c) 800
  20. 20.What is √6724? =
  21. 21.A square garden has an area of 1521 square m. How long is each side (in m)?
  22. 22.What is √729? =
  23. 23.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
  24. 24.A square garden has an area of 2025 square m. How long is each side (in m)?
  25. 25.What is the smallest whole number by which 175 must be multiplied to get a perfect square?
  26. 26.What is the smallest whole number by which 32 must be divided to get a perfect square?
  27. 27.Which of these is a perfect square? (a) 256 (b) 258 (c) 275
  28. 28.What is the smallest whole number by which 540 must be multiplied to get a perfect square?
  29. 29.What is 20²? =
  30. 30.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)?
  31. 31.How many whole numbers lie between 46² and 47²?
  32. 32.What is √4356? =
  33. 33.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
  34. 34.What is 95²? =
  35. 35.A square garden has an area of 484 square m. How long is each side (in m)?
  36. 36.How many whole numbers lie between 48² and 49²?
  37. 37.What is the smallest whole number by which 125 must be divided to get a perfect square?
  38. 38.What is 86²? =
  39. 39.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)?
  40. 40.What is √8649? =

Answer key

  1. 80
  2. 76
  3. 289
  4. 46
  5. 1681
  6. 169
  7. 71
  8. 1225
  9. 10
  10. 6
  11. 10
  12. 74
  13. 625
  14. 96
  15. 58
  16. 17
  17. 54
  18. 16
  19. 784
  20. 82
  21. 39
  22. 27
  23. 25
  24. 45
  25. 7
  26. 2
  27. 256
  28. 15
  29. 400
  30. 441
  31. 92
  32. 66
  33. 121
  34. 9025
  35. 22
  36. 96
  37. 5
  38. 7396
  39. 484
  40. 93

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