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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 457 · 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) 674 (b) 628 (c) 625
  2. 2.Which of these is a perfect square? (a) 792 (b) 784 (c) 817
  3. 3.How many whole numbers lie between 8² and 9²?
  4. 4.A square garden has an area of 529 square m. How long is each side (in m)?
  5. 5.What is the smallest whole number by which 24 must be divided to get a perfect square?
  6. 6.What is √7921? =
  7. 7.A square garden has an area of 64 square m. How long is each side (in m)?
  8. 8.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)?
  9. 9.Which of these is a perfect square? (a) 772 (b) 732 (c) 729
  10. 10.What is 32²? =
  11. 11.What is the smallest whole number by which 128 must be multiplied to get a perfect square?
  12. 12.What is √8100? =
  13. 13.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)?
  14. 14.What is 50²? =
  15. 15.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)?
  16. 16.What is √225? =
  17. 17.What is √2209? =
  18. 18.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
  19. 19.How many whole numbers lie between 43² and 44²?
  20. 20.How many whole numbers lie between 23² and 24²?
  21. 21.What is the smallest whole number by which 45 must be multiplied to get a perfect square?
  22. 22.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)?
  23. 23.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)?
  24. 24.Which of these is a perfect square? (a) 364 (b) 361 (c) 379
  25. 25.What is √7569? =
  26. 26.How many whole numbers lie between 9² and 10²?
  27. 27.What is √784? =
  28. 28.What is √5929? =
  29. 29.What is √8281? =
  30. 30.How many whole numbers lie between 24² and 25²?
  31. 31.What is the smallest whole number by which 20 must be divided to get a perfect square?
  32. 32.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)?
  33. 33.Which of these is a perfect square? (a) 194 (b) 181 (c) 169
  34. 34.A square garden has an area of 441 square m. How long is each side (in m)?
  35. 35.How many whole numbers lie between 14² and 15²?
  36. 36.What is √4225? =
  37. 37.Which of these is a perfect square? (a) 121 (b) 127 (c) 139
  38. 38.What is 30²? =
  39. 39.What is 56²? =
  40. 40.What is the smallest whole number by which 250 must be divided to get a perfect square?

Answer key

  1. 625
  2. 784
  3. 16
  4. 23
  5. 6
  6. 89
  7. 8
  8. 529
  9. 729
  10. 1024
  11. 2
  12. 90
  13. 484
  14. 2500
  15. 196
  16. 15
  17. 47
  18. 49
  19. 86
  20. 46
  21. 5
  22. 676
  23. 100
  24. 361
  25. 87
  26. 18
  27. 28
  28. 77
  29. 91
  30. 48
  31. 5
  32. 225
  33. 169
  34. 21
  35. 28
  36. 65
  37. 121
  38. 900
  39. 3136
  40. 10

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