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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 479 · 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) 584 (b) 576 (c) 582
  2. 2.What is 94²? =
  3. 3.What is the smallest whole number by which 486 must be multiplied to get a perfect square?
  4. 4.How many whole numbers lie between 25² and 26²?
  5. 5.How many whole numbers lie between 14² and 15²?
  6. 6.Which of these is a perfect square? (a) 784 (b) 823 (c) 833
  7. 7.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)?
  8. 8.What is √784? =
  9. 9.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
  10. 10.Which of these is a perfect square? (a) 769 (b) 777 (c) 729
  11. 11.Which of these is a perfect square? (a) 149 (b) 144 (c) 164
  12. 12.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)?
  13. 13.What is the smallest whole number by which 12 must be multiplied to get a perfect square?
  14. 14.How many whole numbers lie between 10² and 11²?
  15. 15.What is the smallest whole number by which 98 must be multiplied to get a perfect square?
  16. 16.What is √5184? =
  17. 17.What is the smallest whole number by which 72 must be multiplied to get a perfect square?
  18. 18.What is the smallest whole number by which 175 must be divided to get a perfect square?
  19. 19.How many whole numbers lie between 18² and 19²?
  20. 20.What is √6889? =
  21. 21.Which of these is a perfect square? (a) 1089 (b) 1149 (c) 1098
  22. 22.What is √7569? =
  23. 23.Which of these is a perfect square? (a) 355 (b) 358 (c) 324
  24. 24.Which of these is a perfect square? (a) 958 (b) 900 (c) 930
  25. 25.What is the smallest whole number by which 12 must be divided to get a perfect square?
  26. 26.What is √3136? =
  27. 27.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)?
  28. 28.What is 34²? =
  29. 29.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)?
  30. 30.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?
  31. 31.What is √2500? =
  32. 32.What is √2116? =
  33. 33.How many whole numbers lie between 40² and 41²?
  34. 34.What is 42²? =
  35. 35.What is √529? =
  36. 36.How many whole numbers lie between 13² and 14²?
  37. 37.What is √6561? =
  38. 38.What is the smallest whole number by which 640 must be divided to get a perfect square?
  39. 39.Which of these is a perfect square? (a) 260 (b) 261 (c) 256
  40. 40.Which of these is a perfect square? (a) 1600 (b) 1656 (c) 1605

Answer key

  1. 576
  2. 8836
  3. 6
  4. 50
  5. 28
  6. 784
  7. 144
  8. 28
  9. 49
  10. 729
  11. 144
  12. 256
  13. 3
  14. 20
  15. 2
  16. 72
  17. 2
  18. 7
  19. 36
  20. 83
  21. 1089
  22. 87
  23. 324
  24. 900
  25. 3
  26. 56
  27. 196
  28. 1156
  29. 529
  30. 289
  31. 50
  32. 46
  33. 80
  34. 1764
  35. 23
  36. 26
  37. 81
  38. 10
  39. 256
  40. 1600

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