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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 464 · 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 12²? =
  2. 2.What is the smallest whole number by which 12 must be divided to get a perfect square?
  3. 3.What is √529? =
  4. 4.Which of these is a perfect square? (a) 870 (b) 888 (c) 841
  5. 5.What is √1296? =
  6. 6.How many whole numbers lie between 40² and 41²?
  7. 7.How many whole numbers lie between 15² and 16²?
  8. 8.What is √4356? =
  9. 9.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)?
  10. 10.What is 42²? =
  11. 11.How many whole numbers lie between 23² and 24²?
  12. 12.What is √1444? =
  13. 13.What is 51²? =
  14. 14.A square garden has an area of 1156 square m. How long is each side (in m)?
  15. 15.How many whole numbers lie between 41² and 42²?
  16. 16.A square garden has an area of 841 square m. How long is each side (in m)?
  17. 17.What is 96²? =
  18. 18.Which of these is a perfect square? (a) 1398 (b) 1415 (c) 1369
  19. 19.Which of these is a perfect square? (a) 1156 (b) 1184 (c) 1162
  20. 20.What is the smallest whole number by which 240 must be multiplied to get a perfect square?
  21. 21.Which of these is a perfect square? (a) 1444 (b) 1498 (c) 1455
  22. 22.Which of these is a perfect square? (a) 593 (b) 576 (c) 598
  23. 23.A square garden has an area of 3481 square m. How long is each side (in m)?
  24. 24.What is 36²? =
  25. 25.What is the smallest whole number by which 48 must be multiplied to get a perfect square?
  26. 26.What is the smallest whole number by which 243 must be divided to get a perfect square?
  27. 27.How many whole numbers lie between 25² and 26²?
  28. 28.What is the smallest whole number by which 396 must be multiplied to get a perfect square?
  29. 29.What is √729? =
  30. 30.How many whole numbers lie between 39² and 40²?
  31. 31.What is √1156? =
  32. 32.A square garden has an area of 64 square m. How long is each side (in m)?
  33. 33.A square garden has an area of 1089 square m. How long is each side (in m)?
  34. 34.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
  35. 35.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
  36. 36.Which of these is a perfect square? (a) 285 (b) 256 (c) 260
  37. 37.How many whole numbers lie between 29² and 30²?
  38. 38.What is the smallest whole number by which 80 must be multiplied to get a perfect square?
  39. 39.How many whole numbers lie between 49² and 50²?
  40. 40.What is the smallest whole number by which 112 must be divided to get a perfect square?

Answer key

  1. 144
  2. 3
  3. 23
  4. 841
  5. 36
  6. 80
  7. 30
  8. 66
  9. 576
  10. 1764
  11. 46
  12. 38
  13. 2601
  14. 34
  15. 82
  16. 29
  17. 9216
  18. 1369
  19. 1156
  20. 15
  21. 1444
  22. 576
  23. 59
  24. 1296
  25. 3
  26. 3
  27. 50
  28. 11
  29. 27
  30. 78
  31. 34
  32. 8
  33. 33
  34. 49
  35. 25
  36. 256
  37. 58
  38. 5
  39. 98
  40. 7

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