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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 90 · 40 questions
TalentJR

How to do it in your head (Guess, divide, average): Division: round the divisor to the nearest ten and find the closest multiple of it. Square root: guess the nearest whole root, then divide the number by your guess. Average the guess and the answer of the division, and round to 1 decimal place.

NameDateTime takenScore ___ / 40
  1. 1.Best estimate of 1504 ÷ 64? (a) 2500 (b) 250 (c) 25
  2. 2.Best estimate of 5848 ÷ 77? (a) 7300 (b) 73 (c) 730
  3. 3.Best estimate of 3375 ÷ 56? (a) 56 (b) 560 (c) 5600
  4. 4.√27 to 1 decimal place? (a) 5.3 (b) 5.2 (c) 5.1 (d) 5.0
  5. 5.Best estimate of 1539 ÷ 76? (a) 190 (b) 1900 (c) 19
  6. 6.Best estimate of 5175 ÷ 67? (a) 740 (b) 7400 (c) 74
  7. 7.√94 to 1 decimal place? (a) 9.5 (b) 9.7 (c) 9.6 (d) 9.8
  8. 8.Best estimate of 1560 ÷ 87? (a) 17 (b) 170 (c) 1700
  9. 9.√24 to 1 decimal place? (a) 5.1 (b) 5.0 (c) 5.2 (d) 4.9
  10. 10.√34 to 1 decimal place? (a) 5.5 (b) 5.8 (c) 5.7 (d) 5.6
  11. 11.Best estimate of 663 ÷ 32? (a) 2200 (b) 220 (c) 22
  12. 12.Best estimate of 5969 ÷ 68? (a) 850 (b) 85 (c) 8500
  13. 13.Best estimate of 1433 ÷ 49? (a) 2900 (b) 29 (c) 290
  14. 14.√58 to 1 decimal place? (a) 7.7 (b) 7.9 (c) 7.6 (d) 7.8
  15. 15.Best estimate of 6961 ÷ 79? (a) 870 (b) 87 (c) 8700
  16. 16.Best estimate of 3079 ÷ 76? (a) 3800 (b) 38 (c) 380
  17. 17.Best estimate of 2408 ÷ 28? (a) 80 (b) 8000 (c) 800
  18. 18.Best estimate of 3535 ÷ 62? (a) 5900 (b) 59 (c) 590
  19. 19.√28 to 1 decimal place? (a) 5.3 (b) 5.6 (c) 5.5 (d) 5.4
  20. 20.Best estimate of 3778 ÷ 46? (a) 7600 (b) 760 (c) 76
  21. 21.√85 to 1 decimal place? (a) 9.2 (b) 9.1 (c) 9.3 (d) 9.0
  22. 22.Best estimate of 1330 ÷ 32? (a) 44 (b) 4400 (c) 440
  23. 23.Best estimate of 3063 ÷ 42? (a) 7700 (b) 77 (c) 770
  24. 24.Best estimate of 2162 ÷ 28? (a) 7200 (b) 720 (c) 72
  25. 25.Best estimate of 1865 ÷ 43? (a) 4700 (b) 470 (c) 47
  26. 26.Best estimate of 2678 ÷ 46? (a) 5400 (b) 540 (c) 54
  27. 27.Best estimate of 1220 ÷ 29? (a) 410 (b) 4100 (c) 41
  28. 28.√70 to 1 decimal place? (a) 8.5 (b) 8.6 (c) 8.4 (d) 8.7
  29. 29.√69 to 1 decimal place? (a) 8.4 (b) 8.5 (c) 8.3 (d) 8.6
  30. 30.√52 to 1 decimal place? (a) 7.1 (b) 7.4 (c) 7.3 (d) 7.2
  31. 31.√67 to 1 decimal place? (a) 8.1 (b) 8.2 (c) 8.0 (d) 8.3
  32. 32.Best estimate of 2494 ÷ 49? (a) 50 (b) 500 (c) 5000
  33. 33.Best estimate of 1189 ÷ 22? (a) 5900 (b) 59 (c) 590
  34. 34.Best estimate of 2023 ÷ 82? (a) 2500 (b) 250 (c) 25
  35. 35.√35 to 1 decimal place? (a) 5.9 (b) 5.7 (c) 5.6 (d) 5.8
  36. 36.√90 to 1 decimal place? (a) 9.4 (b) 9.6 (c) 9.7 (d) 9.5
  37. 37.Best estimate of 4427 ÷ 84? (a) 55 (b) 5500 (c) 550
  38. 38.Best estimate of 1690 ÷ 29? (a) 560 (b) 5600 (c) 56
  39. 39.Best estimate of 4664 ÷ 49? (a) 9300 (b) 93 (c) 930
  40. 40.√55 to 1 decimal place? (a) 7.3 (b) 7.6 (c) 7.5 (d) 7.4

Answer key

  1. 25
  2. 73
  3. 56
  4. 5.2
  5. 19
  6. 74
  7. 9.7
  8. 17
  9. 4.9
  10. 5.8
  11. 22
  12. 85
  13. 29
  14. 7.6
  15. 87
  16. 38
  17. 80
  18. 59
  19. 5.3
  20. 76
  21. 9.2
  22. 44
  23. 77
  24. 72
  25. 47
  26. 54
  27. 41
  28. 8.4
  29. 8.3
  30. 7.2
  31. 8.2
  32. 50
  33. 59
  34. 25
  35. 5.9
  36. 9.5
  37. 55
  38. 56
  39. 93
  40. 7.4

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