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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 365 · 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 2888 ÷ 46? (a) 580 (b) 58 (c) 5800
  2. 2.Best estimate of 3413 ÷ 86? (a) 380 (b) 3800 (c) 38
  3. 3.√47 to 1 decimal place? (a) 7.0 (b) 7.2 (c) 7.1 (d) 6.9
  4. 4.√42 to 1 decimal place? (a) 6.8 (b) 6.5 (c) 6.7 (d) 6.6
  5. 5.Best estimate of 2591 ÷ 86? (a) 2900 (b) 290 (c) 29
  6. 6.√74 to 1 decimal place? (a) 8.7 (b) 8.6 (c) 8.5 (d) 8.8
  7. 7.Best estimate of 1566 ÷ 21? (a) 780 (b) 7800 (c) 78
  8. 8.Best estimate of 1915 ÷ 72? (a) 2700 (b) 270 (c) 27
  9. 9.Best estimate of 3643 ÷ 56? (a) 6100 (b) 610 (c) 61
  10. 10.Best estimate of 5035 ÷ 84? (a) 630 (b) 6300 (c) 63
  11. 11.Best estimate of 5017 ÷ 54? (a) 1000 (b) 10000 (c) 100
  12. 12.√46 to 1 decimal place? (a) 7.0 (b) 6.9 (c) 6.8 (d) 7.1
  13. 13.Best estimate of 6848 ÷ 77? (a) 8600 (b) 860 (c) 86
  14. 14.√38 to 1 decimal place? (a) 6.3 (b) 6.4 (c) 6.5 (d) 6.2
  15. 15.√80 to 1 decimal place? (a) 8.9 (b) 8.8 (c) 8.7 (d) 9.0
  16. 16.√75 to 1 decimal place? (a) 8.7 (b) 8.9 (c) 8.8 (d) 9.0
  17. 17.Best estimate of 1297 ÷ 29? (a) 43 (b) 4300 (c) 430
  18. 18.√89 to 1 decimal place? (a) 9.5 (b) 9.4 (c) 9.3 (d) 9.2
  19. 19.Best estimate of 4773 ÷ 87? (a) 5300 (b) 530 (c) 53
  20. 20.Best estimate of 4116 ÷ 62? (a) 690 (b) 69 (c) 6900
  21. 21.Best estimate of 510 ÷ 36? (a) 13 (b) 130 (c) 1300
  22. 22.Best estimate of 2375 ÷ 49? (a) 48 (b) 480 (c) 4800
  23. 23.Best estimate of 2688 ÷ 86? (a) 3000 (b) 300 (c) 30
  24. 24.√65 to 1 decimal place? (a) 8.1 (b) 7.8 (c) 7.9 (d) 8.0
  25. 25.Best estimate of 2570 ÷ 89? (a) 290 (b) 2900 (c) 29
  26. 26.Best estimate of 687 ÷ 29? (a) 230 (b) 23 (c) 2300
  27. 27.Best estimate of 1806 ÷ 83? (a) 2300 (b) 230 (c) 23
  28. 28.Best estimate of 4512 ÷ 64? (a) 75 (b) 7500 (c) 750
  29. 29.√29 to 1 decimal place? (a) 5.4 (b) 5.6 (c) 5.5 (d) 5.7
  30. 30.Best estimate of 3284 ÷ 66? (a) 4700 (b) 470 (c) 47
  31. 31.Best estimate of 2022 ÷ 26? (a) 6700 (b) 67 (c) 670
  32. 32.√53 to 1 decimal place? (a) 7.3 (b) 7.2 (c) 7.1 (d) 7.0
  33. 33.Best estimate of 1859 ÷ 37? (a) 4600 (b) 460 (c) 46
  34. 34.Best estimate of 2502 ÷ 36? (a) 630 (b) 6300 (c) 63
  35. 35.Best estimate of 2320 ÷ 42? (a) 580 (b) 58 (c) 5800
  36. 36.√28 to 1 decimal place? (a) 5.3 (b) 5.2 (c) 5.4 (d) 5.1
  37. 37.√32 to 1 decimal place? (a) 5.4 (b) 5.7 (c) 5.5 (d) 5.6
  38. 38.√20 to 1 decimal place? (a) 4.5 (b) 4.4 (c) 4.3 (d) 4.2
  39. 39.Best estimate of 3416 ÷ 36? (a) 850 (b) 8500 (c) 85
  40. 40.√40 to 1 decimal place? (a) 6.3 (b) 6.6 (c) 6.4 (d) 6.5

Answer key

  1. 58
  2. 38
  3. 6.9
  4. 6.5
  5. 29
  6. 8.6
  7. 78
  8. 27
  9. 61
  10. 63
  11. 100
  12. 6.8
  13. 86
  14. 6.2
  15. 8.9
  16. 8.7
  17. 43
  18. 9.4
  19. 53
  20. 69
  21. 13
  22. 48
  23. 30
  24. 8.1
  25. 29
  26. 23
  27. 23
  28. 75
  29. 5.4
  30. 47
  31. 67
  32. 7.3
  33. 46
  34. 63
  35. 58
  36. 5.3
  37. 5.7
  38. 4.5
  39. 85
  40. 6.3

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