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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 148 · 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 3434 ÷ 46? (a) 690 (b) 69 (c) 6900
  2. 2.Best estimate of 2907 ÷ 39? (a) 730 (b) 7300 (c) 73
  3. 3.Best estimate of 850 ÷ 41? (a) 21 (b) 2100 (c) 210
  4. 4.√21 to 1 decimal place? (a) 4.7 (b) 4.5 (c) 4.6 (d) 4.8
  5. 5.Best estimate of 2711 ÷ 51? (a) 5400 (b) 540 (c) 54
  6. 6.√31 to 1 decimal place? (a) 5.9 (b) 5.6 (c) 5.8 (d) 5.7
  7. 7.Best estimate of 7174 ÷ 88? (a) 80 (b) 8000 (c) 800
  8. 8.Best estimate of 1697 ÷ 68? (a) 240 (b) 24 (c) 2400
  9. 9.Best estimate of 4472 ÷ 62? (a) 750 (b) 75 (c) 7500
  10. 10.√38 to 1 decimal place? (a) 6.3 (b) 6.4 (c) 6.5 (d) 6.2
  11. 11.Best estimate of 1307 ÷ 26? (a) 4400 (b) 44 (c) 440
  12. 12.Best estimate of 2114 ÷ 48? (a) 420 (b) 4200 (c) 42
  13. 13.Best estimate of 570 ÷ 29? (a) 1900 (b) 190 (c) 19
  14. 14.√96 to 1 decimal place? (a) 10.1 (b) 10.0 (c) 9.8 (d) 9.9
  15. 15.√24 to 1 decimal place? (a) 4.7 (b) 4.9 (c) 5.0 (d) 4.8
  16. 16.Best estimate of 1929 ÷ 54? (a) 39 (b) 3900 (c) 390
  17. 17.√34 to 1 decimal place? (a) 5.8 (b) 5.6 (c) 5.5 (d) 5.7
  18. 18.√56 to 1 decimal place? (a) 7.3 (b) 7.4 (c) 7.2 (d) 7.5
  19. 19.√69 to 1 decimal place? (a) 8.3 (b) 8.4 (c) 8.5 (d) 8.6
  20. 20.Best estimate of 5218 ÷ 56? (a) 87 (b) 8700 (c) 870
  21. 21.Best estimate of 785 ÷ 26? (a) 260 (b) 26 (c) 2600
  22. 22.Best estimate of 2267 ÷ 81? (a) 280 (b) 28 (c) 2800
  23. 23.√50 to 1 decimal place? (a) 7.4 (b) 7.2 (c) 7.3 (d) 7.1
  24. 24.Best estimate of 2499 ÷ 33? (a) 8300 (b) 830 (c) 83
  25. 25.Best estimate of 2336 ÷ 54? (a) 4700 (b) 470 (c) 47
  26. 26.√48 to 1 decimal place? (a) 6.8 (b) 6.9 (c) 7.0 (d) 6.7
  27. 27.Best estimate of 2138 ÷ 29? (a) 71 (b) 7100 (c) 710
  28. 28.√66 to 1 decimal place? (a) 8.4 (b) 8.1 (c) 8.3 (d) 8.2
  29. 29.Best estimate of 1703 ÷ 62? (a) 2800 (b) 28 (c) 280
  30. 30.Best estimate of 2076 ÷ 71? (a) 300 (b) 30 (c) 3000
  31. 31.√52 to 1 decimal place? (a) 7.2 (b) 7.0 (c) 6.9 (d) 7.1
  32. 32.√42 to 1 decimal place? (a) 6.4 (b) 6.5 (c) 6.6 (d) 6.7
  33. 33.Best estimate of 3380 ÷ 42? (a) 8500 (b) 85 (c) 850
  34. 34.√32 to 1 decimal place? (a) 5.7 (b) 5.6 (c) 5.9 (d) 5.8
  35. 35.Best estimate of 855 ÷ 23? (a) 430 (b) 43 (c) 4300
  36. 36.Best estimate of 623 ÷ 38? (a) 160 (b) 1600 (c) 16
  37. 37.Best estimate of 1885 ÷ 66? (a) 270 (b) 2700 (c) 27
  38. 38.Best estimate of 2181 ÷ 28? (a) 730 (b) 7300 (c) 73
  39. 39.√30 to 1 decimal place? (a) 5.6 (b) 5.5 (c) 5.3 (d) 5.4
  40. 40.Best estimate of 471 ÷ 26? (a) 1600 (b) 16 (c) 160

Answer key

  1. 69
  2. 73
  3. 21
  4. 4.6
  5. 54
  6. 5.6
  7. 80
  8. 24
  9. 75
  10. 6.2
  11. 44
  12. 42
  13. 19
  14. 9.8
  15. 4.9
  16. 39
  17. 5.8
  18. 7.5
  19. 8.3
  20. 87
  21. 26
  22. 28
  23. 7.1
  24. 83
  25. 47
  26. 6.9
  27. 71
  28. 8.1
  29. 28
  30. 30
  31. 7.2
  32. 6.5
  33. 85
  34. 5.7
  35. 43
  36. 16
  37. 27
  38. 73
  39. 5.5
  40. 16

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