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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 857 · 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 3549 ÷ 56? (a) 59 (b) 590 (c) 5900
  2. 2.Best estimate of 1474 ÷ 82? (a) 18 (b) 1800 (c) 180
  3. 3.Best estimate of 2714 ÷ 39? (a) 68 (b) 680 (c) 6800
  4. 4.Best estimate of 771 ÷ 36? (a) 1900 (b) 19 (c) 190
  5. 5.√50 to 1 decimal place? (a) 7.2 (b) 7.3 (c) 7.4 (d) 7.1
  6. 6.Best estimate of 3952 ÷ 73? (a) 560 (b) 56 (c) 5600
  7. 7.Best estimate of 1292 ÷ 52? (a) 26 (b) 260 (c) 2600
  8. 8.Best estimate of 4382 ÷ 46? (a) 8800 (b) 88 (c) 880
  9. 9.Best estimate of 1791 ÷ 28? (a) 6000 (b) 60 (c) 600
  10. 10.Best estimate of 3426 ÷ 52? (a) 6900 (b) 69 (c) 690
  11. 11.√74 to 1 decimal place? (a) 8.3 (b) 8.4 (c) 8.5 (d) 8.6
  12. 12.√34 to 1 decimal place? (a) 5.6 (b) 5.8 (c) 5.7 (d) 5.5
  13. 13.√32 to 1 decimal place? (a) 5.8 (b) 5.9 (c) 5.6 (d) 5.7
  14. 14.Best estimate of 4158 ÷ 63? (a) 6900 (b) 690 (c) 69
  15. 15.√47 to 1 decimal place? (a) 6.8 (b) 6.7 (c) 6.9 (d) 7.0
  16. 16.Best estimate of 6633 ÷ 89? (a) 7400 (b) 740 (c) 74
  17. 17.√53 to 1 decimal place? (a) 7.4 (b) 7.2 (c) 7.5 (d) 7.3
  18. 18.√30 to 1 decimal place? (a) 5.8 (b) 5.5 (c) 5.6 (d) 5.7
  19. 19.Best estimate of 1757 ÷ 36? (a) 440 (b) 4400 (c) 44
  20. 20.√98 to 1 decimal place? (a) 10.1 (b) 10.2 (c) 10.0 (d) 9.9
  21. 21.Best estimate of 3779 ÷ 62? (a) 630 (b) 63 (c) 6300
  22. 22.Best estimate of 862 ÷ 28? (a) 2900 (b) 290 (c) 29
  23. 23.Best estimate of 1095 ÷ 21? (a) 55 (b) 550 (c) 5500
  24. 24.Best estimate of 3372 ÷ 38? (a) 840 (b) 8400 (c) 84
  25. 25.√37 to 1 decimal place? (a) 6.1 (b) 6.0 (c) 6.3 (d) 6.2
  26. 26.√42 to 1 decimal place? (a) 6.3 (b) 6.5 (c) 6.4 (d) 6.6
  27. 27.Best estimate of 5959 ÷ 89? (a) 660 (b) 66 (c) 6600
  28. 28.Best estimate of 1255 ÷ 31? (a) 4200 (b) 42 (c) 420
  29. 29.√41 to 1 decimal place? (a) 6.4 (b) 6.5 (c) 6.6 (d) 6.7
  30. 30.Best estimate of 5328 ÷ 63? (a) 89 (b) 8900 (c) 890
  31. 31.Best estimate of 1762 ÷ 84? (a) 2200 (b) 220 (c) 22
  32. 32.√78 to 1 decimal place? (a) 9.1 (b) 8.9 (c) 9.0 (d) 8.8
  33. 33.√61 to 1 decimal place? (a) 7.8 (b) 7.6 (c) 7.7 (d) 7.9
  34. 34.Best estimate of 2431 ÷ 32? (a) 8100 (b) 810 (c) 81
  35. 35.Best estimate of 3268 ÷ 46? (a) 65 (b) 650 (c) 6500
  36. 36.Best estimate of 5134 ÷ 68? (a) 73 (b) 7300 (c) 730
  37. 37.Best estimate of 1066 ÷ 63? (a) 1800 (b) 180 (c) 18
  38. 38.Best estimate of 5462 ÷ 58? (a) 9100 (b) 910 (c) 91
  39. 39.Best estimate of 2229 ÷ 31? (a) 740 (b) 7400 (c) 74
  40. 40.Best estimate of 4324 ÷ 46? (a) 860 (b) 8600 (c) 86

Answer key

  1. 59
  2. 18
  3. 68
  4. 19
  5. 7.1
  6. 56
  7. 26
  8. 88
  9. 60
  10. 69
  11. 8.6
  12. 5.8
  13. 5.7
  14. 69
  15. 6.9
  16. 74
  17. 7.3
  18. 5.5
  19. 44
  20. 9.9
  21. 63
  22. 29
  23. 55
  24. 84
  25. 6.1
  26. 6.5
  27. 66
  28. 42
  29. 6.4
  30. 89
  31. 22
  32. 8.8
  33. 7.8
  34. 81
  35. 65
  36. 73
  37. 18
  38. 91
  39. 74
  40. 86

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