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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 314 · 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 2949 ÷ 48? (a) 590 (b) 5900 (c) 59
  2. 2.√31 to 1 decimal place? (a) 5.5 (b) 5.3 (c) 5.6 (d) 5.4
  3. 3.√69 to 1 decimal place? (a) 8.2 (b) 8.0 (c) 8.3 (d) 8.1
  4. 4.Best estimate of 5486 ÷ 66? (a) 7800 (b) 78 (c) 780
  5. 5.Best estimate of 4307 ÷ 76? (a) 540 (b) 54 (c) 5400
  6. 6.Best estimate of 4774 ÷ 62? (a) 8000 (b) 800 (c) 80
  7. 7.√37 to 1 decimal place? (a) 5.9 (b) 6.2 (c) 6.1 (d) 6.0
  8. 8.√71 to 1 decimal place? (a) 8.1 (b) 8.3 (c) 8.4 (d) 8.2
  9. 9.Best estimate of 471 ÷ 32? (a) 160 (b) 1600 (c) 16
  10. 10.Best estimate of 5079 ÷ 63? (a) 8500 (b) 85 (c) 850
  11. 11.√42 to 1 decimal place? (a) 6.6 (b) 6.5 (c) 6.7 (d) 6.4
  12. 12.Best estimate of 3771 ÷ 86? (a) 420 (b) 42 (c) 4200
  13. 13.Best estimate of 4083 ÷ 54? (a) 820 (b) 8200 (c) 82
  14. 14.√50 to 1 decimal place? (a) 7.3 (b) 7.2 (c) 7.4 (d) 7.1
  15. 15.√74 to 1 decimal place? (a) 8.3 (b) 8.6 (c) 8.5 (d) 8.4
  16. 16.√26 to 1 decimal place? (a) 5.1 (b) 5.3 (c) 5.2 (d) 5.0
  17. 17.Best estimate of 2848 ÷ 31? (a) 9500 (b) 950 (c) 95
  18. 18.Best estimate of 883 ÷ 66? (a) 1300 (b) 13 (c) 130
  19. 19.Best estimate of 2468 ÷ 52? (a) 49 (b) 490 (c) 4900
  20. 20.Best estimate of 6533 ÷ 87? (a) 73 (b) 7300 (c) 730
  21. 21.Best estimate of 789 ÷ 24? (a) 390 (b) 39 (c) 3900
  22. 22.Best estimate of 3410 ÷ 64? (a) 57 (b) 570 (c) 5700
  23. 23.Best estimate of 1679 ÷ 24? (a) 840 (b) 8400 (c) 84
  24. 24.√79 to 1 decimal place? (a) 9.0 (b) 8.9 (c) 8.7 (d) 8.8
  25. 25.Best estimate of 4113 ÷ 84? (a) 510 (b) 51 (c) 5100
  26. 26.Best estimate of 1458 ÷ 68? (a) 210 (b) 21 (c) 2100
  27. 27.Best estimate of 4598 ÷ 78? (a) 5700 (b) 57 (c) 570
  28. 28.Best estimate of 2646 ÷ 44? (a) 66 (b) 6600 (c) 660
  29. 29.Best estimate of 3740 ÷ 84? (a) 470 (b) 47 (c) 4700
  30. 30.Best estimate of 1846 ÷ 51? (a) 370 (b) 37 (c) 3700
  31. 31.√98 to 1 decimal place? (a) 9.9 (b) 10.0 (c) 9.8 (d) 10.1
  32. 32.√44 to 1 decimal place? (a) 6.4 (b) 6.5 (c) 6.6 (d) 6.3
  33. 33.√48 to 1 decimal place? (a) 7.1 (b) 7.0 (c) 6.9 (d) 6.8
  34. 34.Best estimate of 1705 ÷ 71? (a) 2400 (b) 24 (c) 240
  35. 35.√82 to 1 decimal place? (a) 9.3 (b) 9.2 (c) 9.1 (d) 9.4
  36. 36.Best estimate of 6671 ÷ 74? (a) 95 (b) 950 (c) 9500
  37. 37.Best estimate of 3766 ÷ 41? (a) 9400 (b) 94 (c) 940
  38. 38.√27 to 1 decimal place? (a) 5.4 (b) 5.3 (c) 5.2 (d) 5.1
  39. 39.Best estimate of 4607 ÷ 82? (a) 580 (b) 58 (c) 5800
  40. 40.√92 to 1 decimal place? (a) 9.8 (b) 9.6 (c) 9.9 (d) 9.7

Answer key

  1. 59
  2. 5.6
  3. 8.3
  4. 78
  5. 54
  6. 80
  7. 6.1
  8. 8.4
  9. 16
  10. 85
  11. 6.5
  12. 42
  13. 82
  14. 7.1
  15. 8.6
  16. 5.1
  17. 95
  18. 13
  19. 49
  20. 73
  21. 39
  22. 57
  23. 84
  24. 8.9
  25. 51
  26. 21
  27. 57
  28. 66
  29. 47
  30. 37
  31. 9.9
  32. 6.6
  33. 6.9
  34. 24
  35. 9.1
  36. 95
  37. 94
  38. 5.2
  39. 58
  40. 9.6

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