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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 675 · 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 469 ÷ 36? (a) 12 (b) 1200 (c) 120
  2. 2.Best estimate of 5688 ÷ 86? (a) 63 (b) 6300 (c) 630
  3. 3.Best estimate of 511 ÷ 34? (a) 1700 (b) 17 (c) 170
  4. 4.Best estimate of 6174 ÷ 72? (a) 88 (b) 8800 (c) 880
  5. 5.Best estimate of 332 ÷ 26? (a) 110 (b) 1100 (c) 11
  6. 6.√41 to 1 decimal place? (a) 6.7 (b) 6.4 (c) 6.5 (d) 6.6
  7. 7.Best estimate of 1231 ÷ 66? (a) 18 (b) 180 (c) 1800
  8. 8.√38 to 1 decimal place? (a) 6.1 (b) 6.2 (c) 6.3 (d) 6.0
  9. 9.Best estimate of 6583 ÷ 89? (a) 730 (b) 7300 (c) 73
  10. 10.√43 to 1 decimal place? (a) 6.8 (b) 6.6 (c) 6.9 (d) 6.7
  11. 11.Best estimate of 2688 ÷ 67? (a) 380 (b) 3800 (c) 38
  12. 12.Best estimate of 6298 ÷ 72? (a) 9000 (b) 900 (c) 90
  13. 13.Best estimate of 4606 ÷ 57? (a) 7700 (b) 77 (c) 770
  14. 14.√37 to 1 decimal place? (a) 5.9 (b) 6.1 (c) 6.0 (d) 5.8
  15. 15.√56 to 1 decimal place? (a) 7.6 (b) 7.7 (c) 7.8 (d) 7.5
  16. 16.√30 to 1 decimal place? (a) 5.7 (b) 5.4 (c) 5.5 (d) 5.6
  17. 17.Best estimate of 1056 ÷ 58? (a) 180 (b) 18 (c) 1800
  18. 18.Best estimate of 3428 ÷ 71? (a) 4900 (b) 49 (c) 490
  19. 19.Best estimate of 3114 ÷ 37? (a) 7800 (b) 78 (c) 780
  20. 20.Best estimate of 4190 ÷ 84? (a) 520 (b) 52 (c) 5200
  21. 21.Best estimate of 1314 ÷ 41? (a) 3300 (b) 330 (c) 33
  22. 22.√65 to 1 decimal place? (a) 8.1 (b) 8.3 (c) 8.2 (d) 8.0
  23. 23.√98 to 1 decimal place? (a) 9.7 (b) 9.9 (c) 9.8 (d) 9.6
  24. 24.√34 to 1 decimal place? (a) 6.0 (b) 5.9 (c) 5.8 (d) 6.1
  25. 25.Best estimate of 2440 ÷ 27? (a) 810 (b) 81 (c) 8100
  26. 26.√79 to 1 decimal place? (a) 9.1 (b) 9.2 (c) 8.9 (d) 9.0
  27. 27.Best estimate of 5037 ÷ 66? (a) 7200 (b) 720 (c) 72
  28. 28.√50 to 1 decimal place? (a) 6.8 (b) 7.0 (c) 7.1 (d) 6.9
  29. 29.Best estimate of 5146 ÷ 86? (a) 570 (b) 57 (c) 5700
  30. 30.Best estimate of 7473 ÷ 86? (a) 830 (b) 83 (c) 8300
  31. 31.Best estimate of 1183 ÷ 21? (a) 590 (b) 59 (c) 5900
  32. 32.Best estimate of 5284 ÷ 61? (a) 880 (b) 88 (c) 8800
  33. 33.√47 to 1 decimal place? (a) 7.0 (b) 7.1 (c) 6.9 (d) 6.8
  34. 34.Best estimate of 1481 ÷ 27? (a) 4900 (b) 49 (c) 490
  35. 35.√86 to 1 decimal place? (a) 9.0 (b) 9.2 (c) 9.3 (d) 9.1
  36. 36.√58 to 1 decimal place? (a) 7.5 (b) 7.7 (c) 7.8 (d) 7.6
  37. 37.Best estimate of 4219 ÷ 62? (a) 70 (b) 7000 (c) 700
  38. 38.√71 to 1 decimal place? (a) 8.4 (b) 8.3 (c) 8.2 (d) 8.1
  39. 39.√80 to 1 decimal place? (a) 9.0 (b) 9.2 (c) 8.9 (d) 9.1
  40. 40.Best estimate of 4831 ÷ 76? (a) 60 (b) 6000 (c) 600

Answer key

  1. 12
  2. 63
  3. 17
  4. 88
  5. 11
  6. 6.4
  7. 18
  8. 6.2
  9. 73
  10. 6.6
  11. 38
  12. 90
  13. 77
  14. 6.1
  15. 7.5
  16. 5.5
  17. 18
  18. 49
  19. 78
  20. 52
  21. 33
  22. 8.1
  23. 9.9
  24. 5.8
  25. 81
  26. 8.9
  27. 72
  28. 7.1
  29. 57
  30. 83
  31. 59
  32. 88
  33. 6.9
  34. 49
  35. 9.3
  36. 7.6
  37. 70
  38. 8.4
  39. 8.9
  40. 60

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