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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 770 · 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 1562 ÷ 38? (a) 390 (b) 3900 (c) 39
  2. 2.Best estimate of 3386 ÷ 64? (a) 5600 (b) 560 (c) 56
  3. 3.Best estimate of 3709 ÷ 39? (a) 93 (b) 930 (c) 9300
  4. 4.Best estimate of 729 ÷ 36? (a) 18 (b) 180 (c) 1800
  5. 5.Best estimate of 3551 ÷ 86? (a) 3900 (b) 390 (c) 39
  6. 6.Best estimate of 2284 ÷ 33? (a) 7600 (b) 760 (c) 76
  7. 7.Best estimate of 1223 ÷ 83? (a) 15 (b) 1500 (c) 150
  8. 8.√34 to 1 decimal place? (a) 6.1 (b) 6.0 (c) 5.8 (d) 5.9
  9. 9.√44 to 1 decimal place? (a) 6.6 (b) 6.8 (c) 6.7 (d) 6.5
  10. 10.Best estimate of 1383 ÷ 36? (a) 3500 (b) 35 (c) 350
  11. 11.Best estimate of 2511 ÷ 31? (a) 8400 (b) 840 (c) 84
  12. 12.√21 to 1 decimal place? (a) 4.6 (b) 4.5 (c) 4.4 (d) 4.3
  13. 13.√59 to 1 decimal place? (a) 7.6 (b) 7.4 (c) 7.5 (d) 7.7
  14. 14.√98 to 1 decimal place? (a) 10.1 (b) 9.9 (c) 10.2 (d) 10.0
  15. 15.√31 to 1 decimal place? (a) 5.8 (b) 5.6 (c) 5.5 (d) 5.7
  16. 16.Best estimate of 2634 ÷ 77? (a) 33 (b) 330 (c) 3300
  17. 17.Best estimate of 3593 ÷ 86? (a) 40 (b) 4000 (c) 400
  18. 18.Best estimate of 3297 ÷ 36? (a) 82 (b) 820 (c) 8200
  19. 19.√70 to 1 decimal place? (a) 8.3 (b) 8.4 (c) 8.5 (d) 8.6
  20. 20.Best estimate of 4769 ÷ 72? (a) 680 (b) 68 (c) 6800
  21. 21.Best estimate of 5182 ÷ 69? (a) 740 (b) 74 (c) 7400
  22. 22.Best estimate of 1354 ÷ 27? (a) 4500 (b) 450 (c) 45
  23. 23.√66 to 1 decimal place? (a) 8.2 (b) 8.3 (c) 8.1 (d) 8.4
  24. 24.Best estimate of 5597 ÷ 83? (a) 700 (b) 70 (c) 7000
  25. 25.√94 to 1 decimal place? (a) 9.5 (b) 9.7 (c) 9.4 (d) 9.6
  26. 26.√27 to 1 decimal place? (a) 5.2 (b) 5.4 (c) 5.1 (d) 5.3
  27. 27.Best estimate of 7083 ÷ 77? (a) 8900 (b) 89 (c) 890
  28. 28.Best estimate of 6242 ÷ 67? (a) 89 (b) 890 (c) 8900
  29. 29.√69 to 1 decimal place? (a) 8.4 (b) 8.6 (c) 8.5 (d) 8.3
  30. 30.Best estimate of 2547 ÷ 68? (a) 3600 (b) 360 (c) 36
  31. 31.√82 to 1 decimal place? (a) 9.2 (b) 9.1 (c) 9.3 (d) 9.0
  32. 32.Best estimate of 2162 ÷ 26? (a) 720 (b) 72 (c) 7200
  33. 33.Best estimate of 4046 ÷ 84? (a) 51 (b) 510 (c) 5100
  34. 34.Best estimate of 2038 ÷ 83? (a) 250 (b) 25 (c) 2500
  35. 35.√51 to 1 decimal place? (a) 7.2 (b) 7.1 (c) 7.0 (d) 6.9
  36. 36.Best estimate of 4831 ÷ 66? (a) 6900 (b) 690 (c) 69
  37. 37.Best estimate of 3249 ÷ 56? (a) 54 (b) 540 (c) 5400
  38. 38.Best estimate of 1118 ÷ 82? (a) 1400 (b) 140 (c) 14
  39. 39.√28 to 1 decimal place? (a) 5.0 (b) 5.1 (c) 5.3 (d) 5.2
  40. 40.Best estimate of 3880 ÷ 43? (a) 9700 (b) 970 (c) 97

Answer key

  1. 39
  2. 56
  3. 93
  4. 18
  5. 39
  6. 76
  7. 15
  8. 5.8
  9. 6.6
  10. 35
  11. 84
  12. 4.6
  13. 7.7
  14. 9.9
  15. 5.6
  16. 33
  17. 40
  18. 82
  19. 8.4
  20. 68
  21. 74
  22. 45
  23. 8.1
  24. 70
  25. 9.7
  26. 5.2
  27. 89
  28. 89
  29. 8.3
  30. 36
  31. 9.1
  32. 72
  33. 51
  34. 25
  35. 7.1
  36. 69
  37. 54
  38. 14
  39. 5.3
  40. 97

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