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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 946 · 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.√41 to 1 decimal place? (a) 6.3 (b) 6.4 (c) 6.1 (d) 6.2
  2. 2.Best estimate of 2874 ÷ 32? (a) 960 (b) 96 (c) 9600
  3. 3.Best estimate of 2968 ÷ 46? (a) 5900 (b) 590 (c) 59
  4. 4.√58 to 1 decimal place? (a) 7.6 (b) 7.8 (c) 7.7 (d) 7.5
  5. 5.Best estimate of 2706 ÷ 38? (a) 6800 (b) 680 (c) 68
  6. 6.√47 to 1 decimal place? (a) 6.9 (b) 6.8 (c) 7.0 (d) 6.7
  7. 7.Best estimate of 4905 ÷ 54? (a) 98 (b) 980 (c) 9800
  8. 8.√38 to 1 decimal place? (a) 6.0 (b) 6.2 (c) 6.1 (d) 5.9
  9. 9.Best estimate of 2511 ÷ 36? (a) 6300 (b) 63 (c) 630
  10. 10.√21 to 1 decimal place? (a) 4.8 (b) 4.6 (c) 4.7 (d) 4.5
  11. 11.Best estimate of 682 ÷ 51? (a) 14 (b) 1400 (c) 140
  12. 12.√50 to 1 decimal place? (a) 7.0 (b) 7.3 (c) 7.1 (d) 7.2
  13. 13.Best estimate of 4941 ÷ 63? (a) 820 (b) 82 (c) 8200
  14. 14.√85 to 1 decimal place? (a) 9.4 (b) 9.2 (c) 9.1 (d) 9.3
  15. 15.√34 to 1 decimal place? (a) 5.7 (b) 6.0 (c) 5.9 (d) 5.8
  16. 16.Best estimate of 2928 ÷ 64? (a) 4900 (b) 49 (c) 490
  17. 17.√56 to 1 decimal place? (a) 7.5 (b) 7.6 (c) 7.4 (d) 7.7
  18. 18.Best estimate of 4604 ÷ 56? (a) 77 (b) 770 (c) 7700
  19. 19.Best estimate of 682 ÷ 28? (a) 2300 (b) 230 (c) 23
  20. 20.√45 to 1 decimal place? (a) 6.5 (b) 6.6 (c) 6.4 (d) 6.7
  21. 21.√61 to 1 decimal place? (a) 7.8 (b) 7.6 (c) 7.7 (d) 7.5
  22. 22.√94 to 1 decimal place? (a) 9.7 (b) 9.8 (c) 10.0 (d) 9.9
  23. 23.√65 to 1 decimal place? (a) 7.8 (b) 8.1 (c) 7.9 (d) 8.0
  24. 24.√44 to 1 decimal place? (a) 6.8 (b) 6.7 (c) 6.9 (d) 6.6
  25. 25.Best estimate of 1215 ÷ 26? (a) 4100 (b) 41 (c) 410
  26. 26.Best estimate of 650 ÷ 28? (a) 22 (b) 220 (c) 2200
  27. 27.Best estimate of 2414 ÷ 42? (a) 6000 (b) 60 (c) 600
  28. 28.√20 to 1 decimal place? (a) 4.5 (b) 4.2 (c) 4.3 (d) 4.4
  29. 29.Best estimate of 648 ÷ 34? (a) 2200 (b) 22 (c) 220
  30. 30.√82 to 1 decimal place? (a) 9.3 (b) 9.4 (c) 9.1 (d) 9.2
  31. 31.Best estimate of 1064 ÷ 29? (a) 35 (b) 350 (c) 3500
  32. 32.Best estimate of 800 ÷ 62? (a) 130 (b) 1300 (c) 13
  33. 33.√40 to 1 decimal place? (a) 6.5 (b) 6.4 (c) 6.3 (d) 6.2
  34. 34.Best estimate of 414 ÷ 34? (a) 1400 (b) 14 (c) 140
  35. 35.Best estimate of 4180 ÷ 46? (a) 8400 (b) 840 (c) 84
  36. 36.Best estimate of 1178 ÷ 56? (a) 20 (b) 2000 (c) 200
  37. 37.Best estimate of 1367 ÷ 21? (a) 680 (b) 6800 (c) 68
  38. 38.Best estimate of 1157 ÷ 21? (a) 5800 (b) 580 (c) 58
  39. 39.√71 to 1 decimal place? (a) 8.2 (b) 8.4 (c) 8.3 (d) 8.5
  40. 40.Best estimate of 4439 ÷ 59? (a) 74 (b) 740 (c) 7400

Answer key

  1. 6.4
  2. 96
  3. 59
  4. 7.6
  5. 68
  6. 6.9
  7. 98
  8. 6.2
  9. 63
  10. 4.6
  11. 14
  12. 7.1
  13. 82
  14. 9.2
  15. 5.8
  16. 49
  17. 7.5
  18. 77
  19. 23
  20. 6.7
  21. 7.8
  22. 9.7
  23. 8.1
  24. 6.6
  25. 41
  26. 22
  27. 60
  28. 4.5
  29. 22
  30. 9.1
  31. 35
  32. 13
  33. 6.3
  34. 14
  35. 84
  36. 20
  37. 68
  38. 58
  39. 8.4
  40. 74

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