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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 60 · 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 3978 ÷ 66? (a) 5700 (b) 57 (c) 570
  2. 2.Best estimate of 1981 ÷ 48? (a) 4000 (b) 40 (c) 400
  3. 3.Best estimate of 765 ÷ 46? (a) 1500 (b) 150 (c) 15
  4. 4.Best estimate of 1535 ÷ 23? (a) 7700 (b) 77 (c) 770
  5. 5.Best estimate of 2117 ÷ 48? (a) 4200 (b) 42 (c) 420
  6. 6.√34 to 1 decimal place? (a) 5.9 (b) 6.0 (c) 5.7 (d) 5.8
  7. 7.Best estimate of 5416 ÷ 57? (a) 900 (b) 90 (c) 9000
  8. 8.Best estimate of 2808 ÷ 64? (a) 470 (b) 4700 (c) 47
  9. 9.Best estimate of 350 ÷ 29? (a) 120 (b) 12 (c) 1200
  10. 10.Best estimate of 1742 ÷ 32? (a) 580 (b) 58 (c) 5800
  11. 11.Best estimate of 436 ÷ 36? (a) 11 (b) 110 (c) 1100
  12. 12.√32 to 1 decimal place? (a) 5.9 (b) 6.0 (c) 5.7 (d) 5.8
  13. 13.Best estimate of 3801 ÷ 86? (a) 420 (b) 4200 (c) 42
  14. 14.Best estimate of 2741 ÷ 68? (a) 3900 (b) 39 (c) 390
  15. 15.Best estimate of 1028 ÷ 46? (a) 210 (b) 2100 (c) 21
  16. 16.√87 to 1 decimal place? (a) 9.2 (b) 9.3 (c) 9.4 (d) 9.1
  17. 17.√24 to 1 decimal place? (a) 4.9 (b) 4.6 (c) 4.7 (d) 4.8
  18. 18.√70 to 1 decimal place? (a) 8.3 (b) 8.4 (c) 8.6 (d) 8.5
  19. 19.√55 to 1 decimal place? (a) 7.4 (b) 7.3 (c) 7.2 (d) 7.1
  20. 20.Best estimate of 7583 ÷ 86? (a) 8400 (b) 84 (c) 840
  21. 21.Best estimate of 5937 ÷ 67? (a) 850 (b) 85 (c) 8500
  22. 22.√98 to 1 decimal place? (a) 10.1 (b) 10.0 (c) 10.2 (d) 9.9
  23. 23.√61 to 1 decimal place? (a) 7.7 (b) 7.6 (c) 7.5 (d) 7.8
  24. 24.√51 to 1 decimal place? (a) 7.1 (b) 7.2 (c) 7.0 (d) 7.3
  25. 25.√58 to 1 decimal place? (a) 7.5 (b) 7.3 (c) 7.6 (d) 7.4
  26. 26.Best estimate of 815 ÷ 36? (a) 20 (b) 2000 (c) 200
  27. 27.√45 to 1 decimal place? (a) 6.8 (b) 6.5 (c) 6.7 (d) 6.6
  28. 28.Best estimate of 1229 ÷ 73? (a) 1800 (b) 18 (c) 180
  29. 29.Best estimate of 874 ÷ 21? (a) 4400 (b) 44 (c) 440
  30. 30.√92 to 1 decimal place? (a) 9.8 (b) 9.5 (c) 9.6 (d) 9.7
  31. 31.√96 to 1 decimal place? (a) 9.9 (b) 9.8 (c) 9.6 (d) 9.7
  32. 32.Best estimate of 1676 ÷ 82? (a) 210 (b) 2100 (c) 21
  33. 33.Best estimate of 2410 ÷ 36? (a) 6000 (b) 600 (c) 60
  34. 34.√50 to 1 decimal place? (a) 7.3 (b) 7.1 (c) 7.2 (d) 7.4
  35. 35.Best estimate of 2821 ÷ 57? (a) 470 (b) 47 (c) 4700
  36. 36.Best estimate of 5099 ÷ 56? (a) 850 (b) 85 (c) 8500
  37. 37.Best estimate of 3450 ÷ 39? (a) 86 (b) 8600 (c) 860
  38. 38.√56 to 1 decimal place? (a) 7.3 (b) 7.2 (c) 7.5 (d) 7.4
  39. 39.Best estimate of 2607 ÷ 31? (a) 870 (b) 8700 (c) 87
  40. 40.Best estimate of 4330 ÷ 76? (a) 5400 (b) 540 (c) 54

Answer key

  1. 57
  2. 40
  3. 15
  4. 77
  5. 42
  6. 5.8
  7. 90
  8. 47
  9. 12
  10. 58
  11. 11
  12. 5.7
  13. 42
  14. 39
  15. 21
  16. 9.3
  17. 4.9
  18. 8.4
  19. 7.4
  20. 84
  21. 85
  22. 9.9
  23. 7.8
  24. 7.1
  25. 7.6
  26. 20
  27. 6.7
  28. 18
  29. 44
  30. 9.6
  31. 9.8
  32. 21
  33. 60
  34. 7.1
  35. 47
  36. 85
  37. 86
  38. 7.5
  39. 87
  40. 54

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