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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 580 · 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 1941 ÷ 79? (a) 2400 (b) 240 (c) 24
  2. 2.Best estimate of 1711 ÷ 76? (a) 2100 (b) 21 (c) 210
  3. 3.Best estimate of 2108 ÷ 73? (a) 30 (b) 300 (c) 3000
  4. 4.√55 to 1 decimal place? (a) 7.5 (b) 7.3 (c) 7.2 (d) 7.4
  5. 5.Best estimate of 603 ÷ 23? (a) 30 (b) 300 (c) 3000
  6. 6.Best estimate of 5307 ÷ 62? (a) 880 (b) 88 (c) 8800
  7. 7.√84 to 1 decimal place? (a) 9.1 (b) 9.2 (c) 9.0 (d) 9.3
  8. 8.Best estimate of 2066 ÷ 53? (a) 4100 (b) 41 (c) 410
  9. 9.Best estimate of 1989 ÷ 54? (a) 40 (b) 4000 (c) 400
  10. 10.√79 to 1 decimal place? (a) 9.1 (b) 8.8 (c) 9.0 (d) 8.9
  11. 11.√58 to 1 decimal place? (a) 7.5 (b) 7.8 (c) 7.7 (d) 7.6
  12. 12.Best estimate of 1326 ÷ 46? (a) 270 (b) 27 (c) 2700
  13. 13.Best estimate of 912 ÷ 56? (a) 1500 (b) 150 (c) 15
  14. 14.Best estimate of 6248 ÷ 71? (a) 890 (b) 89 (c) 8900
  15. 15.Best estimate of 710 ÷ 32? (a) 240 (b) 24 (c) 2400
  16. 16.Best estimate of 2114 ÷ 26? (a) 7000 (b) 700 (c) 70
  17. 17.Best estimate of 5902 ÷ 62? (a) 980 (b) 98 (c) 9800
  18. 18.√82 to 1 decimal place? (a) 9.2 (b) 9.4 (c) 9.1 (d) 9.3
  19. 19.Best estimate of 1097 ÷ 23? (a) 550 (b) 5500 (c) 55
  20. 20.Best estimate of 3792 ÷ 82? (a) 4700 (b) 470 (c) 47
  21. 21.Best estimate of 4023 ÷ 59? (a) 6700 (b) 67 (c) 670
  22. 22.√41 to 1 decimal place? (a) 6.5 (b) 6.7 (c) 6.4 (d) 6.6
  23. 23.√65 to 1 decimal place? (a) 8.1 (b) 8.2 (c) 8.3 (d) 8.4
  24. 24.Best estimate of 3833 ÷ 46? (a) 770 (b) 7700 (c) 77
  25. 25.√23 to 1 decimal place? (a) 4.7 (b) 4.5 (c) 4.8 (d) 4.6
  26. 26.Best estimate of 470 ÷ 33? (a) 160 (b) 1600 (c) 16
  27. 27.√89 to 1 decimal place? (a) 9.4 (b) 9.2 (c) 9.3 (d) 9.5
  28. 28.Best estimate of 2745 ÷ 36? (a) 69 (b) 6900 (c) 690
  29. 29.Best estimate of 7574 ÷ 82? (a) 9500 (b) 950 (c) 95
  30. 30.Best estimate of 3443 ÷ 58? (a) 570 (b) 5700 (c) 57
  31. 31.√90 to 1 decimal place? (a) 9.7 (b) 9.6 (c) 9.4 (d) 9.5
  32. 32.√35 to 1 decimal place? (a) 6.1 (b) 6.2 (c) 5.9 (d) 6.0
  33. 33.Best estimate of 4391 ÷ 68? (a) 6300 (b) 63 (c) 630
  34. 34.Best estimate of 2255 ÷ 28? (a) 75 (b) 750 (c) 7500
  35. 35.√37 to 1 decimal place? (a) 6.1 (b) 6.2 (c) 6.0 (d) 6.3
  36. 36.Best estimate of 3789 ÷ 63? (a) 6300 (b) 63 (c) 630
  37. 37.√28 to 1 decimal place? (a) 5.1 (b) 5.3 (c) 5.0 (d) 5.2
  38. 38.Best estimate of 2216 ÷ 76? (a) 280 (b) 28 (c) 2800
  39. 39.√61 to 1 decimal place? (a) 7.9 (b) 8.0 (c) 8.1 (d) 7.8
  40. 40.√77 to 1 decimal place? (a) 8.8 (b) 8.6 (c) 8.7 (d) 8.9

Answer key

  1. 24
  2. 21
  3. 30
  4. 7.4
  5. 30
  6. 88
  7. 9.2
  8. 41
  9. 40
  10. 8.9
  11. 7.6
  12. 27
  13. 15
  14. 89
  15. 24
  16. 70
  17. 98
  18. 9.1
  19. 55
  20. 47
  21. 67
  22. 6.4
  23. 8.1
  24. 77
  25. 4.8
  26. 16
  27. 9.4
  28. 69
  29. 95
  30. 57
  31. 9.5
  32. 5.9
  33. 63
  34. 75
  35. 6.1
  36. 63
  37. 5.3
  38. 28
  39. 7.8
  40. 8.8

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