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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 843 · 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 725 ÷ 52? (a) 150 (b) 15 (c) 1500
  2. 2.√67 to 1 decimal place? (a) 8.2 (b) 8.4 (c) 8.5 (d) 8.3
  3. 3.√66 to 1 decimal place? (a) 8.0 (b) 8.3 (c) 8.2 (d) 8.1
  4. 4.√40 to 1 decimal place? (a) 6.6 (b) 6.4 (c) 6.5 (d) 6.3
  5. 5.Best estimate of 1844 ÷ 81? (a) 230 (b) 23 (c) 2300
  6. 6.Best estimate of 2516 ÷ 66? (a) 36 (b) 3600 (c) 360
  7. 7.Best estimate of 968 ÷ 42? (a) 2400 (b) 24 (c) 240
  8. 8.Best estimate of 3095 ÷ 82? (a) 390 (b) 39 (c) 3900
  9. 9.Best estimate of 652 ÷ 28? (a) 220 (b) 2200 (c) 22
  10. 10.√65 to 1 decimal place? (a) 8.0 (b) 8.3 (c) 8.1 (d) 8.2
  11. 11.Best estimate of 4778 ÷ 78? (a) 6000 (b) 600 (c) 60
  12. 12.Best estimate of 1637 ÷ 28? (a) 5500 (b) 55 (c) 550
  13. 13.√61 to 1 decimal place? (a) 7.9 (b) 7.8 (c) 8.0 (d) 7.7
  14. 14.Best estimate of 979 ÷ 34? (a) 3300 (b) 330 (c) 33
  15. 15.Best estimate of 2412 ÷ 27? (a) 8000 (b) 80 (c) 800
  16. 16.√55 to 1 decimal place? (a) 7.4 (b) 7.5 (c) 7.6 (d) 7.3
  17. 17.Best estimate of 3243 ÷ 42? (a) 81 (b) 810 (c) 8100
  18. 18.Best estimate of 6360 ÷ 67? (a) 910 (b) 91 (c) 9100
  19. 19.√59 to 1 decimal place? (a) 7.7 (b) 7.5 (c) 7.4 (d) 7.6
  20. 20.√48 to 1 decimal place? (a) 6.8 (b) 6.9 (c) 7.0 (d) 6.7
  21. 21.√23 to 1 decimal place? (a) 4.7 (b) 4.6 (c) 4.5 (d) 4.8
  22. 22.√22 to 1 decimal place? (a) 4.6 (b) 4.4 (c) 4.5 (d) 4.7
  23. 23.Best estimate of 4593 ÷ 62? (a) 7700 (b) 770 (c) 77
  24. 24.√20 to 1 decimal place? (a) 4.8 (b) 4.5 (c) 4.6 (d) 4.7
  25. 25.√87 to 1 decimal place? (a) 9.5 (b) 9.4 (c) 9.3 (d) 9.2
  26. 26.Best estimate of 6055 ÷ 89? (a) 67 (b) 6700 (c) 670
  27. 27.Best estimate of 2766 ÷ 82? (a) 35 (b) 3500 (c) 350
  28. 28.Best estimate of 1434 ÷ 31? (a) 48 (b) 480 (c) 4800
  29. 29.Best estimate of 907 ÷ 23? (a) 4500 (b) 450 (c) 45
  30. 30.Best estimate of 1593 ÷ 36? (a) 4000 (b) 40 (c) 400
  31. 31.Best estimate of 2582 ÷ 41? (a) 650 (b) 6500 (c) 65
  32. 32.Best estimate of 2598 ÷ 33? (a) 870 (b) 87 (c) 8700
  33. 33.Best estimate of 2246 ÷ 24? (a) 11200 (b) 1120 (c) 112
  34. 34.√76 to 1 decimal place? (a) 8.9 (b) 8.7 (c) 9.0 (d) 8.8
  35. 35.√78 to 1 decimal place? (a) 8.7 (b) 8.6 (c) 8.5 (d) 8.8
  36. 36.Best estimate of 593 ÷ 42? (a) 1500 (b) 15 (c) 150
  37. 37.Best estimate of 2166 ÷ 28? (a) 7200 (b) 72 (c) 720
  38. 38.√21 to 1 decimal place? (a) 4.6 (b) 4.5 (c) 4.8 (d) 4.7
  39. 39.√94 to 1 decimal place? (a) 9.9 (b) 9.7 (c) 10.0 (d) 9.8
  40. 40.√92 to 1 decimal place? (a) 9.6 (b) 9.8 (c) 9.7 (d) 9.5

Answer key

  1. 15
  2. 8.2
  3. 8.1
  4. 6.3
  5. 23
  6. 36
  7. 24
  8. 39
  9. 22
  10. 8.1
  11. 60
  12. 55
  13. 7.8
  14. 33
  15. 80
  16. 7.4
  17. 81
  18. 91
  19. 7.7
  20. 6.9
  21. 4.8
  22. 4.7
  23. 77
  24. 4.5
  25. 9.3
  26. 67
  27. 35
  28. 48
  29. 45
  30. 40
  31. 65
  32. 87
  33. 112
  34. 8.7
  35. 8.8
  36. 15
  37. 72
  38. 4.6
  39. 9.7
  40. 9.6

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