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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 607 · 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.√52 to 1 decimal place? (a) 7.1 (b) 7.2 (c) 6.9 (d) 7.0
  2. 2.Best estimate of 3590 ÷ 61? (a) 60 (b) 6000 (c) 600
  3. 3.√56 to 1 decimal place? (a) 7.5 (b) 7.3 (c) 7.4 (d) 7.6
  4. 4.√96 to 1 decimal place? (a) 9.8 (b) 9.5 (c) 9.6 (d) 9.7
  5. 5.√42 to 1 decimal place? (a) 6.6 (b) 6.7 (c) 6.8 (d) 6.5
  6. 6.Best estimate of 3415 ÷ 46? (a) 6800 (b) 680 (c) 68
  7. 7.√38 to 1 decimal place? (a) 6.4 (b) 6.1 (c) 6.2 (d) 6.3
  8. 8.Best estimate of 3105 ÷ 69? (a) 4400 (b) 440 (c) 44
  9. 9.√27 to 1 decimal place? (a) 5.0 (b) 5.2 (c) 4.9 (d) 5.1
  10. 10.Best estimate of 1496 ÷ 22? (a) 7500 (b) 75 (c) 750
  11. 11.Best estimate of 3850 ÷ 63? (a) 640 (b) 64 (c) 6400
  12. 12.√65 to 1 decimal place? (a) 8.2 (b) 8.0 (c) 8.1 (d) 7.9
  13. 13.Best estimate of 1623 ÷ 22? (a) 810 (b) 8100 (c) 81
  14. 14.Best estimate of 3962 ÷ 66? (a) 570 (b) 57 (c) 5700
  15. 15.Best estimate of 1468 ÷ 86? (a) 16 (b) 160 (c) 1600
  16. 16.Best estimate of 651 ÷ 31? (a) 2200 (b) 22 (c) 220
  17. 17.√92 to 1 decimal place? (a) 9.6 (b) 9.8 (c) 9.9 (d) 9.7
  18. 18.√58 to 1 decimal place? (a) 7.5 (b) 7.4 (c) 7.3 (d) 7.6
  19. 19.√77 to 1 decimal place? (a) 8.6 (b) 8.8 (c) 8.7 (d) 8.5
  20. 20.Best estimate of 1731 ÷ 54? (a) 350 (b) 35 (c) 3500
  21. 21.Best estimate of 5406 ÷ 66? (a) 7700 (b) 770 (c) 77
  22. 22.Best estimate of 5683 ÷ 63? (a) 95 (b) 9500 (c) 950
  23. 23.Best estimate of 2093 ÷ 36? (a) 5200 (b) 520 (c) 52
  24. 24.Best estimate of 1348 ÷ 23? (a) 670 (b) 67 (c) 6700
  25. 25.√59 to 1 decimal place? (a) 7.8 (b) 7.7 (c) 7.9 (d) 8.0
  26. 26.Best estimate of 2459 ÷ 62? (a) 4100 (b) 410 (c) 41
  27. 27.√55 to 1 decimal place? (a) 7.1 (b) 7.2 (c) 7.4 (d) 7.3
  28. 28.Best estimate of 2081 ÷ 78? (a) 260 (b) 26 (c) 2600
  29. 29.Best estimate of 3184 ÷ 86? (a) 35 (b) 350 (c) 3500
  30. 30.Best estimate of 2614 ÷ 51? (a) 5200 (b) 520 (c) 52
  31. 31.Best estimate of 4018 ÷ 67? (a) 570 (b) 5700 (c) 57
  32. 32.√31 to 1 decimal place? (a) 5.5 (b) 5.7 (c) 5.4 (d) 5.6
  33. 33.Best estimate of 2810 ÷ 74? (a) 4000 (b) 40 (c) 400
  34. 34.Best estimate of 2685 ÷ 73? (a) 38 (b) 380 (c) 3800
  35. 35.√89 to 1 decimal place? (a) 9.6 (b) 9.4 (c) 9.5 (d) 9.7
  36. 36.√34 to 1 decimal place? (a) 5.8 (b) 5.9 (c) 6.0 (d) 5.7
  37. 37.Best estimate of 2990 ÷ 36? (a) 750 (b) 7500 (c) 75
  38. 38.Best estimate of 658 ÷ 23? (a) 3300 (b) 33 (c) 330
  39. 39.√78 to 1 decimal place? (a) 8.7 (b) 8.6 (c) 8.5 (d) 8.8
  40. 40.√88 to 1 decimal place? (a) 9.5 (b) 9.3 (c) 9.4 (d) 9.6

Answer key

  1. 7.2
  2. 60
  3. 7.5
  4. 9.8
  5. 6.5
  6. 68
  7. 6.2
  8. 44
  9. 5.2
  10. 75
  11. 64
  12. 8.1
  13. 81
  14. 57
  15. 16
  16. 22
  17. 9.6
  18. 7.6
  19. 8.8
  20. 35
  21. 77
  22. 95
  23. 52
  24. 67
  25. 7.7
  26. 41
  27. 7.4
  28. 26
  29. 35
  30. 52
  31. 57
  32. 5.6
  33. 40
  34. 38
  35. 9.4
  36. 5.8
  37. 75
  38. 33
  39. 8.8
  40. 9.4

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