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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 625 · 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 6621 ÷ 78? (a) 8300 (b) 830 (c) 83
  2. 2.Best estimate of 2120 ÷ 87? (a) 2400 (b) 240 (c) 24
  3. 3.Best estimate of 1321 ÷ 22? (a) 6600 (b) 660 (c) 66
  4. 4.√70 to 1 decimal place? (a) 8.3 (b) 8.5 (c) 8.6 (d) 8.4
  5. 5.Best estimate of 2114 ÷ 54? (a) 420 (b) 4200 (c) 42
  6. 6.Best estimate of 2132 ÷ 36? (a) 53 (b) 5300 (c) 530
  7. 7.Best estimate of 1976 ÷ 86? (a) 220 (b) 2200 (c) 22
  8. 8.Best estimate of 4113 ÷ 79? (a) 510 (b) 51 (c) 5100
  9. 9.Best estimate of 5537 ÷ 69? (a) 790 (b) 7900 (c) 79
  10. 10.Best estimate of 5573 ÷ 59? (a) 9300 (b) 93 (c) 930
  11. 11.Best estimate of 1539 ÷ 81? (a) 190 (b) 19 (c) 1900
  12. 12.Best estimate of 918 ÷ 62? (a) 150 (b) 15 (c) 1500
  13. 13.Best estimate of 3482 ÷ 79? (a) 44 (b) 440 (c) 4400
  14. 14.Best estimate of 4801 ÷ 63? (a) 800 (b) 8000 (c) 80
  15. 15.√52 to 1 decimal place? (a) 7.3 (b) 7.1 (c) 7.4 (d) 7.2
  16. 16.Best estimate of 2287 ÷ 36? (a) 570 (b) 5700 (c) 57
  17. 17.√84 to 1 decimal place? (a) 9.1 (b) 9.2 (c) 9.3 (d) 9.0
  18. 18.√29 to 1 decimal place? (a) 5.4 (b) 5.5 (c) 5.3 (d) 5.2
  19. 19.Best estimate of 4968 ÷ 54? (a) 99 (b) 990 (c) 9900
  20. 20.Best estimate of 1844 ÷ 73? (a) 26 (b) 260 (c) 2600
  21. 21.√45 to 1 decimal place? (a) 6.7 (b) 7.0 (c) 6.9 (d) 6.8
  22. 22.√62 to 1 decimal place? (a) 8.0 (b) 8.2 (c) 7.9 (d) 8.1
  23. 23.Best estimate of 4773 ÷ 66? (a) 6800 (b) 680 (c) 68
  24. 24.Best estimate of 8227 ÷ 88? (a) 9100 (b) 910 (c) 91
  25. 25.Best estimate of 2824 ÷ 82? (a) 350 (b) 3500 (c) 35
  26. 26.Best estimate of 1399 ÷ 28? (a) 47 (b) 4700 (c) 470
  27. 27.Best estimate of 5038 ÷ 82? (a) 630 (b) 63 (c) 6300
  28. 28.√24 to 1 decimal place? (a) 5.0 (b) 5.1 (c) 4.8 (d) 4.9
  29. 29.Best estimate of 6464 ÷ 73? (a) 92 (b) 920 (c) 9200
  30. 30.√47 to 1 decimal place? (a) 7.0 (b) 7.2 (c) 7.1 (d) 6.9
  31. 31.√28 to 1 decimal place? (a) 5.6 (b) 5.5 (c) 5.4 (d) 5.3
  32. 32.Best estimate of 1233 ÷ 66? (a) 1800 (b) 180 (c) 18
  33. 33.√67 to 1 decimal place? (a) 8.2 (b) 8.3 (c) 8.1 (d) 8.0
  34. 34.Best estimate of 3659 ÷ 74? (a) 52 (b) 520 (c) 5200
  35. 35.√40 to 1 decimal place? (a) 6.2 (b) 6.1 (c) 6.3 (d) 6.4
  36. 36.√82 to 1 decimal place? (a) 8.8 (b) 8.9 (c) 9.1 (d) 9.0
  37. 37.Best estimate of 3704 ÷ 66? (a) 53 (b) 5300 (c) 530
  38. 38.√34 to 1 decimal place? (a) 5.8 (b) 5.7 (c) 5.6 (d) 5.5
  39. 39.√46 to 1 decimal place? (a) 6.7 (b) 6.8 (c) 6.6 (d) 6.5
  40. 40.Best estimate of 3639 ÷ 62? (a) 6100 (b) 61 (c) 610

Answer key

  1. 83
  2. 24
  3. 66
  4. 8.4
  5. 42
  6. 53
  7. 22
  8. 51
  9. 79
  10. 93
  11. 19
  12. 15
  13. 44
  14. 80
  15. 7.2
  16. 57
  17. 9.2
  18. 5.4
  19. 99
  20. 26
  21. 6.7
  22. 7.9
  23. 68
  24. 91
  25. 35
  26. 47
  27. 63
  28. 4.9
  29. 92
  30. 6.9
  31. 5.3
  32. 18
  33. 8.2
  34. 52
  35. 6.3
  36. 9.1
  37. 53
  38. 5.8
  39. 6.8
  40. 61

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