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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 609 · 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.√76 to 1 decimal place? (a) 8.9 (b) 8.8 (c) 8.7 (d) 8.6
  2. 2.Best estimate of 1800 ÷ 36? (a) 4500 (b) 450 (c) 45
  3. 3.Best estimate of 323 ÷ 26? (a) 110 (b) 11 (c) 1100
  4. 4.Best estimate of 4998 ÷ 69? (a) 7100 (b) 710 (c) 71
  5. 5.Best estimate of 597 ÷ 43? (a) 150 (b) 1500 (c) 15
  6. 6.√37 to 1 decimal place? (a) 6.1 (b) 5.9 (c) 6.0 (d) 5.8
  7. 7.Best estimate of 4568 ÷ 77? (a) 5700 (b) 570 (c) 57
  8. 8.Best estimate of 3682 ÷ 56? (a) 610 (b) 61 (c) 6100
  9. 9.√41 to 1 decimal place? (a) 6.5 (b) 6.7 (c) 6.4 (d) 6.6
  10. 10.√26 to 1 decimal place? (a) 4.8 (b) 5.1 (c) 5.0 (d) 4.9
  11. 11.√45 to 1 decimal place? (a) 6.6 (b) 6.4 (c) 6.7 (d) 6.5
  12. 12.Best estimate of 3963 ÷ 46? (a) 790 (b) 7900 (c) 79
  13. 13.Best estimate of 3321 ÷ 37? (a) 830 (b) 8300 (c) 83
  14. 14.√98 to 1 decimal place? (a) 9.9 (b) 10.0 (c) 10.1 (d) 10.2
  15. 15.Best estimate of 2293 ÷ 27? (a) 760 (b) 7600 (c) 76
  16. 16.Best estimate of 2146 ÷ 32? (a) 7200 (b) 720 (c) 72
  17. 17.Best estimate of 1231 ÷ 86? (a) 1400 (b) 14 (c) 140
  18. 18.Best estimate of 2023 ÷ 23? (a) 10100 (b) 101 (c) 1010
  19. 19.Best estimate of 1762 ÷ 42? (a) 4400 (b) 44 (c) 440
  20. 20.√32 to 1 decimal place? (a) 5.8 (b) 5.6 (c) 5.7 (d) 5.9
  21. 21.√75 to 1 decimal place? (a) 8.6 (b) 8.8 (c) 8.7 (d) 8.5
  22. 22.√40 to 1 decimal place? (a) 6.3 (b) 6.1 (c) 6.4 (d) 6.2
  23. 23.Best estimate of 4694 ÷ 51? (a) 9400 (b) 940 (c) 94
  24. 24.Best estimate of 3447 ÷ 38? (a) 8600 (b) 860 (c) 86
  25. 25.Best estimate of 5641 ÷ 62? (a) 940 (b) 94 (c) 9400
  26. 26.Best estimate of 3445 ÷ 53? (a) 690 (b) 6900 (c) 69
  27. 27.Best estimate of 5914 ÷ 76? (a) 74 (b) 7400 (c) 740
  28. 28.Best estimate of 993 ÷ 71? (a) 1400 (b) 14 (c) 140
  29. 29.Best estimate of 932 ÷ 56? (a) 1600 (b) 16 (c) 160
  30. 30.Best estimate of 3384 ÷ 42? (a) 850 (b) 85 (c) 8500
  31. 31.Best estimate of 1791 ÷ 32? (a) 60 (b) 6000 (c) 600
  32. 32.Best estimate of 2233 ÷ 43? (a) 560 (b) 56 (c) 5600
  33. 33.Best estimate of 4923 ÷ 52? (a) 9800 (b) 98 (c) 980
  34. 34.Best estimate of 1094 ÷ 83? (a) 14 (b) 140 (c) 1400
  35. 35.√55 to 1 decimal place? (a) 7.3 (b) 7.4 (c) 7.5 (d) 7.2
  36. 36.√61 to 1 decimal place? (a) 8.0 (b) 8.1 (c) 7.9 (d) 7.8
  37. 37.Best estimate of 6145 ÷ 88? (a) 6800 (b) 68 (c) 680
  38. 38.√69 to 1 decimal place? (a) 8.2 (b) 8.4 (c) 8.3 (d) 8.1
  39. 39.√38 to 1 decimal place? (a) 6.2 (b) 6.0 (c) 6.1 (d) 5.9
  40. 40.Best estimate of 3524 ÷ 49? (a) 700 (b) 70 (c) 7000

Answer key

  1. 8.7
  2. 45
  3. 11
  4. 71
  5. 15
  6. 6.1
  7. 57
  8. 61
  9. 6.4
  10. 5.1
  11. 6.7
  12. 79
  13. 83
  14. 9.9
  15. 76
  16. 72
  17. 14
  18. 101
  19. 44
  20. 5.7
  21. 8.7
  22. 6.3
  23. 94
  24. 86
  25. 94
  26. 69
  27. 74
  28. 14
  29. 16
  30. 85
  31. 60
  32. 56
  33. 98
  34. 14
  35. 7.4
  36. 7.8
  37. 68
  38. 8.3
  39. 6.2
  40. 70

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