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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 103 · 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.√75 to 1 decimal place? (a) 8.9 (b) 8.8 (c) 8.6 (d) 8.7
  2. 2.Best estimate of 3107 ÷ 41? (a) 7800 (b) 78 (c) 780
  3. 3.√38 to 1 decimal place? (a) 6.4 (b) 6.1 (c) 6.2 (d) 6.3
  4. 4.√31 to 1 decimal place? (a) 5.8 (b) 5.7 (c) 5.9 (d) 5.6
  5. 5.Best estimate of 5684 ÷ 84? (a) 7100 (b) 710 (c) 71
  6. 6.√82 to 1 decimal place? (a) 8.8 (b) 8.9 (c) 9.1 (d) 9.0
  7. 7.Best estimate of 6787 ÷ 86? (a) 750 (b) 75 (c) 7500
  8. 8.Best estimate of 702 ÷ 46? (a) 140 (b) 1400 (c) 14
  9. 9.√79 to 1 decimal place? (a) 8.9 (b) 9.0 (c) 9.1 (d) 8.8
  10. 10.Best estimate of 2248 ÷ 53? (a) 4500 (b) 450 (c) 45
  11. 11.√26 to 1 decimal place? (a) 5.1 (b) 5.2 (c) 5.0 (d) 4.9
  12. 12.√44 to 1 decimal place? (a) 6.6 (b) 6.4 (c) 6.7 (d) 6.5
  13. 13.√27 to 1 decimal place? (a) 5.3 (b) 5.4 (c) 5.2 (d) 5.5
  14. 14.Best estimate of 2713 ÷ 66? (a) 390 (b) 3900 (c) 39
  15. 15.√88 to 1 decimal place? (a) 9.5 (b) 9.2 (c) 9.4 (d) 9.3
  16. 16.Best estimate of 6496 ÷ 89? (a) 720 (b) 7200 (c) 72
  17. 17.Best estimate of 720 ÷ 28? (a) 2400 (b) 24 (c) 240
  18. 18.√96 to 1 decimal place? (a) 9.8 (b) 9.9 (c) 10.0 (d) 9.7
  19. 19.Best estimate of 2614 ÷ 62? (a) 440 (b) 4400 (c) 44
  20. 20.√98 to 1 decimal place? (a) 9.9 (b) 9.7 (c) 9.8 (d) 9.6
  21. 21.√46 to 1 decimal place? (a) 6.5 (b) 6.6 (c) 6.8 (d) 6.7
  22. 22.√22 to 1 decimal place? (a) 4.9 (b) 4.7 (c) 4.8 (d) 5.0
  23. 23.√47 to 1 decimal place? (a) 6.9 (b) 6.6 (c) 6.7 (d) 6.8
  24. 24.Best estimate of 1967 ÷ 37? (a) 4900 (b) 49 (c) 490
  25. 25.√20 to 1 decimal place? (a) 4.6 (b) 4.7 (c) 4.8 (d) 4.5
  26. 26.√76 to 1 decimal place? (a) 8.8 (b) 8.9 (c) 9.0 (d) 8.7
  27. 27.Best estimate of 1369 ÷ 46? (a) 27 (b) 2700 (c) 270
  28. 28.Best estimate of 6671 ÷ 79? (a) 83 (b) 830 (c) 8300
  29. 29.Best estimate of 5311 ÷ 76? (a) 660 (b) 66 (c) 6600
  30. 30.√61 to 1 decimal place? (a) 7.6 (b) 7.9 (c) 7.8 (d) 7.7
  31. 31.√55 to 1 decimal place? (a) 7.5 (b) 7.3 (c) 7.2 (d) 7.4
  32. 32.√70 to 1 decimal place? (a) 8.2 (b) 8.3 (c) 8.1 (d) 8.4
  33. 33.√51 to 1 decimal place? (a) 7.3 (b) 7.1 (c) 7.4 (d) 7.2
  34. 34.√37 to 1 decimal place? (a) 6.1 (b) 6.2 (c) 6.3 (d) 6.4
  35. 35.Best estimate of 5677 ÷ 81? (a) 71 (b) 710 (c) 7100
  36. 36.√74 to 1 decimal place? (a) 8.3 (b) 8.4 (c) 8.5 (d) 8.6
  37. 37.Best estimate of 2928 ÷ 64? (a) 490 (b) 49 (c) 4900
  38. 38.Best estimate of 1803 ÷ 54? (a) 360 (b) 3600 (c) 36
  39. 39.Best estimate of 2317 ÷ 36? (a) 580 (b) 58 (c) 5800
  40. 40.Best estimate of 4375 ÷ 76? (a) 55 (b) 550 (c) 5500

Answer key

  1. 8.7
  2. 78
  3. 6.2
  4. 5.6
  5. 71
  6. 9.1
  7. 75
  8. 14
  9. 8.9
  10. 45
  11. 5.1
  12. 6.6
  13. 5.2
  14. 39
  15. 9.4
  16. 72
  17. 24
  18. 9.8
  19. 44
  20. 9.9
  21. 6.8
  22. 4.7
  23. 6.9
  24. 49
  25. 4.5
  26. 8.7
  27. 27
  28. 83
  29. 66
  30. 7.8
  31. 7.4
  32. 8.4
  33. 7.1
  34. 6.1
  35. 71
  36. 8.6
  37. 49
  38. 36
  39. 58
  40. 55

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