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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 244 · 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.√89 to 1 decimal place? (a) 9.3 (b) 9.5 (c) 9.4 (d) 9.6
  2. 2.Best estimate of 1139 ÷ 46? (a) 23 (b) 2300 (c) 230
  3. 3.√66 to 1 decimal place? (a) 7.8 (b) 8.1 (c) 8.0 (d) 7.9
  4. 4.√51 to 1 decimal place? (a) 7.0 (b) 7.2 (c) 7.3 (d) 7.1
  5. 5.√37 to 1 decimal place? (a) 6.3 (b) 6.1 (c) 6.2 (d) 6.4
  6. 6.Best estimate of 884 ÷ 51? (a) 1800 (b) 18 (c) 180
  7. 7.√29 to 1 decimal place? (a) 5.5 (b) 5.4 (c) 5.6 (d) 5.3
  8. 8.Best estimate of 5525 ÷ 74? (a) 7900 (b) 790 (c) 79
  9. 9.√82 to 1 decimal place? (a) 9.0 (b) 9.3 (c) 9.1 (d) 9.2
  10. 10.√78 to 1 decimal place? (a) 8.6 (b) 8.7 (c) 8.8 (d) 8.5
  11. 11.Best estimate of 486 ÷ 36? (a) 120 (b) 1200 (c) 12
  12. 12.√21 to 1 decimal place? (a) 4.6 (b) 4.4 (c) 4.5 (d) 4.7
  13. 13.Best estimate of 7520 ÷ 89? (a) 84 (b) 8400 (c) 840
  14. 14.√71 to 1 decimal place? (a) 8.4 (b) 8.2 (c) 8.3 (d) 8.1
  15. 15.Best estimate of 3553 ÷ 46? (a) 71 (b) 7100 (c) 710
  16. 16.√50 to 1 decimal place? (a) 7.0 (b) 7.1 (c) 7.3 (d) 7.2
  17. 17.Best estimate of 2222 ÷ 34? (a) 740 (b) 7400 (c) 74
  18. 18.√96 to 1 decimal place? (a) 10.1 (b) 9.8 (c) 10.0 (d) 9.9
  19. 19.√62 to 1 decimal place? (a) 7.9 (b) 7.8 (c) 8.0 (d) 7.7
  20. 20.Best estimate of 2723 ÷ 89? (a) 300 (b) 3000 (c) 30
  21. 21.Best estimate of 5863 ÷ 64? (a) 9800 (b) 980 (c) 98
  22. 22.√98 to 1 decimal place? (a) 9.9 (b) 10.2 (c) 10.1 (d) 10.0
  23. 23.√28 to 1 decimal place? (a) 5.4 (b) 5.3 (c) 5.1 (d) 5.2
  24. 24.Best estimate of 2315 ÷ 48? (a) 46 (b) 4600 (c) 460
  25. 25.√80 to 1 decimal place? (a) 8.7 (b) 9.0 (c) 8.8 (d) 8.9
  26. 26.√27 to 1 decimal place? (a) 5.2 (b) 5.0 (c) 5.1 (d) 4.9
  27. 27.Best estimate of 621 ÷ 41? (a) 160 (b) 1600 (c) 16
  28. 28.Best estimate of 1128 ÷ 22? (a) 56 (b) 560 (c) 5600
  29. 29.Best estimate of 1154 ÷ 29? (a) 3800 (b) 38 (c) 380
  30. 30.Best estimate of 1797 ÷ 83? (a) 220 (b) 22 (c) 2200
  31. 31.Best estimate of 5378 ÷ 68? (a) 7700 (b) 77 (c) 770
  32. 32.Best estimate of 6442 ÷ 86? (a) 720 (b) 7200 (c) 72
  33. 33.√55 to 1 decimal place? (a) 7.5 (b) 7.4 (c) 7.7 (d) 7.6
  34. 34.√48 to 1 decimal place? (a) 7.0 (b) 7.2 (c) 6.9 (d) 7.1
  35. 35.√34 to 1 decimal place? (a) 5.8 (b) 5.7 (c) 5.6 (d) 5.5
  36. 36.Best estimate of 1492 ÷ 36? (a) 3700 (b) 37 (c) 370
  37. 37.√76 to 1 decimal place? (a) 8.4 (b) 8.7 (c) 8.6 (d) 8.5
  38. 38.Best estimate of 5480 ÷ 82? (a) 690 (b) 6900 (c) 69
  39. 39.√74 to 1 decimal place? (a) 8.8 (b) 8.6 (c) 8.7 (d) 8.9
  40. 40.√87 to 1 decimal place? (a) 9.2 (b) 9.3 (c) 9.0 (d) 9.1

Answer key

  1. 9.4
  2. 23
  3. 8.1
  4. 7.1
  5. 6.1
  6. 18
  7. 5.4
  8. 79
  9. 9.1
  10. 8.8
  11. 12
  12. 4.6
  13. 84
  14. 8.4
  15. 71
  16. 7.1
  17. 74
  18. 9.8
  19. 7.9
  20. 30
  21. 98
  22. 9.9
  23. 5.3
  24. 46
  25. 8.9
  26. 5.2
  27. 16
  28. 56
  29. 38
  30. 22
  31. 77
  32. 72
  33. 7.4
  34. 6.9
  35. 5.8
  36. 37
  37. 8.7
  38. 69
  39. 8.6
  40. 9.3

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