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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 45 · 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 2579 ÷ 49? (a) 520 (b) 52 (c) 5200
  2. 2.√24 to 1 decimal place? (a) 4.9 (b) 4.6 (c) 4.7 (d) 4.8
  3. 3.√94 to 1 decimal place? (a) 9.9 (b) 9.6 (c) 9.8 (d) 9.7
  4. 4.√34 to 1 decimal place? (a) 5.7 (b) 5.8 (c) 5.6 (d) 5.9
  5. 5.√38 to 1 decimal place? (a) 6.1 (b) 6.2 (c) 6.4 (d) 6.3
  6. 6.Best estimate of 1099 ÷ 46? (a) 2200 (b) 22 (c) 220
  7. 7.√65 to 1 decimal place? (a) 7.9 (b) 8.2 (c) 8.1 (d) 8.0
  8. 8.√80 to 1 decimal place? (a) 8.9 (b) 8.7 (c) 8.8 (d) 9.0
  9. 9.√46 to 1 decimal place? (a) 6.6 (b) 6.9 (c) 6.7 (d) 6.8
  10. 10.Best estimate of 2364 ÷ 64? (a) 39 (b) 390 (c) 3900
  11. 11.Best estimate of 5287 ÷ 58? (a) 880 (b) 8800 (c) 88
  12. 12.Best estimate of 4522 ÷ 83? (a) 5700 (b) 57 (c) 570
  13. 13.√82 to 1 decimal place? (a) 9.2 (b) 9.1 (c) 8.9 (d) 9.0
  14. 14.Best estimate of 5514 ÷ 63? (a) 9200 (b) 920 (c) 92
  15. 15.Best estimate of 3789 ÷ 43? (a) 950 (b) 95 (c) 9500
  16. 16.√37 to 1 decimal place? (a) 6.0 (b) 5.9 (c) 6.2 (d) 6.1
  17. 17.Best estimate of 5980 ÷ 86? (a) 660 (b) 66 (c) 6600
  18. 18.√58 to 1 decimal place? (a) 7.3 (b) 7.4 (c) 7.6 (d) 7.5
  19. 19.Best estimate of 649 ÷ 27? (a) 220 (b) 2200 (c) 22
  20. 20.Best estimate of 2617 ÷ 38? (a) 65 (b) 6500 (c) 650
  21. 21.Best estimate of 2896 ÷ 32? (a) 970 (b) 9700 (c) 97
  22. 22.√35 to 1 decimal place? (a) 6.2 (b) 6.0 (c) 5.9 (d) 6.1
  23. 23.Best estimate of 7778 ÷ 86? (a) 8600 (b) 86 (c) 860
  24. 24.√92 to 1 decimal place? (a) 9.4 (b) 9.6 (c) 9.3 (d) 9.5
  25. 25.√74 to 1 decimal place? (a) 8.7 (b) 8.9 (c) 8.8 (d) 8.6
  26. 26.√28 to 1 decimal place? (a) 5.1 (b) 5.3 (c) 5.2 (d) 5.0
  27. 27.Best estimate of 1685 ÷ 26? (a) 5600 (b) 56 (c) 560
  28. 28.√47 to 1 decimal place? (a) 6.7 (b) 6.9 (c) 6.8 (d) 6.6
  29. 29.√71 to 1 decimal place? (a) 8.6 (b) 8.7 (c) 8.4 (d) 8.5
  30. 30.√61 to 1 decimal place? (a) 7.8 (b) 8.0 (c) 8.1 (d) 7.9
  31. 31.Best estimate of 1626 ÷ 24? (a) 810 (b) 81 (c) 8100
  32. 32.Best estimate of 6625 ÷ 74? (a) 95 (b) 950 (c) 9500
  33. 33.√50 to 1 decimal place? (a) 7.0 (b) 7.1 (c) 6.8 (d) 6.9
  34. 34.√55 to 1 decimal place? (a) 7.4 (b) 7.3 (c) 7.2 (d) 7.1
  35. 35.Best estimate of 285 ÷ 23? (a) 140 (b) 14 (c) 1400
  36. 36.√69 to 1 decimal place? (a) 8.3 (b) 8.4 (c) 8.2 (d) 8.1
  37. 37.√23 to 1 decimal place? (a) 4.5 (b) 4.8 (c) 4.6 (d) 4.7
  38. 38.Best estimate of 2450 ÷ 88? (a) 27 (b) 270 (c) 2700
  39. 39.√41 to 1 decimal place? (a) 6.5 (b) 6.4 (c) 6.6 (d) 6.3
  40. 40.√22 to 1 decimal place? (a) 4.8 (b) 4.9 (c) 4.7 (d) 5.0

Answer key

  1. 52
  2. 4.9
  3. 9.7
  4. 5.8
  5. 6.2
  6. 22
  7. 8.1
  8. 8.9
  9. 6.8
  10. 39
  11. 88
  12. 57
  13. 9.1
  14. 92
  15. 95
  16. 6.1
  17. 66
  18. 7.6
  19. 22
  20. 65
  21. 97
  22. 5.9
  23. 86
  24. 9.6
  25. 8.6
  26. 5.3
  27. 56
  28. 6.9
  29. 8.4
  30. 7.8
  31. 81
  32. 95
  33. 7.1
  34. 7.4
  35. 14
  36. 8.3
  37. 4.8
  38. 27
  39. 6.4
  40. 4.7

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