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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 489 · 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.√45 to 1 decimal place? (a) 6.7 (b) 6.9 (c) 6.8 (d) 6.6
  2. 2.Best estimate of 4679 ÷ 64? (a) 780 (b) 78 (c) 7800
  3. 3.√28 to 1 decimal place? (a) 5.2 (b) 5.1 (c) 5.3 (d) 5.0
  4. 4.Best estimate of 779 ÷ 23? (a) 3900 (b) 39 (c) 390
  5. 5.Best estimate of 6010 ÷ 71? (a) 860 (b) 8600 (c) 86
  6. 6.√90 to 1 decimal place? (a) 9.6 (b) 9.4 (c) 9.3 (d) 9.5
  7. 7.Best estimate of 539 ÷ 39? (a) 130 (b) 13 (c) 1300
  8. 8.√96 to 1 decimal place? (a) 9.8 (b) 9.7 (c) 9.6 (d) 9.9
  9. 9.√46 to 1 decimal place? (a) 6.7 (b) 6.9 (c) 6.6 (d) 6.8
  10. 10.√58 to 1 decimal place? (a) 7.7 (b) 7.6 (c) 7.9 (d) 7.8
  11. 11.Best estimate of 1338 ÷ 68? (a) 190 (b) 1900 (c) 19
  12. 12.√79 to 1 decimal place? (a) 8.7 (b) 8.8 (c) 8.6 (d) 8.9
  13. 13.√74 to 1 decimal place? (a) 8.7 (b) 8.4 (c) 8.6 (d) 8.5
  14. 14.Best estimate of 578 ÷ 28? (a) 19 (b) 1900 (c) 190
  15. 15.√76 to 1 decimal place? (a) 8.9 (b) 8.7 (c) 8.8 (d) 8.6
  16. 16.Best estimate of 1344 ÷ 72? (a) 1900 (b) 190 (c) 19
  17. 17.Best estimate of 1037 ÷ 58? (a) 170 (b) 1700 (c) 17
  18. 18.Best estimate of 1129 ÷ 59? (a) 1900 (b) 190 (c) 19
  19. 19.√83 to 1 decimal place? (a) 9.0 (b) 9.1 (c) 9.3 (d) 9.2
  20. 20.Best estimate of 4889 ÷ 64? (a) 8100 (b) 81 (c) 810
  21. 21.Best estimate of 3437 ÷ 42? (a) 8600 (b) 86 (c) 860
  22. 22.Best estimate of 538 ÷ 42? (a) 1300 (b) 13 (c) 130
  23. 23.Best estimate of 3205 ÷ 57? (a) 530 (b) 53 (c) 5300
  24. 24.√65 to 1 decimal place? (a) 8.1 (b) 8.2 (c) 8.3 (d) 8.0
  25. 25.√78 to 1 decimal place? (a) 8.6 (b) 8.8 (c) 8.9 (d) 8.7
  26. 26.√82 to 1 decimal place? (a) 9.0 (b) 8.8 (c) 8.9 (d) 9.1
  27. 27.Best estimate of 4254 ÷ 46? (a) 85 (b) 850 (c) 8500
  28. 28.√89 to 1 decimal place? (a) 9.4 (b) 9.5 (c) 9.3 (d) 9.2
  29. 29.Best estimate of 1133 ÷ 82? (a) 14 (b) 1400 (c) 140
  30. 30.√34 to 1 decimal place? (a) 5.7 (b) 5.6 (c) 5.8 (d) 5.9
  31. 31.Best estimate of 629 ÷ 46? (a) 130 (b) 13 (c) 1300
  32. 32.Best estimate of 3665 ÷ 77? (a) 46 (b) 460 (c) 4600
  33. 33.Best estimate of 1873 ÷ 66? (a) 2700 (b) 27 (c) 270
  34. 34.√52 to 1 decimal place? (a) 7.2 (b) 7.0 (c) 7.3 (d) 7.1
  35. 35.Best estimate of 6291 ÷ 74? (a) 90 (b) 900 (c) 9000
  36. 36.√40 to 1 decimal place? (a) 6.0 (b) 6.3 (c) 6.2 (d) 6.1
  37. 37.Best estimate of 8445 ÷ 89? (a) 9400 (b) 94 (c) 940
  38. 38.Best estimate of 1570 ÷ 67? (a) 22 (b) 2200 (c) 220
  39. 39.√61 to 1 decimal place? (a) 7.9 (b) 7.8 (c) 8.1 (d) 8.0
  40. 40.Best estimate of 2421 ÷ 72? (a) 350 (b) 35 (c) 3500

Answer key

  1. 6.7
  2. 78
  3. 5.3
  4. 39
  5. 86
  6. 9.5
  7. 13
  8. 9.8
  9. 6.8
  10. 7.6
  11. 19
  12. 8.9
  13. 8.6
  14. 19
  15. 8.7
  16. 19
  17. 17
  18. 19
  19. 9.1
  20. 81
  21. 86
  22. 13
  23. 53
  24. 8.1
  25. 8.8
  26. 9.1
  27. 85
  28. 9.4
  29. 14
  30. 5.8
  31. 13
  32. 46
  33. 27
  34. 7.2
  35. 90
  36. 6.3
  37. 94
  38. 22
  39. 7.8
  40. 35

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