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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 238 · 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.√50 to 1 decimal place? (a) 7.1 (b) 7.0 (c) 7.3 (d) 7.2
  2. 2.Best estimate of 2975 ÷ 44? (a) 7400 (b) 74 (c) 740
  3. 3.Best estimate of 1117 ÷ 28? (a) 370 (b) 37 (c) 3700
  4. 4.Best estimate of 4463 ÷ 74? (a) 640 (b) 64 (c) 6400
  5. 5.√24 to 1 decimal place? (a) 4.8 (b) 4.7 (c) 5.0 (d) 4.9
  6. 6.√32 to 1 decimal place? (a) 5.4 (b) 5.5 (c) 5.7 (d) 5.6
  7. 7.Best estimate of 6430 ÷ 81? (a) 800 (b) 8000 (c) 80
  8. 8.Best estimate of 4322 ÷ 51? (a) 860 (b) 86 (c) 8600
  9. 9.Best estimate of 1451 ÷ 22? (a) 7300 (b) 73 (c) 730
  10. 10.Best estimate of 642 ÷ 21? (a) 3200 (b) 32 (c) 320
  11. 11.√27 to 1 decimal place? (a) 5.0 (b) 5.1 (c) 5.3 (d) 5.2
  12. 12.Best estimate of 1579 ÷ 62? (a) 2600 (b) 260 (c) 26
  13. 13.√37 to 1 decimal place? (a) 5.9 (b) 6.1 (c) 6.2 (d) 6.0
  14. 14.√42 to 1 decimal place? (a) 6.6 (b) 6.4 (c) 6.3 (d) 6.5
  15. 15.Best estimate of 2169 ÷ 42? (a) 540 (b) 54 (c) 5400
  16. 16.Best estimate of 2373 ÷ 82? (a) 3000 (b) 300 (c) 30
  17. 17.√40 to 1 decimal place? (a) 6.1 (b) 6.0 (c) 6.3 (d) 6.2
  18. 18.√71 to 1 decimal place? (a) 8.5 (b) 8.4 (c) 8.6 (d) 8.3
  19. 19.√41 to 1 decimal place? (a) 6.7 (b) 6.5 (c) 6.6 (d) 6.4
  20. 20.Best estimate of 405 ÷ 33? (a) 14 (b) 1400 (c) 140
  21. 21.Best estimate of 4739 ÷ 61? (a) 7900 (b) 790 (c) 79
  22. 22.Best estimate of 3491 ÷ 47? (a) 7000 (b) 700 (c) 70
  23. 23.√51 to 1 decimal place? (a) 6.9 (b) 7.0 (c) 7.1 (d) 6.8
  24. 24.Best estimate of 6791 ÷ 86? (a) 7500 (b) 75 (c) 750
  25. 25.Best estimate of 1054 ÷ 47? (a) 21 (b) 210 (c) 2100
  26. 26.Best estimate of 4006 ÷ 66? (a) 5700 (b) 570 (c) 57
  27. 27.√78 to 1 decimal place? (a) 8.9 (b) 9.0 (c) 9.1 (d) 8.8
  28. 28.Best estimate of 2055 ÷ 39? (a) 51 (b) 5100 (c) 510
  29. 29.√70 to 1 decimal place? (a) 8.2 (b) 8.1 (c) 8.4 (d) 8.3
  30. 30.√45 to 1 decimal place? (a) 6.6 (b) 6.8 (c) 6.5 (d) 6.7
  31. 31.√66 to 1 decimal place? (a) 8.1 (b) 7.9 (c) 8.0 (d) 8.2
  32. 32.Best estimate of 1369 ÷ 24? (a) 6800 (b) 680 (c) 68
  33. 33.√38 to 1 decimal place? (a) 5.9 (b) 6.0 (c) 6.1 (d) 6.2
  34. 34.Best estimate of 486 ÷ 28? (a) 1600 (b) 16 (c) 160
  35. 35.√63 to 1 decimal place? (a) 7.8 (b) 7.7 (c) 7.6 (d) 7.9
  36. 36.√26 to 1 decimal place? (a) 5.1 (b) 5.2 (c) 5.0 (d) 4.9
  37. 37.√47 to 1 decimal place? (a) 6.9 (b) 7.1 (c) 7.0 (d) 7.2
  38. 38.Best estimate of 2416 ÷ 82? (a) 30 (b) 3000 (c) 300
  39. 39.Best estimate of 2889 ÷ 54? (a) 58 (b) 5800 (c) 580
  40. 40.√96 to 1 decimal place? (a) 9.7 (b) 9.9 (c) 9.8 (d) 9.6

Answer key

  1. 7.1
  2. 74
  3. 37
  4. 64
  5. 4.9
  6. 5.7
  7. 80
  8. 86
  9. 73
  10. 32
  11. 5.2
  12. 26
  13. 6.1
  14. 6.5
  15. 54
  16. 30
  17. 6.3
  18. 8.4
  19. 6.4
  20. 14
  21. 79
  22. 70
  23. 7.1
  24. 75
  25. 21
  26. 57
  27. 8.8
  28. 51
  29. 8.4
  30. 6.7
  31. 8.1
  32. 68
  33. 6.2
  34. 16
  35. 7.9
  36. 5.1
  37. 6.9
  38. 30
  39. 58
  40. 9.8

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