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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 29 · 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 3642 ÷ 63? (a) 61 (b) 610 (c) 6100
  2. 2.Best estimate of 299 ÷ 22? (a) 1500 (b) 15 (c) 150
  3. 3.Best estimate of 5785 ÷ 83? (a) 7200 (b) 720 (c) 72
  4. 4.√86 to 1 decimal place? (a) 9.1 (b) 9.3 (c) 9.2 (d) 9.4
  5. 5.√48 to 1 decimal place? (a) 6.8 (b) 7.0 (c) 6.9 (d) 6.7
  6. 6.√27 to 1 decimal place? (a) 5.2 (b) 5.1 (c) 5.0 (d) 4.9
  7. 7.√85 to 1 decimal place? (a) 9.3 (b) 9.2 (c) 9.0 (d) 9.1
  8. 8.√69 to 1 decimal place? (a) 8.1 (b) 8.4 (c) 8.2 (d) 8.3
  9. 9.√62 to 1 decimal place? (a) 8.0 (b) 7.8 (c) 7.7 (d) 7.9
  10. 10.Best estimate of 3837 ÷ 73? (a) 550 (b) 5500 (c) 55
  11. 11.√76 to 1 decimal place? (a) 8.8 (b) 8.6 (c) 8.5 (d) 8.7
  12. 12.Best estimate of 3063 ÷ 51? (a) 6100 (b) 61 (c) 610
  13. 13.√40 to 1 decimal place? (a) 6.6 (b) 6.5 (c) 6.3 (d) 6.4
  14. 14.√89 to 1 decimal place? (a) 9.1 (b) 9.4 (c) 9.3 (d) 9.2
  15. 15.Best estimate of 2787 ÷ 43? (a) 70 (b) 7000 (c) 700
  16. 16.Best estimate of 2983 ÷ 42? (a) 75 (b) 7500 (c) 750
  17. 17.√23 to 1 decimal place? (a) 4.8 (b) 4.5 (c) 4.6 (d) 4.7
  18. 18.Best estimate of 1890 ÷ 27? (a) 63 (b) 6300 (c) 630
  19. 19.√88 to 1 decimal place? (a) 9.3 (b) 9.4 (c) 9.1 (d) 9.2
  20. 20.Best estimate of 1109 ÷ 36? (a) 280 (b) 2800 (c) 28
  21. 21.Best estimate of 836 ÷ 28? (a) 280 (b) 2800 (c) 28
  22. 22.Best estimate of 1639 ÷ 59? (a) 27 (b) 2700 (c) 270
  23. 23.Best estimate of 1278 ÷ 82? (a) 16 (b) 160 (c) 1600
  24. 24.√74 to 1 decimal place? (a) 8.7 (b) 8.5 (c) 8.4 (d) 8.6
  25. 25.Best estimate of 1332 ÷ 21? (a) 67 (b) 6700 (c) 670
  26. 26.√20 to 1 decimal place? (a) 4.4 (b) 4.2 (c) 4.3 (d) 4.5
  27. 27.Best estimate of 2963 ÷ 42? (a) 740 (b) 7400 (c) 74
  28. 28.√65 to 1 decimal place? (a) 7.8 (b) 7.9 (c) 8.1 (d) 8.0
  29. 29.√38 to 1 decimal place? (a) 6.1 (b) 6.2 (c) 5.9 (d) 6.0
  30. 30.Best estimate of 803 ÷ 22? (a) 40 (b) 400 (c) 4000
  31. 31.√56 to 1 decimal place? (a) 7.6 (b) 7.5 (c) 7.4 (d) 7.3
  32. 32.√37 to 1 decimal place? (a) 6.2 (b) 6.0 (c) 6.1 (d) 6.3
  33. 33.√42 to 1 decimal place? (a) 6.6 (b) 6.5 (c) 6.8 (d) 6.7
  34. 34.Best estimate of 1375 ÷ 62? (a) 23 (b) 2300 (c) 230
  35. 35.Best estimate of 2218 ÷ 56? (a) 37 (b) 3700 (c) 370
  36. 36.Best estimate of 2946 ÷ 36? (a) 74 (b) 7400 (c) 740
  37. 37.Best estimate of 1246 ÷ 27? (a) 4200 (b) 42 (c) 420
  38. 38.Best estimate of 3081 ÷ 48? (a) 62 (b) 6200 (c) 620
  39. 39.Best estimate of 1031 ÷ 64? (a) 1700 (b) 17 (c) 170
  40. 40.√98 to 1 decimal place? (a) 9.9 (b) 10.1 (c) 10.2 (d) 10.0

Answer key

  1. 61
  2. 15
  3. 72
  4. 9.3
  5. 6.9
  6. 5.2
  7. 9.2
  8. 8.3
  9. 7.9
  10. 55
  11. 8.7
  12. 61
  13. 6.3
  14. 9.4
  15. 70
  16. 75
  17. 4.8
  18. 63
  19. 9.4
  20. 28
  21. 28
  22. 27
  23. 16
  24. 8.6
  25. 67
  26. 4.5
  27. 74
  28. 8.1
  29. 6.2
  30. 40
  31. 7.5
  32. 6.1
  33. 6.5
  34. 23
  35. 37
  36. 74
  37. 42
  38. 62
  39. 17
  40. 9.9

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