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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 761 · 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 1724 ÷ 66? (a) 25 (b) 2500 (c) 250
  2. 2.√56 to 1 decimal place? (a) 7.5 (b) 7.4 (c) 7.6 (d) 7.3
  3. 3.√45 to 1 decimal place? (a) 6.8 (b) 6.9 (c) 6.7 (d) 7.0
  4. 4.Best estimate of 3092 ÷ 71? (a) 4400 (b) 440 (c) 44
  5. 5.√65 to 1 decimal place? (a) 8.1 (b) 7.9 (c) 8.0 (d) 7.8
  6. 6.√31 to 1 decimal place? (a) 5.6 (b) 5.8 (c) 5.5 (d) 5.7
  7. 7.√20 to 1 decimal place? (a) 4.4 (b) 4.3 (c) 4.5 (d) 4.6
  8. 8.Best estimate of 1054 ÷ 83? (a) 13 (b) 130 (c) 1300
  9. 9.√82 to 1 decimal place? (a) 9.4 (b) 9.2 (c) 9.1 (d) 9.3
  10. 10.Best estimate of 4075 ÷ 86? (a) 45 (b) 4500 (c) 450
  11. 11.Best estimate of 5200 ÷ 61? (a) 870 (b) 8700 (c) 87
  12. 12.√58 to 1 decimal place? (a) 7.7 (b) 7.6 (c) 7.5 (d) 7.4
  13. 13.Best estimate of 1174 ÷ 26? (a) 390 (b) 3900 (c) 39
  14. 14.Best estimate of 1699 ÷ 36? (a) 42 (b) 420 (c) 4200
  15. 15.√41 to 1 decimal place? (a) 6.5 (b) 6.6 (c) 6.3 (d) 6.4
  16. 16.Best estimate of 1795 ÷ 68? (a) 26 (b) 260 (c) 2600
  17. 17.√83 to 1 decimal place? (a) 9.0 (b) 8.9 (c) 9.1 (d) 8.8
  18. 18.Best estimate of 4639 ÷ 56? (a) 7700 (b) 77 (c) 770
  19. 19.√74 to 1 decimal place? (a) 8.5 (b) 8.7 (c) 8.6 (d) 8.4
  20. 20.Best estimate of 1609 ÷ 73? (a) 23 (b) 2300 (c) 230
  21. 21.√27 to 1 decimal place? (a) 5.1 (b) 5.0 (c) 4.9 (d) 5.2
  22. 22.√71 to 1 decimal place? (a) 8.4 (b) 8.6 (c) 8.7 (d) 8.5
  23. 23.Best estimate of 2522 ÷ 28? (a) 8400 (b) 840 (c) 84
  24. 24.Best estimate of 2214 ÷ 32? (a) 74 (b) 7400 (c) 740
  25. 25.Best estimate of 848 ÷ 28? (a) 280 (b) 2800 (c) 28
  26. 26.√85 to 1 decimal place? (a) 9.3 (b) 9.2 (c) 9.4 (d) 9.1
  27. 27.Best estimate of 3077 ÷ 68? (a) 44 (b) 440 (c) 4400
  28. 28.Best estimate of 2568 ÷ 27? (a) 86 (b) 860 (c) 8600
  29. 29.Best estimate of 2054 ÷ 22? (a) 1030 (b) 10300 (c) 103
  30. 30.Best estimate of 3566 ÷ 67? (a) 5100 (b) 51 (c) 510
  31. 31.√94 to 1 decimal place? (a) 9.7 (b) 9.8 (c) 9.9 (d) 9.6
  32. 32.Best estimate of 2338 ÷ 61? (a) 3900 (b) 39 (c) 390
  33. 33.√28 to 1 decimal place? (a) 5.1 (b) 5.0 (c) 5.2 (d) 5.3
  34. 34.Best estimate of 3341 ÷ 89? (a) 37 (b) 370 (c) 3700
  35. 35.√84 to 1 decimal place? (a) 9.3 (b) 9.2 (c) 9.1 (d) 9.4
  36. 36.Best estimate of 577 ÷ 24? (a) 2900 (b) 290 (c) 29
  37. 37.√29 to 1 decimal place? (a) 5.4 (b) 5.2 (c) 5.3 (d) 5.5
  38. 38.√51 to 1 decimal place? (a) 7.1 (b) 7.2 (c) 7.0 (d) 6.9
  39. 39.√52 to 1 decimal place? (a) 7.1 (b) 7.4 (c) 7.2 (d) 7.3
  40. 40.√40 to 1 decimal place? (a) 6.2 (b) 6.4 (c) 6.3 (d) 6.1

Answer key

  1. 25
  2. 7.5
  3. 6.7
  4. 44
  5. 8.1
  6. 5.6
  7. 4.5
  8. 13
  9. 9.1
  10. 45
  11. 87
  12. 7.6
  13. 39
  14. 42
  15. 6.4
  16. 26
  17. 9.1
  18. 77
  19. 8.6
  20. 23
  21. 5.2
  22. 8.4
  23. 84
  24. 74
  25. 28
  26. 9.2
  27. 44
  28. 86
  29. 103
  30. 51
  31. 9.7
  32. 39
  33. 5.3
  34. 37
  35. 9.2
  36. 29
  37. 5.4
  38. 7.1
  39. 7.2
  40. 6.3

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