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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 6 · 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 1400 ÷ 28? (a) 47 (b) 470 (c) 4700
  2. 2.Best estimate of 621 ÷ 29? (a) 21 (b) 2100 (c) 210
  3. 3.√61 to 1 decimal place? (a) 7.9 (b) 7.7 (c) 7.8 (d) 8.0
  4. 4.√32 to 1 decimal place? (a) 5.8 (b) 5.7 (c) 5.6 (d) 5.5
  5. 5.√79 to 1 decimal place? (a) 9.0 (b) 9.2 (c) 9.1 (d) 8.9
  6. 6.√24 to 1 decimal place? (a) 5.0 (b) 4.7 (c) 4.8 (d) 4.9
  7. 7.Best estimate of 710 ÷ 52? (a) 140 (b) 14 (c) 1400
  8. 8.Best estimate of 705 ÷ 53? (a) 140 (b) 1400 (c) 14
  9. 9.√56 to 1 decimal place? (a) 7.4 (b) 7.3 (c) 7.2 (d) 7.5
  10. 10.√84 to 1 decimal place? (a) 9.1 (b) 9.0 (c) 9.2 (d) 9.3
  11. 11.√37 to 1 decimal place? (a) 6.4 (b) 6.2 (c) 6.1 (d) 6.3
  12. 12.Best estimate of 687 ÷ 24? (a) 34 (b) 3400 (c) 340
  13. 13.Best estimate of 2762 ÷ 72? (a) 39 (b) 390 (c) 3900
  14. 14.√77 to 1 decimal place? (a) 8.6 (b) 8.8 (c) 8.7 (d) 8.5
  15. 15.Best estimate of 1643 ÷ 66? (a) 230 (b) 2300 (c) 23
  16. 16.√82 to 1 decimal place? (a) 9.2 (b) 9.1 (c) 9.3 (d) 9.4
  17. 17.√87 to 1 decimal place? (a) 9.3 (b) 9.4 (c) 9.6 (d) 9.5
  18. 18.√40 to 1 decimal place? (a) 6.1 (b) 6.3 (c) 6.2 (d) 6.0
  19. 19.√74 to 1 decimal place? (a) 8.6 (b) 8.7 (c) 8.4 (d) 8.5
  20. 20.Best estimate of 888 ÷ 62? (a) 1500 (b) 15 (c) 150
  21. 21.√31 to 1 decimal place? (a) 5.8 (b) 5.6 (c) 5.7 (d) 5.5
  22. 22.Best estimate of 5858 ÷ 76? (a) 7300 (b) 73 (c) 730
  23. 23.Best estimate of 2564 ÷ 68? (a) 370 (b) 3700 (c) 37
  24. 24.Best estimate of 5362 ÷ 69? (a) 770 (b) 77 (c) 7700
  25. 25.√41 to 1 decimal place? (a) 6.4 (b) 6.3 (c) 6.5 (d) 6.6
  26. 26.Best estimate of 2494 ÷ 76? (a) 310 (b) 31 (c) 3100
  27. 27.Best estimate of 2252 ÷ 82? (a) 2800 (b) 28 (c) 280
  28. 28.Best estimate of 5744 ÷ 64? (a) 960 (b) 9600 (c) 96
  29. 29.Best estimate of 809 ÷ 27? (a) 27 (b) 2700 (c) 270
  30. 30.Best estimate of 2437 ÷ 37? (a) 6100 (b) 61 (c) 610
  31. 31.√50 to 1 decimal place? (a) 7.0 (b) 7.2 (c) 7.1 (d) 7.3
  32. 32.Best estimate of 3449 ÷ 66? (a) 490 (b) 4900 (c) 49
  33. 33.√23 to 1 decimal place? (a) 4.9 (b) 4.8 (c) 5.0 (d) 4.7
  34. 34.√44 to 1 decimal place? (a) 6.7 (b) 6.6 (c) 6.8 (d) 6.9
  35. 35.Best estimate of 5919 ÷ 74? (a) 8500 (b) 850 (c) 85
  36. 36.√45 to 1 decimal place? (a) 6.8 (b) 6.9 (c) 7.0 (d) 6.7
  37. 37.Best estimate of 2805 ÷ 86? (a) 3100 (b) 31 (c) 310
  38. 38.Best estimate of 2583 ÷ 88? (a) 290 (b) 2900 (c) 29
  39. 39.√34 to 1 decimal place? (a) 6.0 (b) 6.1 (c) 5.8 (d) 5.9
  40. 40.Best estimate of 5442 ÷ 57? (a) 9100 (b) 910 (c) 91

Answer key

  1. 47
  2. 21
  3. 7.8
  4. 5.7
  5. 8.9
  6. 4.9
  7. 14
  8. 14
  9. 7.5
  10. 9.2
  11. 6.1
  12. 34
  13. 39
  14. 8.8
  15. 23
  16. 9.1
  17. 9.3
  18. 6.3
  19. 8.6
  20. 15
  21. 5.6
  22. 73
  23. 37
  24. 77
  25. 6.4
  26. 31
  27. 28
  28. 96
  29. 27
  30. 61
  31. 7.1
  32. 49
  33. 4.8
  34. 6.6
  35. 85
  36. 6.7
  37. 31
  38. 29
  39. 5.8
  40. 91

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