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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 387 · 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.√29 to 1 decimal place? (a) 5.6 (b) 5.4 (c) 5.7 (d) 5.5
  2. 2.Best estimate of 1810 ÷ 57? (a) 300 (b) 3000 (c) 30
  3. 3.Best estimate of 1473 ÷ 56? (a) 250 (b) 25 (c) 2500
  4. 4.Best estimate of 1080 ÷ 62? (a) 1800 (b) 180 (c) 18
  5. 5.Best estimate of 5869 ÷ 86? (a) 650 (b) 65 (c) 6500
  6. 6.Best estimate of 1444 ÷ 46? (a) 290 (b) 2900 (c) 29
  7. 7.√96 to 1 decimal place? (a) 9.9 (b) 10.0 (c) 10.1 (d) 9.8
  8. 8.Best estimate of 1162 ÷ 36? (a) 290 (b) 29 (c) 2900
  9. 9.Best estimate of 1116 ÷ 26? (a) 3700 (b) 370 (c) 37
  10. 10.√69 to 1 decimal place? (a) 8.1 (b) 8.3 (c) 8.2 (d) 8.4
  11. 11.√24 to 1 decimal place? (a) 4.9 (b) 4.8 (c) 4.7 (d) 5.0
  12. 12.Best estimate of 949 ÷ 22? (a) 4700 (b) 47 (c) 470
  13. 13.√83 to 1 decimal place? (a) 8.8 (b) 8.9 (c) 9.0 (d) 9.1
  14. 14.Best estimate of 1834 ÷ 33? (a) 610 (b) 61 (c) 6100
  15. 15.√31 to 1 decimal place? (a) 5.6 (b) 5.5 (c) 5.7 (d) 5.4
  16. 16.Best estimate of 4610 ÷ 57? (a) 7700 (b) 770 (c) 77
  17. 17.√58 to 1 decimal place? (a) 7.8 (b) 7.7 (c) 7.9 (d) 7.6
  18. 18.Best estimate of 3838 ÷ 59? (a) 6400 (b) 640 (c) 64
  19. 19.Best estimate of 5704 ÷ 68? (a) 81 (b) 8100 (c) 810
  20. 20.√28 to 1 decimal place? (a) 5.3 (b) 5.6 (c) 5.5 (d) 5.4
  21. 21.Best estimate of 3735 ÷ 56? (a) 620 (b) 6200 (c) 62
  22. 22.√27 to 1 decimal place? (a) 4.9 (b) 5.0 (c) 5.2 (d) 5.1
  23. 23.√48 to 1 decimal place? (a) 7.0 (b) 6.8 (c) 7.1 (d) 6.9
  24. 24.Best estimate of 2338 ÷ 37? (a) 5800 (b) 58 (c) 580
  25. 25.Best estimate of 4041 ÷ 51? (a) 81 (b) 810 (c) 8100
  26. 26.Best estimate of 1182 ÷ 31? (a) 390 (b) 39 (c) 3900
  27. 27.Best estimate of 799 ÷ 26? (a) 2700 (b) 27 (c) 270
  28. 28.Best estimate of 3862 ÷ 87? (a) 4300 (b) 430 (c) 43
  29. 29.Best estimate of 4507 ÷ 68? (a) 64 (b) 640 (c) 6400
  30. 30.Best estimate of 2723 ÷ 52? (a) 5400 (b) 540 (c) 54
  31. 31.Best estimate of 2040 ÷ 34? (a) 68 (b) 6800 (c) 680
  32. 32.√65 to 1 decimal place? (a) 7.9 (b) 8.1 (c) 8.0 (d) 7.8
  33. 33.√46 to 1 decimal place? (a) 6.9 (b) 6.8 (c) 6.6 (d) 6.7
  34. 34.√98 to 1 decimal place? (a) 10.0 (b) 9.8 (c) 9.7 (d) 9.9
  35. 35.√51 to 1 decimal place? (a) 7.2 (b) 7.0 (c) 7.1 (d) 6.9
  36. 36.√71 to 1 decimal place? (a) 8.6 (b) 8.7 (c) 8.5 (d) 8.4
  37. 37.Best estimate of 2577 ÷ 54? (a) 52 (b) 520 (c) 5200
  38. 38.√21 to 1 decimal place? (a) 4.5 (b) 4.4 (c) 4.7 (d) 4.6
  39. 39.√40 to 1 decimal place? (a) 6.2 (b) 6.3 (c) 6.4 (d) 6.1
  40. 40.Best estimate of 2512 ÷ 28? (a) 840 (b) 8400 (c) 84

Answer key

  1. 5.4
  2. 30
  3. 25
  4. 18
  5. 65
  6. 29
  7. 9.8
  8. 29
  9. 37
  10. 8.3
  11. 4.9
  12. 47
  13. 9.1
  14. 61
  15. 5.6
  16. 77
  17. 7.6
  18. 64
  19. 81
  20. 5.3
  21. 62
  22. 5.2
  23. 6.9
  24. 58
  25. 81
  26. 39
  27. 27
  28. 43
  29. 64
  30. 54
  31. 68
  32. 8.1
  33. 6.8
  34. 9.9
  35. 7.1
  36. 8.4
  37. 52
  38. 4.6
  39. 6.3
  40. 84

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