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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 322 · 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 3052 ÷ 68? (a) 4400 (b) 44 (c) 440
  2. 2.Best estimate of 5005 ÷ 53? (a) 100 (b) 10000 (c) 1000
  3. 3.Best estimate of 3121 ÷ 43? (a) 7800 (b) 780 (c) 78
  4. 4.√40 to 1 decimal place? (a) 6.3 (b) 6.2 (c) 6.1 (d) 6.4
  5. 5.Best estimate of 3383 ÷ 46? (a) 68 (b) 680 (c) 6800
  6. 6.Best estimate of 1834 ÷ 79? (a) 2300 (b) 23 (c) 230
  7. 7.√96 to 1 decimal place? (a) 10.0 (b) 10.1 (c) 9.8 (d) 9.9
  8. 8.√62 to 1 decimal place? (a) 7.9 (b) 8.1 (c) 8.0 (d) 7.8
  9. 9.Best estimate of 3645 ÷ 54? (a) 7300 (b) 73 (c) 730
  10. 10.Best estimate of 1365 ÷ 48? (a) 270 (b) 2700 (c) 27
  11. 11.√47 to 1 decimal place? (a) 7.2 (b) 7.1 (c) 7.0 (d) 6.9
  12. 12.Best estimate of 324 ÷ 22? (a) 160 (b) 16 (c) 1600
  13. 13.Best estimate of 1991 ÷ 41? (a) 50 (b) 500 (c) 5000
  14. 14.Best estimate of 2048 ÷ 82? (a) 260 (b) 2600 (c) 26
  15. 15.√76 to 1 decimal place? (a) 8.8 (b) 8.9 (c) 8.7 (d) 8.6
  16. 16.√66 to 1 decimal place? (a) 8.1 (b) 8.0 (c) 8.2 (d) 7.9
  17. 17.Best estimate of 2981 ÷ 53? (a) 600 (b) 60 (c) 6000
  18. 18.Best estimate of 8037 ÷ 87? (a) 89 (b) 8900 (c) 890
  19. 19.Best estimate of 2762 ÷ 73? (a) 39 (b) 3900 (c) 390
  20. 20.Best estimate of 1292 ÷ 28? (a) 43 (b) 430 (c) 4300
  21. 21.√84 to 1 decimal place? (a) 9.4 (b) 9.3 (c) 9.2 (d) 9.5
  22. 22.√21 to 1 decimal place? (a) 4.8 (b) 4.9 (c) 4.6 (d) 4.7
  23. 23.√98 to 1 decimal place? (a) 10.1 (b) 10.0 (c) 9.8 (d) 9.9
  24. 24.√58 to 1 decimal place? (a) 7.6 (b) 7.4 (c) 7.7 (d) 7.5
  25. 25.Best estimate of 4945 ÷ 71? (a) 710 (b) 71 (c) 7100
  26. 26.√82 to 1 decimal place? (a) 9.4 (b) 9.1 (c) 9.2 (d) 9.3
  27. 27.Best estimate of 1911 ÷ 22? (a) 96 (b) 960 (c) 9600
  28. 28.√22 to 1 decimal place? (a) 4.6 (b) 4.9 (c) 4.7 (d) 4.8
  29. 29.√44 to 1 decimal place? (a) 6.7 (b) 6.6 (c) 6.8 (d) 6.5
  30. 30.√38 to 1 decimal place? (a) 6.1 (b) 6.0 (c) 6.2 (d) 6.3
  31. 31.Best estimate of 1104 ÷ 36? (a) 280 (b) 28 (c) 2800
  32. 32.Best estimate of 2631 ÷ 41? (a) 66 (b) 6600 (c) 660
  33. 33.√35 to 1 decimal place? (a) 5.7 (b) 5.9 (c) 5.8 (d) 5.6
  34. 34.Best estimate of 1075 ÷ 47? (a) 220 (b) 22 (c) 2200
  35. 35.√46 to 1 decimal place? (a) 7.1 (b) 6.9 (c) 7.0 (d) 6.8
  36. 36.Best estimate of 4362 ÷ 56? (a) 730 (b) 73 (c) 7300
  37. 37.Best estimate of 3945 ÷ 61? (a) 660 (b) 66 (c) 6600
  38. 38.Best estimate of 1633 ÷ 47? (a) 330 (b) 3300 (c) 33
  39. 39.√50 to 1 decimal place? (a) 6.8 (b) 7.0 (c) 7.1 (d) 6.9
  40. 40.Best estimate of 5645 ÷ 71? (a) 810 (b) 8100 (c) 81

Answer key

  1. 44
  2. 100
  3. 78
  4. 6.3
  5. 68
  6. 23
  7. 9.8
  8. 7.9
  9. 73
  10. 27
  11. 6.9
  12. 16
  13. 50
  14. 26
  15. 8.7
  16. 8.1
  17. 60
  18. 89
  19. 39
  20. 43
  21. 9.2
  22. 4.6
  23. 9.9
  24. 7.6
  25. 71
  26. 9.1
  27. 96
  28. 4.7
  29. 6.6
  30. 6.2
  31. 28
  32. 66
  33. 5.9
  34. 22
  35. 6.8
  36. 73
  37. 66
  38. 33
  39. 7.1
  40. 81

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