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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 266 · 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 4017 ÷ 52? (a) 8000 (b) 80 (c) 800
  2. 2.Best estimate of 1878 ÷ 26? (a) 63 (b) 630 (c) 6300
  3. 3.√61 to 1 decimal place? (a) 7.9 (b) 7.7 (c) 7.8 (d) 7.6
  4. 4.√85 to 1 decimal place? (a) 9.2 (b) 9.4 (c) 9.1 (d) 9.3
  5. 5.√75 to 1 decimal place? (a) 8.8 (b) 8.6 (c) 8.9 (d) 8.7
  6. 6.Best estimate of 807 ÷ 29? (a) 270 (b) 27 (c) 2700
  7. 7.√20 to 1 decimal place? (a) 4.2 (b) 4.3 (c) 4.4 (d) 4.5
  8. 8.Best estimate of 948 ÷ 37? (a) 240 (b) 24 (c) 2400
  9. 9.Best estimate of 5201 ÷ 62? (a) 870 (b) 8700 (c) 87
  10. 10.√27 to 1 decimal place? (a) 5.0 (b) 5.2 (c) 4.9 (d) 5.1
  11. 11.Best estimate of 3389 ÷ 54? (a) 6800 (b) 680 (c) 68
  12. 12.Best estimate of 2138 ÷ 32? (a) 7100 (b) 71 (c) 710
  13. 13.Best estimate of 1764 ÷ 61? (a) 29 (b) 290 (c) 2900
  14. 14.Best estimate of 4015 ÷ 84? (a) 5000 (b) 500 (c) 50
  15. 15.√63 to 1 decimal place? (a) 7.9 (b) 8.0 (c) 8.1 (d) 8.2
  16. 16.√37 to 1 decimal place? (a) 6.1 (b) 6.0 (c) 6.2 (d) 5.9
  17. 17.Best estimate of 5911 ÷ 73? (a) 84 (b) 8400 (c) 840
  18. 18.Best estimate of 2334 ÷ 27? (a) 78 (b) 780 (c) 7800
  19. 19.Best estimate of 6436 ÷ 82? (a) 800 (b) 8000 (c) 80
  20. 20.√30 to 1 decimal place? (a) 5.7 (b) 5.6 (c) 5.4 (d) 5.5
  21. 21.√32 to 1 decimal place? (a) 5.4 (b) 5.7 (c) 5.6 (d) 5.5
  22. 22.Best estimate of 3474 ÷ 46? (a) 69 (b) 690 (c) 6900
  23. 23.√46 to 1 decimal place? (a) 6.8 (b) 6.6 (c) 6.5 (d) 6.7
  24. 24.Best estimate of 3315 ÷ 83? (a) 4100 (b) 410 (c) 41
  25. 25.Best estimate of 2573 ÷ 34? (a) 86 (b) 8600 (c) 860
  26. 26.Best estimate of 2627 ÷ 34? (a) 8800 (b) 880 (c) 88
  27. 27.Best estimate of 4099 ÷ 47? (a) 8200 (b) 82 (c) 820
  28. 28.√34 to 1 decimal place? (a) 5.7 (b) 5.5 (c) 5.8 (d) 5.6
  29. 29.Best estimate of 3628 ÷ 42? (a) 910 (b) 9100 (c) 91
  30. 30.Best estimate of 3448 ÷ 64? (a) 5700 (b) 570 (c) 57
  31. 31.√69 to 1 decimal place? (a) 8.5 (b) 8.3 (c) 8.2 (d) 8.4
  32. 32.Best estimate of 1960 ÷ 84? (a) 2500 (b) 250 (c) 25
  33. 33.Best estimate of 4082 ÷ 67? (a) 58 (b) 5800 (c) 580
  34. 34.Best estimate of 4967 ÷ 57? (a) 83 (b) 830 (c) 8300
  35. 35.√67 to 1 decimal place? (a) 8.5 (b) 8.3 (c) 8.2 (d) 8.4
  36. 36.Best estimate of 3905 ÷ 62? (a) 650 (b) 6500 (c) 65
  37. 37.√42 to 1 decimal place? (a) 6.6 (b) 6.8 (c) 6.7 (d) 6.5
  38. 38.√43 to 1 decimal place? (a) 6.4 (b) 6.5 (c) 6.6 (d) 6.7
  39. 39.√74 to 1 decimal place? (a) 8.5 (b) 8.8 (c) 8.6 (d) 8.7
  40. 40.Best estimate of 1199 ÷ 62? (a) 20 (b) 200 (c) 2000

Answer key

  1. 80
  2. 63
  3. 7.8
  4. 9.2
  5. 8.7
  6. 27
  7. 4.5
  8. 24
  9. 87
  10. 5.2
  11. 68
  12. 71
  13. 29
  14. 50
  15. 7.9
  16. 6.1
  17. 84
  18. 78
  19. 80
  20. 5.5
  21. 5.7
  22. 69
  23. 6.8
  24. 41
  25. 86
  26. 88
  27. 82
  28. 5.8
  29. 91
  30. 57
  31. 8.3
  32. 25
  33. 58
  34. 83
  35. 8.2
  36. 65
  37. 6.5
  38. 6.6
  39. 8.6
  40. 20

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