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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 509 · 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 904 ÷ 41? (a) 23 (b) 2300 (c) 230
  2. 2.Best estimate of 824 ÷ 29? (a) 27 (b) 2700 (c) 270
  3. 3.√98 to 1 decimal place? (a) 9.9 (b) 10.1 (c) 10.0 (d) 10.2
  4. 4.Best estimate of 4896 ÷ 58? (a) 82 (b) 820 (c) 8200
  5. 5.Best estimate of 1625 ÷ 34? (a) 54 (b) 5400 (c) 540
  6. 6.√41 to 1 decimal place? (a) 6.5 (b) 6.2 (c) 6.3 (d) 6.4
  7. 7.√61 to 1 decimal place? (a) 8.0 (b) 8.1 (c) 7.8 (d) 7.9
  8. 8.Best estimate of 7219 ÷ 88? (a) 8000 (b) 80 (c) 800
  9. 9.√50 to 1 decimal place? (a) 6.9 (b) 7.0 (c) 7.1 (d) 6.8
  10. 10.Best estimate of 1085 ÷ 28? (a) 3600 (b) 36 (c) 360
  11. 11.√78 to 1 decimal place? (a) 8.9 (b) 8.7 (c) 8.8 (d) 8.6
  12. 12.Best estimate of 1475 ÷ 33? (a) 4900 (b) 490 (c) 49
  13. 13.√56 to 1 decimal place? (a) 7.5 (b) 7.7 (c) 7.8 (d) 7.6
  14. 14.Best estimate of 1676 ÷ 32? (a) 56 (b) 560 (c) 5600
  15. 15.Best estimate of 2072 ÷ 84? (a) 260 (b) 26 (c) 2600
  16. 16.√59 to 1 decimal place? (a) 7.8 (b) 7.6 (c) 7.9 (d) 7.7
  17. 17.√84 to 1 decimal place? (a) 9.3 (b) 9.0 (c) 9.1 (d) 9.2
  18. 18.√90 to 1 decimal place? (a) 9.4 (b) 9.5 (c) 9.6 (d) 9.3
  19. 19.Best estimate of 2723 ÷ 38? (a) 680 (b) 68 (c) 6800
  20. 20.√26 to 1 decimal place? (a) 5.2 (b) 5.0 (c) 5.1 (d) 5.3
  21. 21.Best estimate of 2574 ÷ 47? (a) 510 (b) 51 (c) 5100
  22. 22.√42 to 1 decimal place? (a) 6.5 (b) 6.7 (c) 6.6 (d) 6.4
  23. 23.Best estimate of 1968 ÷ 34? (a) 66 (b) 660 (c) 6600
  24. 24.√74 to 1 decimal place? (a) 8.4 (b) 8.3 (c) 8.6 (d) 8.5
  25. 25.Best estimate of 4028 ÷ 69? (a) 580 (b) 5800 (c) 58
  26. 26.Best estimate of 5729 ÷ 66? (a) 820 (b) 8200 (c) 82
  27. 27.Best estimate of 1889 ÷ 82? (a) 240 (b) 24 (c) 2400
  28. 28.√62 to 1 decimal place? (a) 7.9 (b) 8.0 (c) 7.8 (d) 8.1
  29. 29.√40 to 1 decimal place? (a) 6.1 (b) 6.2 (c) 6.3 (d) 6.0
  30. 30.Best estimate of 6293 ÷ 76? (a) 790 (b) 7900 (c) 79
  31. 31.√28 to 1 decimal place? (a) 5.3 (b) 5.5 (c) 5.6 (d) 5.4
  32. 32.Best estimate of 2323 ÷ 72? (a) 33 (b) 330 (c) 3300
  33. 33.Best estimate of 2156 ÷ 62? (a) 3600 (b) 36 (c) 360
  34. 34.Best estimate of 1629 ÷ 58? (a) 2700 (b) 270 (c) 27
  35. 35.Best estimate of 4731 ÷ 68? (a) 680 (b) 68 (c) 6800
  36. 36.Best estimate of 4638 ÷ 68? (a) 6600 (b) 660 (c) 66
  37. 37.√22 to 1 decimal place? (a) 4.8 (b) 4.7 (c) 4.9 (d) 5.0
  38. 38.√75 to 1 decimal place? (a) 8.7 (b) 8.9 (c) 8.8 (d) 8.6
  39. 39.Best estimate of 1083 ÷ 56? (a) 18 (b) 1800 (c) 180
  40. 40.√80 to 1 decimal place? (a) 9.2 (b) 9.0 (c) 9.1 (d) 8.9

Answer key

  1. 23
  2. 27
  3. 9.9
  4. 82
  5. 54
  6. 6.4
  7. 7.8
  8. 80
  9. 7.1
  10. 36
  11. 8.8
  12. 49
  13. 7.5
  14. 56
  15. 26
  16. 7.7
  17. 9.2
  18. 9.5
  19. 68
  20. 5.1
  21. 51
  22. 6.5
  23. 66
  24. 8.6
  25. 58
  26. 82
  27. 24
  28. 7.9
  29. 6.3
  30. 79
  31. 5.3
  32. 33
  33. 36
  34. 27
  35. 68
  36. 66
  37. 4.7
  38. 8.7
  39. 18
  40. 8.9

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