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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 717 · 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.√62 to 1 decimal place? (a) 8.0 (b) 8.2 (c) 8.1 (d) 7.9
  2. 2.√41 to 1 decimal place? (a) 6.5 (b) 6.6 (c) 6.3 (d) 6.4
  3. 3.Best estimate of 3711 ÷ 41? (a) 930 (b) 9300 (c) 93
  4. 4.√40 to 1 decimal place? (a) 6.5 (b) 6.4 (c) 6.6 (d) 6.3
  5. 5.√74 to 1 decimal place? (a) 8.5 (b) 8.4 (c) 8.6 (d) 8.7
  6. 6.Best estimate of 4801 ÷ 76? (a) 60 (b) 600 (c) 6000
  7. 7.√26 to 1 decimal place? (a) 4.9 (b) 5.0 (c) 5.1 (d) 4.8
  8. 8.√28 to 1 decimal place? (a) 5.1 (b) 5.0 (c) 5.2 (d) 5.3
  9. 9.Best estimate of 7162 ÷ 84? (a) 9000 (b) 90 (c) 900
  10. 10.Best estimate of 3948 ÷ 44? (a) 990 (b) 99 (c) 9900
  11. 11.√70 to 1 decimal place? (a) 8.6 (b) 8.7 (c) 8.4 (d) 8.5
  12. 12.√89 to 1 decimal place? (a) 9.4 (b) 9.6 (c) 9.7 (d) 9.5
  13. 13.Best estimate of 1154 ÷ 89? (a) 1300 (b) 130 (c) 13
  14. 14.√37 to 1 decimal place? (a) 6.1 (b) 6.4 (c) 6.2 (d) 6.3
  15. 15.√84 to 1 decimal place? (a) 9.2 (b) 9.1 (c) 9.3 (d) 9.4
  16. 16.Best estimate of 1697 ÷ 61? (a) 280 (b) 2800 (c) 28
  17. 17.√38 to 1 decimal place? (a) 6.3 (b) 6.4 (c) 6.5 (d) 6.2
  18. 18.√27 to 1 decimal place? (a) 5.3 (b) 5.2 (c) 5.1 (d) 5.4
  19. 19.Best estimate of 1860 ÷ 46? (a) 370 (b) 3700 (c) 37
  20. 20.Best estimate of 3217 ÷ 49? (a) 640 (b) 6400 (c) 64
  21. 21.√43 to 1 decimal place? (a) 6.5 (b) 6.6 (c) 6.7 (d) 6.4
  22. 22.√34 to 1 decimal place? (a) 5.9 (b) 6.0 (c) 5.8 (d) 6.1
  23. 23.Best estimate of 1327 ÷ 58? (a) 2200 (b) 22 (c) 220
  24. 24.√61 to 1 decimal place? (a) 8.0 (b) 8.1 (c) 7.8 (d) 7.9
  25. 25.√92 to 1 decimal place? (a) 9.8 (b) 9.7 (c) 9.6 (d) 9.9
  26. 26.√94 to 1 decimal place? (a) 9.7 (b) 9.8 (c) 9.6 (d) 9.9
  27. 27.Best estimate of 2068 ÷ 47? (a) 410 (b) 4100 (c) 41
  28. 28.Best estimate of 853 ÷ 28? (a) 28 (b) 2800 (c) 280
  29. 29.√96 to 1 decimal place? (a) 9.6 (b) 9.5 (c) 9.8 (d) 9.7
  30. 30.Best estimate of 2584 ÷ 68? (a) 370 (b) 37 (c) 3700
  31. 31.√86 to 1 decimal place? (a) 9.6 (b) 9.5 (c) 9.3 (d) 9.4
  32. 32.Best estimate of 1486 ÷ 23? (a) 7400 (b) 74 (c) 740
  33. 33.Best estimate of 2283 ÷ 29? (a) 760 (b) 76 (c) 7600
  34. 34.Best estimate of 1784 ÷ 23? (a) 89 (b) 890 (c) 8900
  35. 35.Best estimate of 406 ÷ 23? (a) 200 (b) 20 (c) 2000
  36. 36.Best estimate of 3177 ÷ 82? (a) 4000 (b) 40 (c) 400
  37. 37.Best estimate of 3368 ÷ 36? (a) 84 (b) 840 (c) 8400
  38. 38.√29 to 1 decimal place? (a) 5.1 (b) 5.2 (c) 5.4 (d) 5.3
  39. 39.Best estimate of 6362 ÷ 76? (a) 800 (b) 8000 (c) 80
  40. 40.Best estimate of 3563 ÷ 48? (a) 7100 (b) 710 (c) 71

Answer key

  1. 7.9
  2. 6.4
  3. 93
  4. 6.3
  5. 8.6
  6. 60
  7. 5.1
  8. 5.3
  9. 90
  10. 99
  11. 8.4
  12. 9.4
  13. 13
  14. 6.1
  15. 9.2
  16. 28
  17. 6.2
  18. 5.2
  19. 37
  20. 64
  21. 6.6
  22. 5.8
  23. 22
  24. 7.8
  25. 9.6
  26. 9.7
  27. 41
  28. 28
  29. 9.8
  30. 37
  31. 9.3
  32. 74
  33. 76
  34. 89
  35. 20
  36. 40
  37. 84
  38. 5.4
  39. 80
  40. 71

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