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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 701 · 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.√58 to 1 decimal place? (a) 7.3 (b) 7.4 (c) 7.6 (d) 7.5
  2. 2.√40 to 1 decimal place? (a) 6.2 (b) 6.5 (c) 6.3 (d) 6.4
  3. 3.√82 to 1 decimal place? (a) 9.0 (b) 9.2 (c) 9.1 (d) 8.9
  4. 4.√77 to 1 decimal place? (a) 8.8 (b) 9.0 (c) 8.9 (d) 8.7
  5. 5.√26 to 1 decimal place? (a) 5.4 (b) 5.3 (c) 5.2 (d) 5.1
  6. 6.Best estimate of 2692 ÷ 69? (a) 3800 (b) 38 (c) 380
  7. 7.Best estimate of 2699 ÷ 44? (a) 670 (b) 67 (c) 6700
  8. 8.√43 to 1 decimal place? (a) 6.5 (b) 6.4 (c) 6.6 (d) 6.7
  9. 9.Best estimate of 6878 ÷ 72? (a) 9800 (b) 980 (c) 98
  10. 10.Best estimate of 1092 ÷ 31? (a) 36 (b) 360 (c) 3600
  11. 11.Best estimate of 1996 ÷ 33? (a) 6700 (b) 670 (c) 67
  12. 12.√56 to 1 decimal place? (a) 7.6 (b) 7.4 (c) 7.5 (d) 7.3
  13. 13.√32 to 1 decimal place? (a) 5.8 (b) 5.5 (c) 5.6 (d) 5.7
  14. 14.Best estimate of 1325 ÷ 42? (a) 3300 (b) 330 (c) 33
  15. 15.√37 to 1 decimal place? (a) 6.2 (b) 6.3 (c) 6.0 (d) 6.1
  16. 16.Best estimate of 1746 ÷ 38? (a) 4400 (b) 440 (c) 44
  17. 17.Best estimate of 1841 ÷ 21? (a) 920 (b) 9200 (c) 92
  18. 18.Best estimate of 1011 ÷ 56? (a) 1700 (b) 170 (c) 17
  19. 19.Best estimate of 4681 ÷ 56? (a) 7800 (b) 780 (c) 78
  20. 20.√48 to 1 decimal place? (a) 7.1 (b) 7.0 (c) 6.9 (d) 7.2
  21. 21.Best estimate of 3293 ÷ 86? (a) 37 (b) 3700 (c) 370
  22. 22.Best estimate of 5121 ÷ 59? (a) 850 (b) 85 (c) 8500
  23. 23.Best estimate of 1526 ÷ 41? (a) 38 (b) 380 (c) 3800
  24. 24.√21 to 1 decimal place? (a) 4.4 (b) 4.5 (c) 4.6 (d) 4.7
  25. 25.√28 to 1 decimal place? (a) 5.3 (b) 5.4 (c) 5.2 (d) 5.5
  26. 26.√38 to 1 decimal place? (a) 6.0 (b) 6.1 (c) 5.9 (d) 6.2
  27. 27.Best estimate of 3244 ÷ 83? (a) 4100 (b) 410 (c) 41
  28. 28.√89 to 1 decimal place? (a) 9.5 (b) 9.4 (c) 9.6 (d) 9.3
  29. 29.√53 to 1 decimal place? (a) 7.3 (b) 7.4 (c) 7.2 (d) 7.1
  30. 30.Best estimate of 5120 ÷ 72? (a) 730 (b) 7300 (c) 73
  31. 31.√92 to 1 decimal place? (a) 9.5 (b) 9.4 (c) 9.3 (d) 9.6
  32. 32.√96 to 1 decimal place? (a) 10.1 (b) 9.9 (c) 10.0 (d) 9.8
  33. 33.Best estimate of 943 ÷ 64? (a) 1600 (b) 16 (c) 160
  34. 34.Best estimate of 7565 ÷ 81? (a) 9500 (b) 95 (c) 950
  35. 35.Best estimate of 815 ÷ 27? (a) 2700 (b) 27 (c) 270
  36. 36.√24 to 1 decimal place? (a) 5.2 (b) 4.9 (c) 5.0 (d) 5.1
  37. 37.Best estimate of 2511 ÷ 27? (a) 84 (b) 840 (c) 8400
  38. 38.Best estimate of 4703 ÷ 64? (a) 780 (b) 78 (c) 7800
  39. 39.√74 to 1 decimal place? (a) 8.3 (b) 8.5 (c) 8.4 (d) 8.6
  40. 40.Best estimate of 2148 ÷ 37? (a) 5400 (b) 54 (c) 540

Answer key

  1. 7.6
  2. 6.3
  3. 9.1
  4. 8.8
  5. 5.1
  6. 38
  7. 67
  8. 6.6
  9. 98
  10. 36
  11. 67
  12. 7.5
  13. 5.7
  14. 33
  15. 6.1
  16. 44
  17. 92
  18. 17
  19. 78
  20. 6.9
  21. 37
  22. 85
  23. 38
  24. 4.6
  25. 5.3
  26. 6.2
  27. 41
  28. 9.4
  29. 7.3
  30. 73
  31. 9.6
  32. 9.8
  33. 16
  34. 95
  35. 27
  36. 4.9
  37. 84
  38. 78
  39. 8.6
  40. 54

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