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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 867 · 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.√40 to 1 decimal place? (a) 6.6 (b) 6.5 (c) 6.4 (d) 6.3
  2. 2.√52 to 1 decimal place? (a) 7.1 (b) 7.0 (c) 7.2 (d) 6.9
  3. 3.√35 to 1 decimal place? (a) 6.2 (b) 6.1 (c) 6.0 (d) 5.9
  4. 4.Best estimate of 5858 ÷ 79? (a) 7300 (b) 730 (c) 73
  5. 5.√88 to 1 decimal place? (a) 9.2 (b) 9.3 (c) 9.4 (d) 9.1
  6. 6.√23 to 1 decimal place? (a) 5.0 (b) 4.8 (c) 4.9 (d) 4.7
  7. 7.Best estimate of 2738 ÷ 42? (a) 6800 (b) 68 (c) 680
  8. 8.Best estimate of 743 ÷ 27? (a) 25 (b) 250 (c) 2500
  9. 9.Best estimate of 2563 ÷ 53? (a) 510 (b) 51 (c) 5100
  10. 10.√76 to 1 decimal place? (a) 8.5 (b) 8.7 (c) 8.6 (d) 8.4
  11. 11.Best estimate of 1091 ÷ 28? (a) 360 (b) 36 (c) 3600
  12. 12.√94 to 1 decimal place? (a) 9.7 (b) 9.5 (c) 9.4 (d) 9.6
  13. 13.Best estimate of 1078 ÷ 64? (a) 1800 (b) 180 (c) 18
  14. 14.Best estimate of 1962 ÷ 43? (a) 49 (b) 490 (c) 4900
  15. 15.√44 to 1 decimal place? (a) 6.6 (b) 6.4 (c) 6.5 (d) 6.3
  16. 16.√29 to 1 decimal place? (a) 5.4 (b) 5.3 (c) 5.2 (d) 5.1
  17. 17.√85 to 1 decimal place? (a) 9.2 (b) 9.3 (c) 9.1 (d) 9.0
  18. 18.√71 to 1 decimal place? (a) 8.5 (b) 8.4 (c) 8.3 (d) 8.6
  19. 19.√26 to 1 decimal place? (a) 5.4 (b) 5.2 (c) 5.1 (d) 5.3
  20. 20.√41 to 1 decimal place? (a) 6.5 (b) 6.4 (c) 6.7 (d) 6.6
  21. 21.Best estimate of 6764 ÷ 73? (a) 9700 (b) 97 (c) 970
  22. 22.Best estimate of 3084 ÷ 71? (a) 440 (b) 4400 (c) 44
  23. 23.√30 to 1 decimal place? (a) 5.5 (b) 5.7 (c) 5.8 (d) 5.6
  24. 24.Best estimate of 5430 ÷ 66? (a) 7800 (b) 78 (c) 780
  25. 25.Best estimate of 1915 ÷ 86? (a) 21 (b) 210 (c) 2100
  26. 26.√86 to 1 decimal place? (a) 9.4 (b) 9.6 (c) 9.3 (d) 9.5
  27. 27.√79 to 1 decimal place? (a) 8.8 (b) 9.0 (c) 8.9 (d) 9.1
  28. 28.√66 to 1 decimal place? (a) 8.3 (b) 8.1 (c) 8.2 (d) 8.0
  29. 29.√37 to 1 decimal place? (a) 6.4 (b) 6.1 (c) 6.3 (d) 6.2
  30. 30.Best estimate of 2709 ÷ 52? (a) 540 (b) 54 (c) 5400
  31. 31.Best estimate of 3143 ÷ 48? (a) 6300 (b) 63 (c) 630
  32. 32.√50 to 1 decimal place? (a) 7.4 (b) 7.2 (c) 7.1 (d) 7.3
  33. 33.Best estimate of 5620 ÷ 62? (a) 940 (b) 9400 (c) 94
  34. 34.Best estimate of 4766 ÷ 61? (a) 7900 (b) 79 (c) 790
  35. 35.Best estimate of 4907 ÷ 53? (a) 9800 (b) 980 (c) 98
  36. 36.Best estimate of 6676 ÷ 86? (a) 7400 (b) 74 (c) 740
  37. 37.Best estimate of 5129 ÷ 83? (a) 64 (b) 640 (c) 6400
  38. 38.Best estimate of 3185 ÷ 39? (a) 800 (b) 80 (c) 8000
  39. 39.Best estimate of 829 ÷ 22? (a) 410 (b) 4100 (c) 41
  40. 40.Best estimate of 2570 ÷ 29? (a) 860 (b) 8600 (c) 86

Answer key

  1. 6.3
  2. 7.2
  3. 5.9
  4. 73
  5. 9.4
  6. 4.8
  7. 68
  8. 25
  9. 51
  10. 8.7
  11. 36
  12. 9.7
  13. 18
  14. 49
  15. 6.6
  16. 5.4
  17. 9.2
  18. 8.4
  19. 5.1
  20. 6.4
  21. 97
  22. 44
  23. 5.5
  24. 78
  25. 21
  26. 9.3
  27. 8.9
  28. 8.1
  29. 6.1
  30. 54
  31. 63
  32. 7.1
  33. 94
  34. 79
  35. 98
  36. 74
  37. 64
  38. 80
  39. 41
  40. 86

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