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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 28 · 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 2558 ÷ 27? (a) 850 (b) 8500 (c) 85
  2. 2.Best estimate of 2073 ÷ 62? (a) 3500 (b) 35 (c) 350
  3. 3.Best estimate of 1346 ÷ 26? (a) 45 (b) 450 (c) 4500
  4. 4.√62 to 1 decimal place? (a) 8.1 (b) 7.9 (c) 7.8 (d) 8.0
  5. 5.Best estimate of 2520 ÷ 71? (a) 3600 (b) 36 (c) 360
  6. 6.√67 to 1 decimal place? (a) 8.2 (b) 8.3 (c) 8.1 (d) 8.4
  7. 7.√38 to 1 decimal place? (a) 6.2 (b) 6.3 (c) 6.1 (d) 6.4
  8. 8.√88 to 1 decimal place? (a) 9.4 (b) 9.3 (c) 9.6 (d) 9.5
  9. 9.√45 to 1 decimal place? (a) 6.4 (b) 6.6 (c) 6.5 (d) 6.7
  10. 10.√94 to 1 decimal place? (a) 9.8 (b) 9.7 (c) 9.9 (d) 9.6
  11. 11.Best estimate of 2678 ÷ 33? (a) 89 (b) 890 (c) 8900
  12. 12.Best estimate of 2719 ÷ 32? (a) 9100 (b) 91 (c) 910
  13. 13.Best estimate of 2815 ÷ 88? (a) 310 (b) 31 (c) 3100
  14. 14.Best estimate of 1546 ÷ 34? (a) 52 (b) 520 (c) 5200
  15. 15.√82 to 1 decimal place? (a) 9.1 (b) 9.0 (c) 8.8 (d) 8.9
  16. 16.√98 to 1 decimal place? (a) 9.9 (b) 9.7 (c) 9.6 (d) 9.8
  17. 17.Best estimate of 956 ÷ 26? (a) 320 (b) 32 (c) 3200
  18. 18.√20 to 1 decimal place? (a) 4.5 (b) 4.6 (c) 4.4 (d) 4.7
  19. 19.√56 to 1 decimal place? (a) 7.6 (b) 7.5 (c) 7.8 (d) 7.7
  20. 20.Best estimate of 2843 ÷ 34? (a) 9500 (b) 95 (c) 950
  21. 21.√76 to 1 decimal place? (a) 8.5 (b) 8.8 (c) 8.7 (d) 8.6
  22. 22.√92 to 1 decimal place? (a) 9.6 (b) 9.4 (c) 9.5 (d) 9.3
  23. 23.√63 to 1 decimal place? (a) 8.2 (b) 8.0 (c) 7.9 (d) 8.1
  24. 24.Best estimate of 5936 ÷ 87? (a) 66 (b) 660 (c) 6600
  25. 25.√41 to 1 decimal place? (a) 6.4 (b) 6.5 (c) 6.6 (d) 6.7
  26. 26.√58 to 1 decimal place? (a) 7.5 (b) 7.3 (c) 7.6 (d) 7.4
  27. 27.Best estimate of 1389 ÷ 59? (a) 2300 (b) 230 (c) 23
  28. 28.Best estimate of 2040 ÷ 62? (a) 34 (b) 3400 (c) 340
  29. 29.Best estimate of 2927 ÷ 33? (a) 9800 (b) 980 (c) 98
  30. 30.√29 to 1 decimal place? (a) 5.6 (b) 5.7 (c) 5.4 (d) 5.5
  31. 31.√48 to 1 decimal place? (a) 6.9 (b) 6.7 (c) 6.6 (d) 6.8
  32. 32.√40 to 1 decimal place? (a) 6.0 (b) 6.1 (c) 6.3 (d) 6.2
  33. 33.√71 to 1 decimal place? (a) 8.6 (b) 8.5 (c) 8.3 (d) 8.4
  34. 34.Best estimate of 3353 ÷ 62? (a) 5600 (b) 560 (c) 56
  35. 35.Best estimate of 2131 ÷ 82? (a) 27 (b) 270 (c) 2700
  36. 36.Best estimate of 8321 ÷ 88? (a) 920 (b) 92 (c) 9200
  37. 37.√24 to 1 decimal place? (a) 5.1 (b) 5.2 (c) 5.0 (d) 4.9
  38. 38.Best estimate of 4177 ÷ 66? (a) 60 (b) 6000 (c) 600
  39. 39.√34 to 1 decimal place? (a) 5.9 (b) 5.8 (c) 6.0 (d) 6.1
  40. 40.√90 to 1 decimal place? (a) 9.6 (b) 9.7 (c) 9.5 (d) 9.8

Answer key

  1. 85
  2. 35
  3. 45
  4. 7.9
  5. 36
  6. 8.2
  7. 6.2
  8. 9.4
  9. 6.7
  10. 9.7
  11. 89
  12. 91
  13. 31
  14. 52
  15. 9.1
  16. 9.9
  17. 32
  18. 4.5
  19. 7.5
  20. 95
  21. 8.7
  22. 9.6
  23. 7.9
  24. 66
  25. 6.4
  26. 7.6
  27. 23
  28. 34
  29. 98
  30. 5.4
  31. 6.9
  32. 6.3
  33. 8.4
  34. 56
  35. 27
  36. 92
  37. 4.9
  38. 60
  39. 5.8
  40. 9.5

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