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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 465 · 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) 6.2 (b) 6.3 (c) 6.5 (d) 6.4
  2. 2.Best estimate of 2035 ÷ 59? (a) 340 (b) 3400 (c) 34
  3. 3.√45 to 1 decimal place? (a) 6.6 (b) 6.9 (c) 6.8 (d) 6.7
  4. 4.√92 to 1 decimal place? (a) 9.7 (b) 9.9 (c) 9.6 (d) 9.8
  5. 5.Best estimate of 945 ÷ 42? (a) 240 (b) 2400 (c) 24
  6. 6.√82 to 1 decimal place? (a) 9.0 (b) 8.9 (c) 9.1 (d) 9.2
  7. 7.√61 to 1 decimal place? (a) 7.8 (b) 8.1 (c) 7.9 (d) 8.0
  8. 8.Best estimate of 608 ÷ 42? (a) 150 (b) 1500 (c) 15
  9. 9.Best estimate of 2174 ÷ 67? (a) 3100 (b) 310 (c) 31
  10. 10.Best estimate of 293 ÷ 23? (a) 150 (b) 1500 (c) 15
  11. 11.Best estimate of 965 ÷ 44? (a) 2400 (b) 240 (c) 24
  12. 12.Best estimate of 6782 ÷ 77? (a) 8500 (b) 850 (c) 85
  13. 13.√56 to 1 decimal place? (a) 7.4 (b) 7.6 (c) 7.7 (d) 7.5
  14. 14.√69 to 1 decimal place? (a) 8.5 (b) 8.4 (c) 8.6 (d) 8.3
  15. 15.√32 to 1 decimal place? (a) 5.9 (b) 5.7 (c) 6.0 (d) 5.8
  16. 16.√37 to 1 decimal place? (a) 6.2 (b) 6.0 (c) 5.9 (d) 6.1
  17. 17.Best estimate of 4352 ÷ 73? (a) 620 (b) 6200 (c) 62
  18. 18.√85 to 1 decimal place? (a) 9.4 (b) 9.2 (c) 9.1 (d) 9.3
  19. 19.Best estimate of 2454 ÷ 86? (a) 27 (b) 270 (c) 2700
  20. 20.Best estimate of 1158 ÷ 49? (a) 230 (b) 2300 (c) 23
  21. 21.√83 to 1 decimal place? (a) 9.2 (b) 9.4 (c) 9.1 (d) 9.3
  22. 22.√55 to 1 decimal place? (a) 7.4 (b) 7.5 (c) 7.6 (d) 7.3
  23. 23.Best estimate of 1314 ÷ 42? (a) 330 (b) 33 (c) 3300
  24. 24.Best estimate of 660 ÷ 46? (a) 1300 (b) 130 (c) 13
  25. 25.Best estimate of 723 ÷ 48? (a) 140 (b) 14 (c) 1400
  26. 26.√70 to 1 decimal place? (a) 8.2 (b) 8.3 (c) 8.5 (d) 8.4
  27. 27.√74 to 1 decimal place? (a) 8.5 (b) 8.3 (c) 8.4 (d) 8.6
  28. 28.Best estimate of 936 ÷ 61? (a) 160 (b) 1600 (c) 16
  29. 29.Best estimate of 2993 ÷ 66? (a) 43 (b) 430 (c) 4300
  30. 30.Best estimate of 1866 ÷ 38? (a) 47 (b) 470 (c) 4700
  31. 31.√79 to 1 decimal place? (a) 9.1 (b) 9.2 (c) 9.0 (d) 8.9
  32. 32.Best estimate of 2559 ÷ 44? (a) 640 (b) 6400 (c) 64
  33. 33.Best estimate of 613 ÷ 21? (a) 310 (b) 31 (c) 3100
  34. 34.√86 to 1 decimal place? (a) 9.4 (b) 9.6 (c) 9.5 (d) 9.3
  35. 35.Best estimate of 1678 ÷ 49? (a) 34 (b) 340 (c) 3400
  36. 36.Best estimate of 1225 ÷ 86? (a) 140 (b) 1400 (c) 14
  37. 37.Best estimate of 1094 ÷ 32? (a) 36 (b) 3600 (c) 360
  38. 38.Best estimate of 1707 ÷ 23? (a) 8500 (b) 85 (c) 850
  39. 39.√50 to 1 decimal place? (a) 7.4 (b) 7.2 (c) 7.3 (d) 7.1
  40. 40.√23 to 1 decimal place? (a) 5.1 (b) 5.0 (c) 4.8 (d) 4.9

Answer key

  1. 6.3
  2. 34
  3. 6.7
  4. 9.6
  5. 24
  6. 9.1
  7. 7.8
  8. 15
  9. 31
  10. 15
  11. 24
  12. 85
  13. 7.5
  14. 8.3
  15. 5.7
  16. 6.1
  17. 62
  18. 9.2
  19. 27
  20. 23
  21. 9.1
  22. 7.4
  23. 33
  24. 13
  25. 14
  26. 8.4
  27. 8.6
  28. 16
  29. 43
  30. 47
  31. 8.9
  32. 64
  33. 31
  34. 9.3
  35. 34
  36. 14
  37. 36
  38. 85
  39. 7.1
  40. 4.8

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