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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 151 · 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.√82 to 1 decimal place? (a) 9.0 (b) 9.1 (c) 9.2 (d) 8.9
  2. 2.√65 to 1 decimal place? (a) 8.1 (b) 8.3 (c) 8.2 (d) 8.0
  3. 3.√98 to 1 decimal place? (a) 9.9 (b) 9.7 (c) 10.0 (d) 9.8
  4. 4.√29 to 1 decimal place? (a) 5.5 (b) 5.7 (c) 5.6 (d) 5.4
  5. 5.√34 to 1 decimal place? (a) 5.9 (b) 5.8 (c) 5.7 (d) 5.6
  6. 6.√46 to 1 decimal place? (a) 6.6 (b) 6.8 (c) 6.7 (d) 6.9
  7. 7.Best estimate of 1885 ÷ 36? (a) 47 (b) 470 (c) 4700
  8. 8.Best estimate of 2413 ÷ 27? (a) 8000 (b) 80 (c) 800
  9. 9.√71 to 1 decimal place? (a) 8.5 (b) 8.3 (c) 8.4 (d) 8.6
  10. 10.Best estimate of 1147 ÷ 42? (a) 29 (b) 2900 (c) 290
  11. 11.√23 to 1 decimal place? (a) 4.9 (b) 4.8 (c) 4.7 (d) 5.0
  12. 12.√83 to 1 decimal place? (a) 9.4 (b) 9.1 (c) 9.3 (d) 9.2
  13. 13.√90 to 1 decimal place? (a) 9.4 (b) 9.5 (c) 9.6 (d) 9.3
  14. 14.Best estimate of 2889 ÷ 59? (a) 480 (b) 4800 (c) 48
  15. 15.Best estimate of 3196 ÷ 81? (a) 400 (b) 40 (c) 4000
  16. 16.Best estimate of 4151 ÷ 64? (a) 690 (b) 69 (c) 6900
  17. 17.Best estimate of 1465 ÷ 22? (a) 730 (b) 73 (c) 7300
  18. 18.√70 to 1 decimal place? (a) 8.7 (b) 8.6 (c) 8.5 (d) 8.4
  19. 19.√76 to 1 decimal place? (a) 8.9 (b) 8.7 (c) 8.6 (d) 8.8
  20. 20.Best estimate of 5241 ÷ 74? (a) 7500 (b) 750 (c) 75
  21. 21.√27 to 1 decimal place? (a) 5.1 (b) 5.3 (c) 5.2 (d) 5.0
  22. 22.√43 to 1 decimal place? (a) 6.8 (b) 6.5 (c) 6.7 (d) 6.6
  23. 23.Best estimate of 2891 ÷ 66? (a) 41 (b) 4100 (c) 410
  24. 24.Best estimate of 4381 ÷ 72? (a) 630 (b) 6300 (c) 63
  25. 25.Best estimate of 4423 ÷ 57? (a) 740 (b) 7400 (c) 74
  26. 26.Best estimate of 863 ÷ 32? (a) 290 (b) 2900 (c) 29
  27. 27.√32 to 1 decimal place? (a) 5.8 (b) 5.9 (c) 5.6 (d) 5.7
  28. 28.√69 to 1 decimal place? (a) 8.3 (b) 8.2 (c) 8.5 (d) 8.4
  29. 29.√67 to 1 decimal place? (a) 8.4 (b) 8.1 (c) 8.3 (d) 8.2
  30. 30.Best estimate of 864 ÷ 24? (a) 4300 (b) 430 (c) 43
  31. 31.√35 to 1 decimal place? (a) 6.0 (b) 5.8 (c) 5.9 (d) 6.1
  32. 32.Best estimate of 3276 ÷ 38? (a) 820 (b) 8200 (c) 82
  33. 33.Best estimate of 5346 ÷ 87? (a) 5900 (b) 590 (c) 59
  34. 34.Best estimate of 1399 ÷ 28? (a) 470 (b) 4700 (c) 47
  35. 35.Best estimate of 2084 ÷ 86? (a) 23 (b) 2300 (c) 230
  36. 36.√22 to 1 decimal place? (a) 4.8 (b) 4.6 (c) 4.7 (d) 4.9
  37. 37.√41 to 1 decimal place? (a) 6.3 (b) 6.4 (c) 6.2 (d) 6.5
  38. 38.√87 to 1 decimal place? (a) 9.5 (b) 9.3 (c) 9.4 (d) 9.2
  39. 39.√77 to 1 decimal place? (a) 8.8 (b) 8.5 (c) 8.7 (d) 8.6
  40. 40.Best estimate of 3837 ÷ 52? (a) 770 (b) 77 (c) 7700

Answer key

  1. 9.1
  2. 8.1
  3. 9.9
  4. 5.4
  5. 5.8
  6. 6.8
  7. 47
  8. 80
  9. 8.4
  10. 29
  11. 4.8
  12. 9.1
  13. 9.5
  14. 48
  15. 40
  16. 69
  17. 73
  18. 8.4
  19. 8.7
  20. 75
  21. 5.2
  22. 6.6
  23. 41
  24. 63
  25. 74
  26. 29
  27. 5.7
  28. 8.3
  29. 8.2
  30. 43
  31. 5.9
  32. 82
  33. 59
  34. 47
  35. 23
  36. 4.7
  37. 6.4
  38. 9.3
  39. 8.8
  40. 77

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