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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 410 · 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.√50 to 1 decimal place? (a) 7.3 (b) 7.0 (c) 7.1 (d) 7.2
  2. 2.Best estimate of 3393 ÷ 82? (a) 420 (b) 4200 (c) 42
  3. 3.Best estimate of 351 ÷ 24? (a) 180 (b) 1800 (c) 18
  4. 4.Best estimate of 6664 ÷ 71? (a) 950 (b) 9500 (c) 95
  5. 5.√46 to 1 decimal place? (a) 6.7 (b) 6.9 (c) 7.0 (d) 6.8
  6. 6.Best estimate of 4383 ÷ 48? (a) 880 (b) 88 (c) 8800
  7. 7.Best estimate of 4729 ÷ 72? (a) 68 (b) 680 (c) 6800
  8. 8.√30 to 1 decimal place? (a) 5.6 (b) 5.5 (c) 5.4 (d) 5.3
  9. 9.√38 to 1 decimal place? (a) 6.4 (b) 6.3 (c) 6.2 (d) 6.5
  10. 10.Best estimate of 2799 ÷ 31? (a) 9300 (b) 930 (c) 93
  11. 11.√32 to 1 decimal place? (a) 5.7 (b) 5.6 (c) 5.9 (d) 5.8
  12. 12.√65 to 1 decimal place? (a) 8.1 (b) 8.3 (c) 8.2 (d) 8.0
  13. 13.√74 to 1 decimal place? (a) 8.7 (b) 8.6 (c) 8.4 (d) 8.5
  14. 14.√34 to 1 decimal place? (a) 5.9 (b) 5.8 (c) 5.6 (d) 5.7
  15. 15.√26 to 1 decimal place? (a) 4.9 (b) 5.1 (c) 4.8 (d) 5.0
  16. 16.√35 to 1 decimal place? (a) 5.7 (b) 6.0 (c) 5.9 (d) 5.8
  17. 17.√40 to 1 decimal place? (a) 6.4 (b) 6.5 (c) 6.3 (d) 6.2
  18. 18.Best estimate of 6046 ÷ 67? (a) 8600 (b) 860 (c) 86
  19. 19.√79 to 1 decimal place? (a) 9.0 (b) 9.1 (c) 8.9 (d) 9.2
  20. 20.√61 to 1 decimal place? (a) 7.9 (b) 7.8 (c) 7.7 (d) 7.6
  21. 21.Best estimate of 3996 ÷ 79? (a) 5000 (b) 50 (c) 500
  22. 22.√82 to 1 decimal place? (a) 9.1 (b) 9.3 (c) 9.0 (d) 9.2
  23. 23.√22 to 1 decimal place? (a) 4.9 (b) 4.7 (c) 4.8 (d) 4.6
  24. 24.Best estimate of 5215 ÷ 64? (a) 87 (b) 870 (c) 8700
  25. 25.Best estimate of 1461 ÷ 24? (a) 73 (b) 730 (c) 7300
  26. 26.Best estimate of 1612 ÷ 29? (a) 54 (b) 5400 (c) 540
  27. 27.Best estimate of 2095 ÷ 54? (a) 420 (b) 42 (c) 4200
  28. 28.Best estimate of 3304 ÷ 82? (a) 41 (b) 410 (c) 4100
  29. 29.√96 to 1 decimal place? (a) 9.7 (b) 9.9 (c) 9.6 (d) 9.8
  30. 30.√23 to 1 decimal place? (a) 5.1 (b) 4.8 (c) 5.0 (d) 4.9
  31. 31.Best estimate of 2302 ÷ 32? (a) 7700 (b) 77 (c) 770
  32. 32.Best estimate of 1544 ÷ 32? (a) 510 (b) 5100 (c) 51
  33. 33.Best estimate of 5445 ÷ 61? (a) 9100 (b) 910 (c) 91
  34. 34.√86 to 1 decimal place? (a) 9.5 (b) 9.4 (c) 9.6 (d) 9.3
  35. 35.√24 to 1 decimal place? (a) 4.7 (b) 4.8 (c) 4.6 (d) 4.9
  36. 36.Best estimate of 5265 ÷ 56? (a) 8800 (b) 88 (c) 880
  37. 37.Best estimate of 2677 ÷ 28? (a) 8900 (b) 890 (c) 89
  38. 38.Best estimate of 1900 ÷ 61? (a) 32 (b) 3200 (c) 320
  39. 39.√41 to 1 decimal place? (a) 6.3 (b) 6.1 (c) 6.2 (d) 6.4
  40. 40.Best estimate of 3520 ÷ 77? (a) 44 (b) 4400 (c) 440

Answer key

  1. 7.1
  2. 42
  3. 18
  4. 95
  5. 6.8
  6. 88
  7. 68
  8. 5.5
  9. 6.2
  10. 93
  11. 5.7
  12. 8.1
  13. 8.6
  14. 5.8
  15. 5.1
  16. 5.9
  17. 6.3
  18. 86
  19. 8.9
  20. 7.8
  21. 50
  22. 9.1
  23. 4.7
  24. 87
  25. 73
  26. 54
  27. 42
  28. 41
  29. 9.8
  30. 4.8
  31. 77
  32. 51
  33. 91
  34. 9.3
  35. 4.9
  36. 88
  37. 89
  38. 32
  39. 6.4
  40. 44

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