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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 416 · 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 507 ÷ 21? (a) 250 (b) 25 (c) 2500
  2. 2.√34 to 1 decimal place? (a) 5.9 (b) 6.1 (c) 6.0 (d) 5.8
  3. 3.√84 to 1 decimal place? (a) 9.2 (b) 9.5 (c) 9.3 (d) 9.4
  4. 4.√30 to 1 decimal place? (a) 5.4 (b) 5.3 (c) 5.2 (d) 5.5
  5. 5.√38 to 1 decimal place? (a) 6.2 (b) 6.1 (c) 6.0 (d) 6.3
  6. 6.Best estimate of 1080 ÷ 23? (a) 540 (b) 5400 (c) 54
  7. 7.√55 to 1 decimal place? (a) 7.4 (b) 7.2 (c) 7.3 (d) 7.1
  8. 8.Best estimate of 1427 ÷ 29? (a) 48 (b) 4800 (c) 480
  9. 9.Best estimate of 3479 ÷ 74? (a) 5000 (b) 500 (c) 50
  10. 10.√90 to 1 decimal place? (a) 9.3 (b) 9.5 (c) 9.6 (d) 9.4
  11. 11.Best estimate of 6033 ÷ 83? (a) 7500 (b) 750 (c) 75
  12. 12.√94 to 1 decimal place? (a) 9.4 (b) 9.6 (c) 9.7 (d) 9.5
  13. 13.Best estimate of 1596 ÷ 49? (a) 32 (b) 3200 (c) 320
  14. 14.√65 to 1 decimal place? (a) 8.4 (b) 8.1 (c) 8.2 (d) 8.3
  15. 15.Best estimate of 1548 ÷ 62? (a) 2600 (b) 26 (c) 260
  16. 16.√40 to 1 decimal place? (a) 6.4 (b) 6.2 (c) 6.5 (d) 6.3
  17. 17.Best estimate of 2555 ÷ 88? (a) 28 (b) 2800 (c) 280
  18. 18.Best estimate of 7209 ÷ 81? (a) 9000 (b) 900 (c) 90
  19. 19.Best estimate of 3450 ÷ 42? (a) 8600 (b) 86 (c) 860
  20. 20.√76 to 1 decimal place? (a) 8.7 (b) 8.8 (c) 8.5 (d) 8.6
  21. 21.Best estimate of 3195 ÷ 38? (a) 800 (b) 8000 (c) 80
  22. 22.Best estimate of 2503 ÷ 66? (a) 3600 (b) 360 (c) 36
  23. 23.Best estimate of 3203 ÷ 87? (a) 3600 (b) 36 (c) 360
  24. 24.Best estimate of 4535 ÷ 62? (a) 760 (b) 76 (c) 7600
  25. 25.Best estimate of 3367 ÷ 63? (a) 560 (b) 5600 (c) 56
  26. 26.√42 to 1 decimal place? (a) 6.7 (b) 6.5 (c) 6.4 (d) 6.6
  27. 27.√82 to 1 decimal place? (a) 9.1 (b) 8.9 (c) 9.0 (d) 8.8
  28. 28.√80 to 1 decimal place? (a) 8.7 (b) 8.8 (c) 9.0 (d) 8.9
  29. 29.√35 to 1 decimal place? (a) 6.1 (b) 6.0 (c) 6.2 (d) 5.9
  30. 30.√32 to 1 decimal place? (a) 5.7 (b) 5.6 (c) 5.9 (d) 5.8
  31. 31.√27 to 1 decimal place? (a) 5.2 (b) 5.1 (c) 5.3 (d) 5.4
  32. 32.Best estimate of 2083 ÷ 59? (a) 350 (b) 35 (c) 3500
  33. 33.Best estimate of 1584 ÷ 79? (a) 200 (b) 2000 (c) 20
  34. 34.√98 to 1 decimal place? (a) 10.1 (b) 10.2 (c) 9.9 (d) 10.0
  35. 35.Best estimate of 653 ÷ 23? (a) 33 (b) 3300 (c) 330
  36. 36.√23 to 1 decimal place? (a) 4.8 (b) 4.6 (c) 4.7 (d) 4.5
  37. 37.√50 to 1 decimal place? (a) 6.9 (b) 7.0 (c) 7.1 (d) 7.2
  38. 38.√88 to 1 decimal place? (a) 9.6 (b) 9.5 (c) 9.4 (d) 9.7
  39. 39.√20 to 1 decimal place? (a) 4.6 (b) 4.5 (c) 4.3 (d) 4.4
  40. 40.√74 to 1 decimal place? (a) 8.6 (b) 8.3 (c) 8.5 (d) 8.4

Answer key

  1. 25
  2. 5.8
  3. 9.2
  4. 5.5
  5. 6.2
  6. 54
  7. 7.4
  8. 48
  9. 50
  10. 9.5
  11. 75
  12. 9.7
  13. 32
  14. 8.1
  15. 26
  16. 6.3
  17. 28
  18. 90
  19. 86
  20. 8.7
  21. 80
  22. 36
  23. 36
  24. 76
  25. 56
  26. 6.5
  27. 9.1
  28. 8.9
  29. 5.9
  30. 5.7
  31. 5.2
  32. 35
  33. 20
  34. 9.9
  35. 33
  36. 4.8
  37. 7.1
  38. 9.4
  39. 4.5
  40. 8.6

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