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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 768 · 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 7533 ÷ 84? (a) 94 (b) 9400 (c) 940
  2. 2.Best estimate of 2809 ÷ 36? (a) 70 (b) 7000 (c) 700
  3. 3.Best estimate of 3333 ÷ 62? (a) 5600 (b) 560 (c) 56
  4. 4.Best estimate of 664 ÷ 21? (a) 3300 (b) 330 (c) 33
  5. 5.Best estimate of 679 ÷ 41? (a) 17 (b) 170 (c) 1700
  6. 6.√65 to 1 decimal place? (a) 8.0 (b) 8.3 (c) 8.1 (d) 8.2
  7. 7.√63 to 1 decimal place? (a) 7.8 (b) 7.9 (c) 7.7 (d) 8.0
  8. 8.√79 to 1 decimal place? (a) 8.6 (b) 8.9 (c) 8.8 (d) 8.7
  9. 9.√86 to 1 decimal place? (a) 9.0 (b) 9.1 (c) 9.2 (d) 9.3
  10. 10.Best estimate of 3080 ÷ 46? (a) 62 (b) 620 (c) 6200
  11. 11.√76 to 1 decimal place? (a) 8.7 (b) 8.6 (c) 8.8 (d) 8.9
  12. 12.Best estimate of 2561 ÷ 81? (a) 320 (b) 32 (c) 3200
  13. 13.Best estimate of 4680 ÷ 89? (a) 52 (b) 520 (c) 5200
  14. 14.√61 to 1 decimal place? (a) 7.7 (b) 7.8 (c) 7.6 (d) 7.5
  15. 15.√74 to 1 decimal place? (a) 8.6 (b) 8.5 (c) 8.7 (d) 8.4
  16. 16.Best estimate of 3602 ÷ 52? (a) 72 (b) 7200 (c) 720
  17. 17.Best estimate of 1411 ÷ 42? (a) 35 (b) 3500 (c) 350
  18. 18.√40 to 1 decimal place? (a) 6.3 (b) 6.0 (c) 6.1 (d) 6.2
  19. 19.√21 to 1 decimal place? (a) 4.9 (b) 4.6 (c) 4.8 (d) 4.7
  20. 20.Best estimate of 5126 ÷ 88? (a) 570 (b) 57 (c) 5700
  21. 21.Best estimate of 759 ÷ 22? (a) 38 (b) 3800 (c) 380
  22. 22.Best estimate of 2806 ÷ 82? (a) 35 (b) 350 (c) 3500
  23. 23.Best estimate of 1808 ÷ 24? (a) 900 (b) 9000 (c) 90
  24. 24.Best estimate of 3246 ÷ 57? (a) 54 (b) 540 (c) 5400
  25. 25.Best estimate of 1335 ÷ 28? (a) 4500 (b) 45 (c) 450
  26. 26.Best estimate of 1078 ÷ 57? (a) 1800 (b) 18 (c) 180
  27. 27.√35 to 1 decimal place? (a) 6.1 (b) 5.9 (c) 5.8 (d) 6.0
  28. 28.√96 to 1 decimal place? (a) 9.6 (b) 9.7 (c) 9.8 (d) 9.9
  29. 29.Best estimate of 5200 ÷ 66? (a) 740 (b) 7400 (c) 74
  30. 30.√53 to 1 decimal place? (a) 7.0 (b) 7.3 (c) 7.2 (d) 7.1
  31. 31.Best estimate of 2829 ÷ 39? (a) 7100 (b) 710 (c) 71
  32. 32.Best estimate of 361 ÷ 21? (a) 180 (b) 18 (c) 1800
  33. 33.√72 to 1 decimal place? (a) 8.4 (b) 8.5 (c) 8.6 (d) 8.3
  34. 34.Best estimate of 3241 ÷ 83? (a) 4100 (b) 410 (c) 41
  35. 35.√34 to 1 decimal place? (a) 5.9 (b) 6.0 (c) 6.1 (d) 5.8
  36. 36.√43 to 1 decimal place? (a) 6.6 (b) 6.7 (c) 6.5 (d) 6.4
  37. 37.Best estimate of 1300 ÷ 36? (a) 33 (b) 330 (c) 3300
  38. 38.Best estimate of 4540 ÷ 58? (a) 76 (b) 7600 (c) 760
  39. 39.√66 to 1 decimal place? (a) 8.1 (b) 7.9 (c) 8.0 (d) 8.2
  40. 40.√27 to 1 decimal place? (a) 5.3 (b) 5.2 (c) 5.1 (d) 5.4

Answer key

  1. 94
  2. 70
  3. 56
  4. 33
  5. 17
  6. 8.1
  7. 7.9
  8. 8.9
  9. 9.3
  10. 62
  11. 8.7
  12. 32
  13. 52
  14. 7.8
  15. 8.6
  16. 72
  17. 35
  18. 6.3
  19. 4.6
  20. 57
  21. 38
  22. 35
  23. 90
  24. 54
  25. 45
  26. 18
  27. 5.9
  28. 9.8
  29. 74
  30. 7.3
  31. 71
  32. 18
  33. 8.5
  34. 41
  35. 5.8
  36. 6.6
  37. 33
  38. 76
  39. 8.1
  40. 5.2

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