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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 650 · 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 1651 ÷ 62? (a) 2800 (b) 28 (c) 280
  2. 2.Best estimate of 2893 ÷ 38? (a) 7200 (b) 720 (c) 72
  3. 3.Best estimate of 5316 ÷ 71? (a) 760 (b) 7600 (c) 76
  4. 4.Best estimate of 1241 ÷ 78? (a) 16 (b) 1600 (c) 160
  5. 5.Best estimate of 494 ÷ 41? (a) 12 (b) 120 (c) 1200
  6. 6.√80 to 1 decimal place? (a) 8.9 (b) 8.8 (c) 8.6 (d) 8.7
  7. 7.Best estimate of 5238 ÷ 58? (a) 87 (b) 8700 (c) 870
  8. 8.√98 to 1 decimal place? (a) 10.0 (b) 9.9 (c) 10.1 (d) 9.8
  9. 9.√86 to 1 decimal place? (a) 9.3 (b) 9.4 (c) 9.2 (d) 9.5
  10. 10.Best estimate of 1704 ÷ 53? (a) 3400 (b) 340 (c) 34
  11. 11.√78 to 1 decimal place? (a) 9.0 (b) 9.1 (c) 8.8 (d) 8.9
  12. 12.√28 to 1 decimal place? (a) 5.2 (b) 5.4 (c) 5.3 (d) 5.1
  13. 13.Best estimate of 3707 ÷ 49? (a) 740 (b) 74 (c) 7400
  14. 14.√96 to 1 decimal place? (a) 9.8 (b) 9.9 (c) 10.0 (d) 10.1
  15. 15.√65 to 1 decimal place? (a) 8.1 (b) 8.2 (c) 8.4 (d) 8.3
  16. 16.√63 to 1 decimal place? (a) 7.7 (b) 7.8 (c) 7.9 (d) 8.0
  17. 17.Best estimate of 3112 ÷ 46? (a) 620 (b) 6200 (c) 62
  18. 18.Best estimate of 3802 ÷ 48? (a) 760 (b) 7600 (c) 76
  19. 19.Best estimate of 2300 ÷ 24? (a) 115 (b) 11500 (c) 1150
  20. 20.√58 to 1 decimal place? (a) 7.6 (b) 7.8 (c) 7.7 (d) 7.5
  21. 21.Best estimate of 1948 ÷ 51? (a) 390 (b) 39 (c) 3900
  22. 22.Best estimate of 1359 ÷ 42? (a) 3400 (b) 34 (c) 340
  23. 23.Best estimate of 1379 ÷ 77? (a) 1700 (b) 17 (c) 170
  24. 24.√21 to 1 decimal place? (a) 4.4 (b) 4.3 (c) 4.6 (d) 4.5
  25. 25.Best estimate of 3199 ÷ 44? (a) 8000 (b) 800 (c) 80
  26. 26.Best estimate of 1810 ÷ 39? (a) 4500 (b) 450 (c) 45
  27. 27.√22 to 1 decimal place? (a) 4.7 (b) 4.8 (c) 4.9 (d) 4.6
  28. 28.Best estimate of 765 ÷ 42? (a) 1900 (b) 19 (c) 190
  29. 29.√75 to 1 decimal place? (a) 8.9 (b) 8.7 (c) 8.8 (d) 8.6
  30. 30.√52 to 1 decimal place? (a) 7.2 (b) 7.0 (c) 7.1 (d) 6.9
  31. 31.Best estimate of 4790 ÷ 82? (a) 60 (b) 600 (c) 6000
  32. 32.Best estimate of 4955 ÷ 61? (a) 830 (b) 83 (c) 8300
  33. 33.√72 to 1 decimal place? (a) 8.7 (b) 8.5 (c) 8.4 (d) 8.6
  34. 34.Best estimate of 1477 ÷ 46? (a) 300 (b) 3000 (c) 30
  35. 35.√89 to 1 decimal place? (a) 9.5 (b) 9.6 (c) 9.4 (d) 9.3
  36. 36.√40 to 1 decimal place? (a) 6.4 (b) 6.2 (c) 6.1 (d) 6.3
  37. 37.√34 to 1 decimal place? (a) 6.0 (b) 5.8 (c) 6.1 (d) 5.9
  38. 38.Best estimate of 1466 ÷ 33? (a) 490 (b) 4900 (c) 49
  39. 39.Best estimate of 1135 ÷ 42? (a) 280 (b) 2800 (c) 28
  40. 40.Best estimate of 2258 ÷ 32? (a) 75 (b) 750 (c) 7500

Answer key

  1. 28
  2. 72
  3. 76
  4. 16
  5. 12
  6. 8.9
  7. 87
  8. 9.9
  9. 9.3
  10. 34
  11. 8.8
  12. 5.3
  13. 74
  14. 9.8
  15. 8.1
  16. 7.9
  17. 62
  18. 76
  19. 115
  20. 7.6
  21. 39
  22. 34
  23. 17
  24. 4.6
  25. 80
  26. 45
  27. 4.7
  28. 19
  29. 8.7
  30. 7.2
  31. 60
  32. 83
  33. 8.5
  34. 30
  35. 9.4
  36. 6.3
  37. 5.8
  38. 49
  39. 28
  40. 75

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