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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 445 · 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.√45 to 1 decimal place? (a) 6.7 (b) 6.8 (c) 6.6 (d) 6.5
  2. 2.Best estimate of 3229 ÷ 58? (a) 540 (b) 54 (c) 5400
  3. 3.√61 to 1 decimal place? (a) 7.8 (b) 7.6 (c) 7.5 (d) 7.7
  4. 4.√94 to 1 decimal place? (a) 9.7 (b) 9.5 (c) 9.6 (d) 9.4
  5. 5.Best estimate of 2326 ÷ 66? (a) 33 (b) 3300 (c) 330
  6. 6.Best estimate of 1252 ÷ 51? (a) 2500 (b) 250 (c) 25
  7. 7.√75 to 1 decimal place? (a) 8.5 (b) 8.4 (c) 8.6 (d) 8.7
  8. 8.√66 to 1 decimal place? (a) 8.2 (b) 8.4 (c) 8.1 (d) 8.3
  9. 9.Best estimate of 543 ÷ 41? (a) 1400 (b) 14 (c) 140
  10. 10.Best estimate of 1328 ÷ 76? (a) 170 (b) 17 (c) 1700
  11. 11.√58 to 1 decimal place? (a) 7.7 (b) 7.8 (c) 7.5 (d) 7.6
  12. 12.Best estimate of 3090 ÷ 63? (a) 520 (b) 52 (c) 5200
  13. 13.√86 to 1 decimal place? (a) 9.3 (b) 9.0 (c) 9.2 (d) 9.1
  14. 14.Best estimate of 2770 ÷ 32? (a) 920 (b) 9200 (c) 92
  15. 15.√34 to 1 decimal place? (a) 5.5 (b) 5.7 (c) 5.8 (d) 5.6
  16. 16.Best estimate of 1346 ÷ 49? (a) 2700 (b) 270 (c) 27
  17. 17.Best estimate of 967 ÷ 79? (a) 120 (b) 1200 (c) 12
  18. 18.Best estimate of 1120 ÷ 42? (a) 28 (b) 2800 (c) 280
  19. 19.√59 to 1 decimal place? (a) 7.9 (b) 7.8 (c) 8.0 (d) 7.7
  20. 20.√37 to 1 decimal place? (a) 6.1 (b) 6.0 (c) 6.3 (d) 6.2
  21. 21.√55 to 1 decimal place? (a) 7.3 (b) 7.6 (c) 7.5 (d) 7.4
  22. 22.Best estimate of 1972 ÷ 83? (a) 250 (b) 25 (c) 2500
  23. 23.Best estimate of 3914 ÷ 53? (a) 780 (b) 78 (c) 7800
  24. 24.Best estimate of 6542 ÷ 76? (a) 820 (b) 8200 (c) 82
  25. 25.√72 to 1 decimal place? (a) 8.4 (b) 8.6 (c) 8.5 (d) 8.7
  26. 26.√92 to 1 decimal place? (a) 9.5 (b) 9.6 (c) 9.7 (d) 9.4
  27. 27.Best estimate of 1559 ÷ 31? (a) 520 (b) 5200 (c) 52
  28. 28.Best estimate of 2238 ÷ 24? (a) 112 (b) 11200 (c) 1120
  29. 29.Best estimate of 5490 ÷ 69? (a) 780 (b) 78 (c) 7800
  30. 30.√26 to 1 decimal place? (a) 5.0 (b) 4.9 (c) 4.8 (d) 5.1
  31. 31.√56 to 1 decimal place? (a) 7.4 (b) 7.5 (c) 7.3 (d) 7.2
  32. 32.Best estimate of 4892 ÷ 87? (a) 54 (b) 5400 (c) 540
  33. 33.Best estimate of 1482 ÷ 89? (a) 160 (b) 1600 (c) 16
  34. 34.√89 to 1 decimal place? (a) 9.4 (b) 9.2 (c) 9.5 (d) 9.3
  35. 35.Best estimate of 1318 ÷ 22? (a) 660 (b) 6600 (c) 66
  36. 36.√44 to 1 decimal place? (a) 6.4 (b) 6.7 (c) 6.6 (d) 6.5
  37. 37.Best estimate of 868 ÷ 27? (a) 290 (b) 29 (c) 2900
  38. 38.Best estimate of 2029 ÷ 49? (a) 4100 (b) 410 (c) 41
  39. 39.Best estimate of 4517 ÷ 59? (a) 750 (b) 7500 (c) 75
  40. 40.√88 to 1 decimal place? (a) 9.3 (b) 9.1 (c) 9.4 (d) 9.2

Answer key

  1. 6.7
  2. 54
  3. 7.8
  4. 9.7
  5. 33
  6. 25
  7. 8.7
  8. 8.1
  9. 14
  10. 17
  11. 7.6
  12. 52
  13. 9.3
  14. 92
  15. 5.8
  16. 27
  17. 12
  18. 28
  19. 7.7
  20. 6.1
  21. 7.4
  22. 25
  23. 78
  24. 82
  25. 8.5
  26. 9.6
  27. 52
  28. 112
  29. 78
  30. 5.1
  31. 7.5
  32. 54
  33. 16
  34. 9.4
  35. 66
  36. 6.6
  37. 29
  38. 41
  39. 75
  40. 9.4

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