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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 955 · 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.√74 to 1 decimal place? (a) 8.6 (b) 8.4 (c) 8.5 (d) 8.3
  2. 2.Best estimate of 4958 ÷ 72? (a) 71 (b) 7100 (c) 710
  3. 3.Best estimate of 3062 ÷ 46? (a) 61 (b) 6100 (c) 610
  4. 4.Best estimate of 3030 ÷ 37? (a) 76 (b) 7600 (c) 760
  5. 5.√45 to 1 decimal place? (a) 6.9 (b) 6.7 (c) 7.0 (d) 6.8
  6. 6.√34 to 1 decimal place? (a) 5.9 (b) 5.8 (c) 6.0 (d) 5.7
  7. 7.√65 to 1 decimal place? (a) 7.9 (b) 7.8 (c) 8.0 (d) 8.1
  8. 8.Best estimate of 4067 ÷ 44? (a) 10200 (b) 102 (c) 1020
  9. 9.√77 to 1 decimal place? (a) 8.7 (b) 9.0 (c) 8.8 (d) 8.9
  10. 10.Best estimate of 2951 ÷ 34? (a) 98 (b) 9800 (c) 980
  11. 11.√51 to 1 decimal place? (a) 7.1 (b) 7.3 (c) 7.0 (d) 7.2
  12. 12.Best estimate of 1003 ÷ 74? (a) 14 (b) 140 (c) 1400
  13. 13.√40 to 1 decimal place? (a) 6.4 (b) 6.2 (c) 6.5 (d) 6.3
  14. 14.Best estimate of 2306 ÷ 89? (a) 26 (b) 260 (c) 2600
  15. 15.√94 to 1 decimal place? (a) 9.9 (b) 9.7 (c) 9.6 (d) 9.8
  16. 16.√80 to 1 decimal place? (a) 8.8 (b) 8.9 (c) 9.0 (d) 8.7
  17. 17.Best estimate of 772 ÷ 42? (a) 190 (b) 19 (c) 1900
  18. 18.√53 to 1 decimal place? (a) 7.3 (b) 7.2 (c) 7.4 (d) 7.1
  19. 19.Best estimate of 3478 ÷ 37? (a) 8700 (b) 870 (c) 87
  20. 20.√63 to 1 decimal place? (a) 7.8 (b) 7.9 (c) 8.0 (d) 8.1
  21. 21.Best estimate of 1120 ÷ 23? (a) 5600 (b) 560 (c) 56
  22. 22.Best estimate of 323 ÷ 22? (a) 1600 (b) 160 (c) 16
  23. 23.√87 to 1 decimal place? (a) 9.3 (b) 9.4 (c) 9.1 (d) 9.2
  24. 24.Best estimate of 2256 ÷ 42? (a) 560 (b) 5600 (c) 56
  25. 25.Best estimate of 6036 ÷ 72? (a) 860 (b) 86 (c) 8600
  26. 26.√50 to 1 decimal place? (a) 7.2 (b) 7.4 (c) 7.3 (d) 7.1
  27. 27.Best estimate of 835 ÷ 36? (a) 210 (b) 21 (c) 2100
  28. 28.√38 to 1 decimal place? (a) 6.2 (b) 6.1 (c) 6.3 (d) 6.0
  29. 29.√79 to 1 decimal place? (a) 8.8 (b) 8.9 (c) 8.7 (d) 9.0
  30. 30.Best estimate of 8200 ÷ 89? (a) 910 (b) 9100 (c) 91
  31. 31.Best estimate of 1462 ÷ 46? (a) 2900 (b) 29 (c) 290
  32. 32.√70 to 1 decimal place? (a) 8.5 (b) 8.3 (c) 8.2 (d) 8.4
  33. 33.√20 to 1 decimal place? (a) 4.6 (b) 4.5 (c) 4.7 (d) 4.8
  34. 34.√31 to 1 decimal place? (a) 5.9 (b) 5.7 (c) 5.8 (d) 5.6
  35. 35.√32 to 1 decimal place? (a) 5.8 (b) 5.9 (c) 5.7 (d) 6.0
  36. 36.Best estimate of 3049 ÷ 72? (a) 4400 (b) 44 (c) 440
  37. 37.√82 to 1 decimal place? (a) 9.3 (b) 9.1 (c) 9.0 (d) 9.2
  38. 38.√71 to 1 decimal place? (a) 8.1 (b) 8.4 (c) 8.3 (d) 8.2
  39. 39.Best estimate of 606 ÷ 32? (a) 2000 (b) 20 (c) 200
  40. 40.√72 to 1 decimal place? (a) 8.5 (b) 8.2 (c) 8.4 (d) 8.3

Answer key

  1. 8.6
  2. 71
  3. 61
  4. 76
  5. 6.7
  6. 5.8
  7. 8.1
  8. 102
  9. 8.8
  10. 98
  11. 7.1
  12. 14
  13. 6.3
  14. 26
  15. 9.7
  16. 8.9
  17. 19
  18. 7.3
  19. 87
  20. 7.9
  21. 56
  22. 16
  23. 9.3
  24. 56
  25. 86
  26. 7.1
  27. 21
  28. 6.2
  29. 8.9
  30. 91
  31. 29
  32. 8.4
  33. 4.5
  34. 5.6
  35. 5.7
  36. 44
  37. 9.1
  38. 8.4
  39. 20
  40. 8.5

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