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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 639 · 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.√82 to 1 decimal place? (a) 9.2 (b) 8.9 (c) 9.1 (d) 9.0
  2. 2.Best estimate of 1165 ÷ 41? (a) 290 (b) 2900 (c) 29
  3. 3.Best estimate of 1433 ÷ 26? (a) 480 (b) 48 (c) 4800
  4. 4.Best estimate of 467 ÷ 23? (a) 2300 (b) 230 (c) 23
  5. 5.√20 to 1 decimal place? (a) 4.4 (b) 4.6 (c) 4.7 (d) 4.5
  6. 6.√65 to 1 decimal place? (a) 8.3 (b) 8.1 (c) 8.0 (d) 8.2
  7. 7.√92 to 1 decimal place? (a) 9.6 (b) 9.8 (c) 9.7 (d) 9.5
  8. 8.Best estimate of 964 ÷ 61? (a) 160 (b) 1600 (c) 16
  9. 9.Best estimate of 3010 ÷ 86? (a) 330 (b) 33 (c) 3300
  10. 10.√74 to 1 decimal place? (a) 8.6 (b) 8.5 (c) 8.3 (d) 8.4
  11. 11.√34 to 1 decimal place? (a) 5.7 (b) 5.9 (c) 5.8 (d) 6.0
  12. 12.√35 to 1 decimal place? (a) 5.8 (b) 6.0 (c) 5.7 (d) 5.9
  13. 13.√70 to 1 decimal place? (a) 8.6 (b) 8.4 (c) 8.5 (d) 8.7
  14. 14.√48 to 1 decimal place? (a) 7.0 (b) 6.8 (c) 6.7 (d) 6.9
  15. 15.√76 to 1 decimal place? (a) 8.5 (b) 8.8 (c) 8.7 (d) 8.6
  16. 16.Best estimate of 3145 ÷ 86? (a) 35 (b) 350 (c) 3500
  17. 17.Best estimate of 4292 ÷ 81? (a) 540 (b) 5400 (c) 54
  18. 18.Best estimate of 3755 ÷ 42? (a) 9400 (b) 940 (c) 94
  19. 19.Best estimate of 1038 ÷ 49? (a) 210 (b) 2100 (c) 21
  20. 20.Best estimate of 1049 ÷ 23? (a) 52 (b) 520 (c) 5200
  21. 21.√51 to 1 decimal place? (a) 7.0 (b) 7.3 (c) 7.1 (d) 7.2
  22. 22.Best estimate of 5448 ÷ 78? (a) 68 (b) 6800 (c) 680
  23. 23.Best estimate of 1393 ÷ 22? (a) 7000 (b) 70 (c) 700
  24. 24.Best estimate of 1223 ÷ 58? (a) 20 (b) 2000 (c) 200
  25. 25.Best estimate of 742 ÷ 43? (a) 1900 (b) 190 (c) 19
  26. 26.Best estimate of 4944 ÷ 72? (a) 71 (b) 710 (c) 7100
  27. 27.√90 to 1 decimal place? (a) 9.6 (b) 9.8 (c) 9.7 (d) 9.5
  28. 28.Best estimate of 773 ÷ 26? (a) 26 (b) 2600 (c) 260
  29. 29.Best estimate of 1966 ÷ 43? (a) 490 (b) 49 (c) 4900
  30. 30.Best estimate of 3269 ÷ 43? (a) 820 (b) 82 (c) 8200
  31. 31.Best estimate of 2955 ÷ 53? (a) 59 (b) 590 (c) 5900
  32. 32.√71 to 1 decimal place? (a) 8.6 (b) 8.4 (c) 8.5 (d) 8.7
  33. 33.√56 to 1 decimal place? (a) 7.7 (b) 7.5 (c) 7.4 (d) 7.6
  34. 34.√72 to 1 decimal place? (a) 8.7 (b) 8.6 (c) 8.8 (d) 8.5
  35. 35.Best estimate of 6078 ÷ 72? (a) 870 (b) 8700 (c) 87
  36. 36.Best estimate of 3476 ÷ 72? (a) 5000 (b) 500 (c) 50
  37. 37.√69 to 1 decimal place? (a) 8.1 (b) 8.2 (c) 8.0 (d) 8.3
  38. 38.√79 to 1 decimal place? (a) 8.8 (b) 8.9 (c) 8.7 (d) 8.6
  39. 39.√55 to 1 decimal place? (a) 7.4 (b) 7.2 (c) 7.3 (d) 7.5
  40. 40.√32 to 1 decimal place? (a) 5.4 (b) 5.6 (c) 5.5 (d) 5.7

Answer key

  1. 9.1
  2. 29
  3. 48
  4. 23
  5. 4.5
  6. 8.1
  7. 9.6
  8. 16
  9. 33
  10. 8.6
  11. 5.8
  12. 5.9
  13. 8.4
  14. 6.9
  15. 8.7
  16. 35
  17. 54
  18. 94
  19. 21
  20. 52
  21. 7.1
  22. 68
  23. 70
  24. 20
  25. 19
  26. 71
  27. 9.5
  28. 26
  29. 49
  30. 82
  31. 59
  32. 8.4
  33. 7.5
  34. 8.5
  35. 87
  36. 50
  37. 8.3
  38. 8.9
  39. 7.4
  40. 5.7

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