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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 705 · 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 1329 ÷ 32? (a) 44 (b) 440 (c) 4400
  2. 2.√52 to 1 decimal place? (a) 7.1 (b) 6.9 (c) 7.2 (d) 7.0
  3. 3.√77 to 1 decimal place? (a) 8.6 (b) 8.7 (c) 8.5 (d) 8.8
  4. 4.Best estimate of 3252 ÷ 66? (a) 4600 (b) 460 (c) 46
  5. 5.Best estimate of 2395 ÷ 72? (a) 34 (b) 3400 (c) 340
  6. 6.√90 to 1 decimal place? (a) 9.5 (b) 9.2 (c) 9.3 (d) 9.4
  7. 7.Best estimate of 5537 ÷ 78? (a) 690 (b) 6900 (c) 69
  8. 8.√56 to 1 decimal place? (a) 7.4 (b) 7.5 (c) 7.3 (d) 7.6
  9. 9.Best estimate of 1973 ÷ 31? (a) 66 (b) 6600 (c) 660
  10. 10.Best estimate of 1226 ÷ 29? (a) 41 (b) 4100 (c) 410
  11. 11.Best estimate of 1265 ÷ 27? (a) 42 (b) 420 (c) 4200
  12. 12.√58 to 1 decimal place? (a) 7.6 (b) 7.5 (c) 7.4 (d) 7.7
  13. 13.√29 to 1 decimal place? (a) 5.6 (b) 5.4 (c) 5.5 (d) 5.3
  14. 14.Best estimate of 1097 ÷ 52? (a) 220 (b) 22 (c) 2200
  15. 15.√31 to 1 decimal place? (a) 5.8 (b) 5.7 (c) 5.9 (d) 5.6
  16. 16.Best estimate of 1112 ÷ 69? (a) 160 (b) 16 (c) 1600
  17. 17.Best estimate of 848 ÷ 26? (a) 280 (b) 28 (c) 2800
  18. 18.√82 to 1 decimal place? (a) 8.9 (b) 9.1 (c) 9.0 (d) 8.8
  19. 19.Best estimate of 3422 ÷ 69? (a) 49 (b) 4900 (c) 490
  20. 20.Best estimate of 2127 ÷ 66? (a) 300 (b) 3000 (c) 30
  21. 21.Best estimate of 4549 ÷ 82? (a) 570 (b) 5700 (c) 57
  22. 22.√92 to 1 decimal place? (a) 9.7 (b) 9.6 (c) 9.8 (d) 9.5
  23. 23.√43 to 1 decimal place? (a) 6.6 (b) 6.8 (c) 6.7 (d) 6.5
  24. 24.Best estimate of 990 ÷ 49? (a) 2000 (b) 200 (c) 20
  25. 25.Best estimate of 5905 ÷ 82? (a) 74 (b) 740 (c) 7400
  26. 26.√74 to 1 decimal place? (a) 8.8 (b) 8.7 (c) 8.5 (d) 8.6
  27. 27.√27 to 1 decimal place? (a) 5.4 (b) 5.2 (c) 5.1 (d) 5.3
  28. 28.√37 to 1 decimal place? (a) 5.9 (b) 6.2 (c) 6.0 (d) 6.1
  29. 29.√50 to 1 decimal place? (a) 7.3 (b) 7.1 (c) 7.4 (d) 7.2
  30. 30.Best estimate of 1004 ÷ 32? (a) 3300 (b) 330 (c) 33
  31. 31.√84 to 1 decimal place? (a) 9.3 (b) 9.1 (c) 9.2 (d) 9.4
  32. 32.Best estimate of 2153 ÷ 56? (a) 3600 (b) 36 (c) 360
  33. 33.√34 to 1 decimal place? (a) 5.7 (b) 5.9 (c) 6.0 (d) 5.8
  34. 34.Best estimate of 1101 ÷ 29? (a) 370 (b) 37 (c) 3700
  35. 35.Best estimate of 1050 ÷ 87? (a) 12 (b) 120 (c) 1200
  36. 36.√32 to 1 decimal place? (a) 5.8 (b) 6.0 (c) 5.9 (d) 5.7
  37. 37.Best estimate of 3377 ÷ 42? (a) 84 (b) 840 (c) 8400
  38. 38.Best estimate of 1505 ÷ 59? (a) 2500 (b) 250 (c) 25
  39. 39.√55 to 1 decimal place? (a) 7.7 (b) 7.4 (c) 7.5 (d) 7.6
  40. 40.Best estimate of 1220 ÷ 74? (a) 1700 (b) 170 (c) 17

Answer key

  1. 44
  2. 7.2
  3. 8.8
  4. 46
  5. 34
  6. 9.5
  7. 69
  8. 7.5
  9. 66
  10. 41
  11. 42
  12. 7.6
  13. 5.4
  14. 22
  15. 5.6
  16. 16
  17. 28
  18. 9.1
  19. 49
  20. 30
  21. 57
  22. 9.6
  23. 6.6
  24. 20
  25. 74
  26. 8.6
  27. 5.2
  28. 6.1
  29. 7.1
  30. 33
  31. 9.2
  32. 36
  33. 5.8
  34. 37
  35. 12
  36. 5.7
  37. 84
  38. 25
  39. 7.4
  40. 17

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