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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 10 · 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) 8.8 (b) 8.7 (c) 8.9 (d) 8.6
  2. 2.Best estimate of 2672 ÷ 36? (a) 670 (b) 67 (c) 6700
  3. 3.√27 to 1 decimal place? (a) 5.3 (b) 5.2 (c) 5.5 (d) 5.4
  4. 4.Best estimate of 857 ÷ 31? (a) 2900 (b) 29 (c) 290
  5. 5.√94 to 1 decimal place? (a) 9.7 (b) 9.8 (c) 10.0 (d) 9.9
  6. 6.√53 to 1 decimal place? (a) 7.2 (b) 7.3 (c) 7.4 (d) 7.1
  7. 7.√41 to 1 decimal place? (a) 6.6 (b) 6.5 (c) 6.3 (d) 6.4
  8. 8.Best estimate of 2354 ÷ 29? (a) 7800 (b) 78 (c) 780
  9. 9.Best estimate of 1469 ÷ 81? (a) 18 (b) 1800 (c) 180
  10. 10.√56 to 1 decimal place? (a) 7.4 (b) 7.3 (c) 7.5 (d) 7.6
  11. 11.Best estimate of 3315 ÷ 44? (a) 830 (b) 83 (c) 8300
  12. 12.Best estimate of 2101 ÷ 54? (a) 420 (b) 4200 (c) 42
  13. 13.√46 to 1 decimal place? (a) 7.1 (b) 7.0 (c) 6.8 (d) 6.9
  14. 14.Best estimate of 1470 ÷ 23? (a) 74 (b) 7400 (c) 740
  15. 15.√86 to 1 decimal place? (a) 9.2 (b) 9.4 (c) 9.5 (d) 9.3
  16. 16.√92 to 1 decimal place? (a) 9.5 (b) 9.6 (c) 9.8 (d) 9.7
  17. 17.√30 to 1 decimal place? (a) 5.5 (b) 5.6 (c) 5.7 (d) 5.8
  18. 18.√21 to 1 decimal place? (a) 4.9 (b) 4.6 (c) 4.8 (d) 4.7
  19. 19.Best estimate of 3226 ÷ 77? (a) 4000 (b) 400 (c) 40
  20. 20.Best estimate of 2221 ÷ 82? (a) 280 (b) 2800 (c) 28
  21. 21.Best estimate of 1945 ÷ 23? (a) 9700 (b) 970 (c) 97
  22. 22.√47 to 1 decimal place? (a) 7.0 (b) 6.8 (c) 6.9 (d) 7.1
  23. 23.Best estimate of 5880 ÷ 86? (a) 6500 (b) 650 (c) 65
  24. 24.Best estimate of 4798 ÷ 83? (a) 600 (b) 60 (c) 6000
  25. 25.√89 to 1 decimal place? (a) 9.4 (b) 9.7 (c) 9.5 (d) 9.6
  26. 26.Best estimate of 3957 ÷ 66? (a) 570 (b) 5700 (c) 57
  27. 27.Best estimate of 1143 ÷ 69? (a) 160 (b) 16 (c) 1600
  28. 28.Best estimate of 2190 ÷ 26? (a) 730 (b) 7300 (c) 73
  29. 29.Best estimate of 1253 ÷ 48? (a) 2500 (b) 250 (c) 25
  30. 30.√44 to 1 decimal place? (a) 6.6 (b) 6.3 (c) 6.5 (d) 6.4
  31. 31.Best estimate of 4426 ÷ 86? (a) 4900 (b) 490 (c) 49
  32. 32.Best estimate of 1611 ÷ 46? (a) 3200 (b) 32 (c) 320
  33. 33.√42 to 1 decimal place? (a) 6.4 (b) 6.5 (c) 6.3 (d) 6.6
  34. 34.Best estimate of 1829 ÷ 22? (a) 910 (b) 91 (c) 9100
  35. 35.√24 to 1 decimal place? (a) 4.8 (b) 4.9 (c) 4.6 (d) 4.7
  36. 36.√26 to 1 decimal place? (a) 5.4 (b) 5.1 (c) 5.2 (d) 5.3
  37. 37.√59 to 1 decimal place? (a) 7.8 (b) 7.9 (c) 8.0 (d) 7.7
  38. 38.Best estimate of 798 ÷ 38? (a) 20 (b) 2000 (c) 200
  39. 39.√23 to 1 decimal place? (a) 4.6 (b) 4.8 (c) 4.5 (d) 4.7
  40. 40.Best estimate of 574 ÷ 46? (a) 110 (b) 1100 (c) 11

Answer key

  1. 8.6
  2. 67
  3. 5.2
  4. 29
  5. 9.7
  6. 7.3
  7. 6.4
  8. 78
  9. 18
  10. 7.5
  11. 83
  12. 42
  13. 6.8
  14. 74
  15. 9.3
  16. 9.6
  17. 5.5
  18. 4.6
  19. 40
  20. 28
  21. 97
  22. 6.9
  23. 65
  24. 60
  25. 9.4
  26. 57
  27. 16
  28. 73
  29. 25
  30. 6.6
  31. 49
  32. 32
  33. 6.5
  34. 91
  35. 4.9
  36. 5.1
  37. 7.7
  38. 20
  39. 4.8
  40. 11

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