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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 922 · 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.√55 to 1 decimal place? (a) 7.2 (b) 7.4 (c) 7.5 (d) 7.3
  2. 2.√92 to 1 decimal place? (a) 9.5 (b) 9.4 (c) 9.6 (d) 9.3
  3. 3.Best estimate of 1954 ÷ 38? (a) 490 (b) 49 (c) 4900
  4. 4.√65 to 1 decimal place? (a) 7.8 (b) 7.9 (c) 8.1 (d) 8.0
  5. 5.Best estimate of 3483 ÷ 71? (a) 5000 (b) 50 (c) 500
  6. 6.√59 to 1 decimal place? (a) 7.5 (b) 7.6 (c) 7.7 (d) 7.4
  7. 7.Best estimate of 1787 ÷ 24? (a) 890 (b) 8900 (c) 89
  8. 8.Best estimate of 467 ÷ 26? (a) 160 (b) 1600 (c) 16
  9. 9.√37 to 1 decimal place? (a) 6.0 (b) 5.8 (c) 6.1 (d) 5.9
  10. 10.√96 to 1 decimal place? (a) 10.1 (b) 10.0 (c) 9.9 (d) 9.8
  11. 11.√61 to 1 decimal place? (a) 7.8 (b) 7.6 (c) 7.5 (d) 7.7
  12. 12.Best estimate of 4130 ÷ 57? (a) 690 (b) 6900 (c) 69
  13. 13.√34 to 1 decimal place? (a) 5.9 (b) 5.8 (c) 5.7 (d) 5.6
  14. 14.Best estimate of 3108 ÷ 47? (a) 620 (b) 62 (c) 6200
  15. 15.Best estimate of 3567 ÷ 66? (a) 51 (b) 5100 (c) 510
  16. 16.Best estimate of 317 ÷ 22? (a) 16 (b) 1600 (c) 160
  17. 17.√23 to 1 decimal place? (a) 4.8 (b) 4.5 (c) 4.7 (d) 4.6
  18. 18.Best estimate of 1235 ÷ 62? (a) 2100 (b) 210 (c) 21
  19. 19.Best estimate of 4707 ÷ 86? (a) 520 (b) 5200 (c) 52
  20. 20.Best estimate of 3707 ÷ 62? (a) 620 (b) 6200 (c) 62
  21. 21.Best estimate of 4612 ÷ 86? (a) 51 (b) 510 (c) 5100
  22. 22.Best estimate of 2112 ÷ 71? (a) 30 (b) 300 (c) 3000
  23. 23.Best estimate of 4489 ÷ 59? (a) 7500 (b) 75 (c) 750
  24. 24.√45 to 1 decimal place? (a) 6.6 (b) 6.7 (c) 6.4 (d) 6.5
  25. 25.√74 to 1 decimal place? (a) 8.7 (b) 8.4 (c) 8.6 (d) 8.5
  26. 26.Best estimate of 632 ÷ 26? (a) 21 (b) 2100 (c) 210
  27. 27.√80 to 1 decimal place? (a) 9.1 (b) 8.8 (c) 9.0 (d) 8.9
  28. 28.Best estimate of 1882 ÷ 73? (a) 270 (b) 2700 (c) 27
  29. 29.Best estimate of 2506 ÷ 77? (a) 310 (b) 31 (c) 3100
  30. 30.Best estimate of 2298 ÷ 56? (a) 380 (b) 38 (c) 3800
  31. 31.√48 to 1 decimal place? (a) 7.1 (b) 6.9 (c) 7.0 (d) 7.2
  32. 32.√42 to 1 decimal place? (a) 6.7 (b) 6.8 (c) 6.5 (d) 6.6
  33. 33.√87 to 1 decimal place? (a) 9.5 (b) 9.3 (c) 9.6 (d) 9.4
  34. 34.√40 to 1 decimal place? (a) 6.1 (b) 6.4 (c) 6.2 (d) 6.3
  35. 35.Best estimate of 1865 ÷ 86? (a) 2100 (b) 210 (c) 21
  36. 36.Best estimate of 3154 ÷ 88? (a) 350 (b) 35 (c) 3500
  37. 37.√86 to 1 decimal place? (a) 9.3 (b) 9.0 (c) 9.1 (d) 9.2
  38. 38.√78 to 1 decimal place? (a) 8.5 (b) 8.6 (c) 8.7 (d) 8.8
  39. 39.Best estimate of 803 ÷ 23? (a) 400 (b) 40 (c) 4000
  40. 40.Best estimate of 1071 ÷ 23? (a) 540 (b) 54 (c) 5400

Answer key

  1. 7.4
  2. 9.6
  3. 49
  4. 8.1
  5. 50
  6. 7.7
  7. 89
  8. 16
  9. 6.1
  10. 9.8
  11. 7.8
  12. 69
  13. 5.8
  14. 62
  15. 51
  16. 16
  17. 4.8
  18. 21
  19. 52
  20. 62
  21. 51
  22. 30
  23. 75
  24. 6.7
  25. 8.6
  26. 21
  27. 8.9
  28. 27
  29. 31
  30. 38
  31. 6.9
  32. 6.5
  33. 9.3
  34. 6.3
  35. 21
  36. 35
  37. 9.3
  38. 8.8
  39. 40
  40. 54

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