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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 193 · 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 630 ÷ 27? (a) 21 (b) 210 (c) 2100
  2. 2.Best estimate of 518 ÷ 28? (a) 170 (b) 17 (c) 1700
  3. 3.Best estimate of 1608 ÷ 22? (a) 8000 (b) 800 (c) 80
  4. 4.Best estimate of 2334 ÷ 27? (a) 780 (b) 7800 (c) 78
  5. 5.Best estimate of 632 ÷ 24? (a) 3200 (b) 32 (c) 320
  6. 6.Best estimate of 2759 ÷ 56? (a) 460 (b) 4600 (c) 46
  7. 7.Best estimate of 798 ÷ 24? (a) 400 (b) 4000 (c) 40
  8. 8.√65 to 1 decimal place? (a) 7.9 (b) 8.0 (c) 8.2 (d) 8.1
  9. 9.√90 to 1 decimal place? (a) 9.5 (b) 9.6 (c) 9.7 (d) 9.4
  10. 10.√92 to 1 decimal place? (a) 9.4 (b) 9.3 (c) 9.6 (d) 9.5
  11. 11.Best estimate of 7907 ÷ 88? (a) 8800 (b) 88 (c) 880
  12. 12.Best estimate of 1321 ÷ 84? (a) 170 (b) 17 (c) 1700
  13. 13.Best estimate of 3244 ÷ 42? (a) 810 (b) 8100 (c) 81
  14. 14.√31 to 1 decimal place? (a) 5.9 (b) 5.7 (c) 5.6 (d) 5.8
  15. 15.√71 to 1 decimal place? (a) 8.6 (b) 8.3 (c) 8.4 (d) 8.5
  16. 16.Best estimate of 1043 ÷ 78? (a) 13 (b) 130 (c) 1300
  17. 17.√58 to 1 decimal place? (a) 7.6 (b) 7.9 (c) 7.7 (d) 7.8
  18. 18.√38 to 1 decimal place? (a) 6.3 (b) 6.1 (c) 6.0 (d) 6.2
  19. 19.Best estimate of 3602 ÷ 59? (a) 6000 (b) 600 (c) 60
  20. 20.√21 to 1 decimal place? (a) 4.4 (b) 4.6 (c) 4.7 (d) 4.5
  21. 21.Best estimate of 1437 ÷ 26? (a) 48 (b) 480 (c) 4800
  22. 22.√40 to 1 decimal place? (a) 6.2 (b) 6.4 (c) 6.3 (d) 6.1
  23. 23.√66 to 1 decimal place? (a) 8.1 (b) 8.2 (c) 8.0 (d) 8.3
  24. 24.Best estimate of 2605 ÷ 74? (a) 370 (b) 37 (c) 3700
  25. 25.Best estimate of 1685 ÷ 34? (a) 5600 (b) 560 (c) 56
  26. 26.√34 to 1 decimal place? (a) 6.0 (b) 6.1 (c) 5.8 (d) 5.9
  27. 27.√84 to 1 decimal place? (a) 9.3 (b) 9.4 (c) 9.5 (d) 9.2
  28. 28.√41 to 1 decimal place? (a) 6.4 (b) 6.3 (c) 6.5 (d) 6.2
  29. 29.Best estimate of 1366 ÷ 72? (a) 20 (b) 200 (c) 2000
  30. 30.Best estimate of 7059 ÷ 82? (a) 88 (b) 8800 (c) 880
  31. 31.Best estimate of 2108 ÷ 26? (a) 700 (b) 70 (c) 7000
  32. 32.Best estimate of 5191 ÷ 74? (a) 7400 (b) 74 (c) 740
  33. 33.Best estimate of 1413 ÷ 83? (a) 18 (b) 1800 (c) 180
  34. 34.√69 to 1 decimal place? (a) 8.3 (b) 8.2 (c) 8.1 (d) 8.4
  35. 35.√55 to 1 decimal place? (a) 7.6 (b) 7.4 (c) 7.7 (d) 7.5
  36. 36.√52 to 1 decimal place? (a) 7.3 (b) 7.5 (c) 7.4 (d) 7.2
  37. 37.Best estimate of 2356 ÷ 77? (a) 2900 (b) 290 (c) 29
  38. 38.√28 to 1 decimal place? (a) 5.5 (b) 5.3 (c) 5.4 (d) 5.2
  39. 39.√61 to 1 decimal place? (a) 7.6 (b) 7.7 (c) 7.5 (d) 7.8
  40. 40.√26 to 1 decimal place? (a) 5.4 (b) 5.1 (c) 5.2 (d) 5.3

Answer key

  1. 21
  2. 17
  3. 80
  4. 78
  5. 32
  6. 46
  7. 40
  8. 8.1
  9. 9.5
  10. 9.6
  11. 88
  12. 17
  13. 81
  14. 5.6
  15. 8.4
  16. 13
  17. 7.6
  18. 6.2
  19. 60
  20. 4.6
  21. 48
  22. 6.3
  23. 8.1
  24. 37
  25. 56
  26. 5.8
  27. 9.2
  28. 6.4
  29. 20
  30. 88
  31. 70
  32. 74
  33. 18
  34. 8.3
  35. 7.4
  36. 7.2
  37. 29
  38. 5.3
  39. 7.8
  40. 5.1

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