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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 250 · 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 3323 ÷ 59? (a) 55 (b) 5500 (c) 550
  2. 2.√98 to 1 decimal place? (a) 9.9 (b) 9.8 (c) 9.7 (d) 10.0
  3. 3.Best estimate of 2096 ÷ 58? (a) 350 (b) 3500 (c) 35
  4. 4.√52 to 1 decimal place? (a) 7.1 (b) 7.4 (c) 7.2 (d) 7.3
  5. 5.√71 to 1 decimal place? (a) 8.4 (b) 8.5 (c) 8.3 (d) 8.6
  6. 6.Best estimate of 1659 ÷ 66? (a) 2400 (b) 24 (c) 240
  7. 7.√80 to 1 decimal place? (a) 9.1 (b) 9.0 (c) 8.9 (d) 9.2
  8. 8.√70 to 1 decimal place? (a) 8.4 (b) 8.5 (c) 8.6 (d) 8.7
  9. 9.√94 to 1 decimal place? (a) 9.9 (b) 10.0 (c) 9.8 (d) 9.7
  10. 10.√76 to 1 decimal place? (a) 8.7 (b) 8.8 (c) 8.9 (d) 8.6
  11. 11.Best estimate of 2689 ÷ 47? (a) 540 (b) 5400 (c) 54
  12. 12.√88 to 1 decimal place? (a) 9.6 (b) 9.4 (c) 9.3 (d) 9.5
  13. 13.√50 to 1 decimal place? (a) 7.3 (b) 7.1 (c) 7.0 (d) 7.2
  14. 14.√59 to 1 decimal place? (a) 7.5 (b) 7.7 (c) 7.6 (d) 7.4
  15. 15.Best estimate of 1931 ÷ 41? (a) 480 (b) 4800 (c) 48
  16. 16.√37 to 1 decimal place? (a) 6.0 (b) 6.1 (c) 6.2 (d) 6.3
  17. 17.√69 to 1 decimal place? (a) 8.1 (b) 8.2 (c) 8.0 (d) 8.3
  18. 18.Best estimate of 6630 ÷ 78? (a) 8300 (b) 83 (c) 830
  19. 19.Best estimate of 1571 ÷ 28? (a) 5200 (b) 52 (c) 520
  20. 20.√29 to 1 decimal place? (a) 5.7 (b) 5.5 (c) 5.4 (d) 5.6
  21. 21.√43 to 1 decimal place? (a) 6.4 (b) 6.5 (c) 6.6 (d) 6.7
  22. 22.√65 to 1 decimal place? (a) 7.9 (b) 7.8 (c) 8.0 (d) 8.1
  23. 23.Best estimate of 1424 ÷ 27? (a) 47 (b) 4700 (c) 470
  24. 24.Best estimate of 4322 ÷ 67? (a) 6200 (b) 62 (c) 620
  25. 25.√41 to 1 decimal place? (a) 6.2 (b) 6.1 (c) 6.4 (d) 6.3
  26. 26.√40 to 1 decimal place? (a) 6.4 (b) 6.2 (c) 6.3 (d) 6.1
  27. 27.Best estimate of 4998 ÷ 62? (a) 8300 (b) 830 (c) 83
  28. 28.√82 to 1 decimal place? (a) 9.2 (b) 9.0 (c) 8.9 (d) 9.1
  29. 29.√26 to 1 decimal place? (a) 5.2 (b) 5.4 (c) 5.1 (d) 5.3
  30. 30.√92 to 1 decimal place? (a) 9.4 (b) 9.3 (c) 9.5 (d) 9.6
  31. 31.Best estimate of 691 ÷ 23? (a) 350 (b) 35 (c) 3500
  32. 32.Best estimate of 3183 ÷ 34? (a) 106 (b) 1060 (c) 10600
  33. 33.Best estimate of 1217 ÷ 29? (a) 41 (b) 4100 (c) 410
  34. 34.√51 to 1 decimal place? (a) 7.2 (b) 7.1 (c) 7.0 (d) 7.3
  35. 35.√77 to 1 decimal place? (a) 9.1 (b) 9.0 (c) 8.8 (d) 8.9
  36. 36.√55 to 1 decimal place? (a) 7.5 (b) 7.6 (c) 7.4 (d) 7.3
  37. 37.Best estimate of 7890 ÷ 83? (a) 9900 (b) 990 (c) 99
  38. 38.√63 to 1 decimal place? (a) 7.9 (b) 8.1 (c) 8.0 (d) 7.8
  39. 39.√58 to 1 decimal place? (a) 7.7 (b) 7.6 (c) 7.5 (d) 7.4
  40. 40.Best estimate of 3587 ÷ 66? (a) 5100 (b) 510 (c) 51

Answer key

  1. 55
  2. 9.9
  3. 35
  4. 7.2
  5. 8.4
  6. 24
  7. 8.9
  8. 8.4
  9. 9.7
  10. 8.7
  11. 54
  12. 9.4
  13. 7.1
  14. 7.7
  15. 48
  16. 6.1
  17. 8.3
  18. 83
  19. 52
  20. 5.4
  21. 6.6
  22. 8.1
  23. 47
  24. 62
  25. 6.4
  26. 6.3
  27. 83
  28. 9.1
  29. 5.1
  30. 9.6
  31. 35
  32. 106
  33. 41
  34. 7.1
  35. 8.8
  36. 7.4
  37. 99
  38. 7.9
  39. 7.6
  40. 51

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