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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 826 · 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 1789 ÷ 86? (a) 2000 (b) 200 (c) 20
  2. 2.Best estimate of 2235 ÷ 32? (a) 750 (b) 75 (c) 7500
  3. 3.Best estimate of 3434 ÷ 38? (a) 8600 (b) 86 (c) 860
  4. 4.Best estimate of 4463 ÷ 68? (a) 640 (b) 64 (c) 6400
  5. 5.√38 to 1 decimal place? (a) 6.1 (b) 6.3 (c) 6.4 (d) 6.2
  6. 6.√65 to 1 decimal place? (a) 8.4 (b) 8.1 (c) 8.3 (d) 8.2
  7. 7.Best estimate of 1628 ÷ 36? (a) 41 (b) 4100 (c) 410
  8. 8.√30 to 1 decimal place? (a) 5.6 (b) 5.7 (c) 5.4 (d) 5.5
  9. 9.√44 to 1 decimal place? (a) 6.6 (b) 6.5 (c) 6.8 (d) 6.7
  10. 10.Best estimate of 7767 ÷ 86? (a) 8600 (b) 860 (c) 86
  11. 11.Best estimate of 2133 ÷ 42? (a) 53 (b) 5300 (c) 530
  12. 12.√37 to 1 decimal place? (a) 5.9 (b) 6.0 (c) 6.1 (d) 5.8
  13. 13.√20 to 1 decimal place? (a) 4.6 (b) 4.5 (c) 4.7 (d) 4.8
  14. 14.Best estimate of 5027 ÷ 62? (a) 840 (b) 84 (c) 8400
  15. 15.Best estimate of 5665 ÷ 74? (a) 81 (b) 810 (c) 8100
  16. 16.√69 to 1 decimal place? (a) 8.5 (b) 8.4 (c) 8.6 (d) 8.3
  17. 17.√92 to 1 decimal place? (a) 9.5 (b) 9.6 (c) 9.7 (d) 9.4
  18. 18.Best estimate of 1316 ÷ 21? (a) 66 (b) 660 (c) 6600
  19. 19.Best estimate of 3773 ÷ 64? (a) 630 (b) 63 (c) 6300
  20. 20.√61 to 1 decimal place? (a) 7.9 (b) 7.8 (c) 8.0 (d) 7.7
  21. 21.Best estimate of 1519 ÷ 53? (a) 3000 (b) 30 (c) 300
  22. 22.√24 to 1 decimal place? (a) 5.0 (b) 4.9 (c) 4.8 (d) 5.1
  23. 23.√89 to 1 decimal place? (a) 9.6 (b) 9.3 (c) 9.4 (d) 9.5
  24. 24.Best estimate of 2228 ÷ 53? (a) 45 (b) 4500 (c) 450
  25. 25.Best estimate of 1502 ÷ 36? (a) 3800 (b) 380 (c) 38
  26. 26.Best estimate of 2485 ÷ 27? (a) 830 (b) 83 (c) 8300
  27. 27.Best estimate of 2061 ÷ 38? (a) 520 (b) 5200 (c) 52
  28. 28.Best estimate of 4259 ÷ 71? (a) 610 (b) 61 (c) 6100
  29. 29.√86 to 1 decimal place? (a) 9.6 (b) 9.5 (c) 9.3 (d) 9.4
  30. 30.√85 to 1 decimal place? (a) 9.3 (b) 9.0 (c) 9.1 (d) 9.2
  31. 31.√53 to 1 decimal place? (a) 7.3 (b) 7.6 (c) 7.5 (d) 7.4
  32. 32.√40 to 1 decimal place? (a) 6.6 (b) 6.3 (c) 6.5 (d) 6.4
  33. 33.√59 to 1 decimal place? (a) 7.9 (b) 7.6 (c) 7.7 (d) 7.8
  34. 34.√26 to 1 decimal place? (a) 5.0 (b) 4.9 (c) 4.8 (d) 5.1
  35. 35.√58 to 1 decimal place? (a) 7.8 (b) 7.7 (c) 7.9 (d) 7.6
  36. 36.Best estimate of 4949 ÷ 72? (a) 710 (b) 7100 (c) 71
  37. 37.Best estimate of 2329 ÷ 36? (a) 580 (b) 58 (c) 5800
  38. 38.Best estimate of 4387 ÷ 84? (a) 5500 (b) 550 (c) 55
  39. 39.Best estimate of 5343 ÷ 56? (a) 89 (b) 890 (c) 8900
  40. 40.√84 to 1 decimal place? (a) 9.3 (b) 9.1 (c) 9.2 (d) 9.0

Answer key

  1. 20
  2. 75
  3. 86
  4. 64
  5. 6.2
  6. 8.1
  7. 41
  8. 5.5
  9. 6.6
  10. 86
  11. 53
  12. 6.1
  13. 4.5
  14. 84
  15. 81
  16. 8.3
  17. 9.6
  18. 66
  19. 63
  20. 7.8
  21. 30
  22. 4.9
  23. 9.4
  24. 45
  25. 38
  26. 83
  27. 52
  28. 61
  29. 9.3
  30. 9.2
  31. 7.3
  32. 6.3
  33. 7.7
  34. 5.1
  35. 7.6
  36. 71
  37. 58
  38. 55
  39. 89
  40. 9.2

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