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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 503 · 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 3007 ÷ 88? (a) 3300 (b) 330 (c) 33
  2. 2.√37 to 1 decimal place? (a) 5.9 (b) 6.1 (c) 6.0 (d) 5.8
  3. 3.Best estimate of 1333 ÷ 78? (a) 170 (b) 17 (c) 1700
  4. 4.√70 to 1 decimal place? (a) 8.5 (b) 8.6 (c) 8.3 (d) 8.4
  5. 5.√30 to 1 decimal place? (a) 5.8 (b) 5.7 (c) 5.5 (d) 5.6
  6. 6.Best estimate of 3361 ÷ 82? (a) 42 (b) 4200 (c) 420
  7. 7.√80 to 1 decimal place? (a) 9.2 (b) 9.0 (c) 9.1 (d) 8.9
  8. 8.Best estimate of 5055 ÷ 81? (a) 63 (b) 630 (c) 6300
  9. 9.Best estimate of 560 ÷ 36? (a) 140 (b) 14 (c) 1400
  10. 10.Best estimate of 5122 ÷ 59? (a) 8500 (b) 850 (c) 85
  11. 11.√40 to 1 decimal place? (a) 6.2 (b) 6.3 (c) 6.4 (d) 6.5
  12. 12.Best estimate of 7183 ÷ 82? (a) 90 (b) 900 (c) 9000
  13. 13.Best estimate of 1861 ÷ 88? (a) 210 (b) 2100 (c) 21
  14. 14.√83 to 1 decimal place? (a) 8.9 (b) 9.1 (c) 9.2 (d) 9.0
  15. 15.√52 to 1 decimal place? (a) 7.2 (b) 7.4 (c) 7.5 (d) 7.3
  16. 16.√74 to 1 decimal place? (a) 8.8 (b) 8.9 (c) 8.6 (d) 8.7
  17. 17.√69 to 1 decimal place? (a) 8.3 (b) 8.6 (c) 8.4 (d) 8.5
  18. 18.Best estimate of 780 ÷ 47? (a) 1600 (b) 160 (c) 16
  19. 19.√66 to 1 decimal place? (a) 8.2 (b) 8.3 (c) 8.0 (d) 8.1
  20. 20.Best estimate of 2946 ÷ 51? (a) 59 (b) 5900 (c) 590
  21. 21.Best estimate of 3614 ÷ 38? (a) 9000 (b) 90 (c) 900
  22. 22.√38 to 1 decimal place? (a) 6.2 (b) 6.1 (c) 6.4 (d) 6.3
  23. 23.√98 to 1 decimal place? (a) 10.0 (b) 9.7 (c) 9.8 (d) 9.9
  24. 24.√58 to 1 decimal place? (a) 7.7 (b) 7.5 (c) 7.6 (d) 7.8
  25. 25.√27 to 1 decimal place? (a) 5.4 (b) 5.2 (c) 5.1 (d) 5.3
  26. 26.Best estimate of 3275 ÷ 38? (a) 8200 (b) 820 (c) 82
  27. 27.Best estimate of 723 ÷ 34? (a) 24 (b) 2400 (c) 240
  28. 28.√55 to 1 decimal place? (a) 7.5 (b) 7.2 (c) 7.4 (d) 7.3
  29. 29.Best estimate of 4412 ÷ 77? (a) 55 (b) 550 (c) 5500
  30. 30.Best estimate of 2352 ÷ 29? (a) 7800 (b) 780 (c) 78
  31. 31.Best estimate of 4845 ÷ 66? (a) 690 (b) 69 (c) 6900
  32. 32.Best estimate of 6477 ÷ 79? (a) 8100 (b) 81 (c) 810
  33. 33.Best estimate of 4325 ÷ 89? (a) 480 (b) 4800 (c) 48
  34. 34.√43 to 1 decimal place? (a) 6.7 (b) 6.8 (c) 6.6 (d) 6.5
  35. 35.Best estimate of 4777 ÷ 76? (a) 6000 (b) 60 (c) 600
  36. 36.√46 to 1 decimal place? (a) 7.0 (b) 6.8 (c) 6.9 (d) 6.7
  37. 37.√28 to 1 decimal place? (a) 5.3 (b) 5.2 (c) 5.4 (d) 5.1
  38. 38.Best estimate of 2325 ÷ 72? (a) 3300 (b) 330 (c) 33
  39. 39.Best estimate of 599 ÷ 23? (a) 300 (b) 3000 (c) 30
  40. 40.Best estimate of 1172 ÷ 53? (a) 23 (b) 230 (c) 2300

Answer key

  1. 33
  2. 6.1
  3. 17
  4. 8.4
  5. 5.5
  6. 42
  7. 8.9
  8. 63
  9. 14
  10. 85
  11. 6.3
  12. 90
  13. 21
  14. 9.1
  15. 7.2
  16. 8.6
  17. 8.3
  18. 16
  19. 8.1
  20. 59
  21. 90
  22. 6.2
  23. 9.9
  24. 7.6
  25. 5.2
  26. 82
  27. 24
  28. 7.4
  29. 55
  30. 78
  31. 69
  32. 81
  33. 48
  34. 6.6
  35. 60
  36. 6.8
  37. 5.3
  38. 33
  39. 30
  40. 23

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