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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 406 · 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 1876 ÷ 32? (a) 6300 (b) 63 (c) 630
  2. 2.Best estimate of 3319 ÷ 78? (a) 4100 (b) 41 (c) 410
  3. 3.Best estimate of 1928 ÷ 62? (a) 3200 (b) 32 (c) 320
  4. 4.√29 to 1 decimal place? (a) 5.5 (b) 5.7 (c) 5.4 (d) 5.6
  5. 5.Best estimate of 1783 ÷ 51? (a) 3600 (b) 360 (c) 36
  6. 6.√46 to 1 decimal place? (a) 7.0 (b) 7.1 (c) 6.8 (d) 6.9
  7. 7.Best estimate of 1531 ÷ 49? (a) 31 (b) 3100 (c) 310
  8. 8.Best estimate of 1570 ÷ 28? (a) 5200 (b) 520 (c) 52
  9. 9.√34 to 1 decimal place? (a) 5.9 (b) 5.7 (c) 5.8 (d) 6.0
  10. 10.Best estimate of 2804 ÷ 32? (a) 930 (b) 9300 (c) 93
  11. 11.Best estimate of 7577 ÷ 79? (a) 950 (b) 9500 (c) 95
  12. 12.Best estimate of 2162 ÷ 23? (a) 1080 (b) 108 (c) 10800
  13. 13.Best estimate of 7112 ÷ 78? (a) 8900 (b) 890 (c) 89
  14. 14.√69 to 1 decimal place? (a) 8.5 (b) 8.3 (c) 8.4 (d) 8.2
  15. 15.Best estimate of 2994 ÷ 61? (a) 500 (b) 5000 (c) 50
  16. 16.Best estimate of 1220 ÷ 69? (a) 1700 (b) 17 (c) 170
  17. 17.√44 to 1 decimal place? (a) 6.6 (b) 6.5 (c) 6.3 (d) 6.4
  18. 18.Best estimate of 2948 ÷ 43? (a) 7400 (b) 740 (c) 74
  19. 19.√90 to 1 decimal place? (a) 9.4 (b) 9.5 (c) 9.6 (d) 9.3
  20. 20.Best estimate of 2415 ÷ 62? (a) 400 (b) 4000 (c) 40
  21. 21.√70 to 1 decimal place? (a) 8.7 (b) 8.6 (c) 8.4 (d) 8.5
  22. 22.√21 to 1 decimal place? (a) 4.5 (b) 4.7 (c) 4.6 (d) 4.4
  23. 23.√51 to 1 decimal place? (a) 7.2 (b) 7.0 (c) 7.1 (d) 7.3
  24. 24.Best estimate of 2395 ÷ 29? (a) 800 (b) 8000 (c) 80
  25. 25.Best estimate of 443 ÷ 26? (a) 150 (b) 1500 (c) 15
  26. 26.Best estimate of 1118 ÷ 63? (a) 190 (b) 1900 (c) 19
  27. 27.√35 to 1 decimal place? (a) 5.9 (b) 6.0 (c) 6.1 (d) 5.8
  28. 28.Best estimate of 3593 ÷ 47? (a) 72 (b) 7200 (c) 720
  29. 29.Best estimate of 7499 ÷ 87? (a) 830 (b) 83 (c) 8300
  30. 30.√74 to 1 decimal place? (a) 8.6 (b) 8.5 (c) 8.3 (d) 8.4
  31. 31.Best estimate of 1582 ÷ 68? (a) 230 (b) 2300 (c) 23
  32. 32.Best estimate of 2351 ÷ 74? (a) 34 (b) 3400 (c) 340
  33. 33.Best estimate of 4452 ÷ 76? (a) 5600 (b) 56 (c) 560
  34. 34.√72 to 1 decimal place? (a) 8.3 (b) 8.4 (c) 8.2 (d) 8.5
  35. 35.√48 to 1 decimal place? (a) 6.9 (b) 6.7 (c) 6.8 (d) 7.0
  36. 36.√31 to 1 decimal place? (a) 5.8 (b) 5.5 (c) 5.6 (d) 5.7
  37. 37.Best estimate of 2613 ÷ 54? (a) 520 (b) 52 (c) 5200
  38. 38.Best estimate of 2449 ÷ 73? (a) 35 (b) 3500 (c) 350
  39. 39.Best estimate of 3232 ÷ 46? (a) 6500 (b) 650 (c) 65
  40. 40.√82 to 1 decimal place? (a) 8.9 (b) 9.0 (c) 9.1 (d) 8.8

Answer key

  1. 63
  2. 41
  3. 32
  4. 5.4
  5. 36
  6. 6.8
  7. 31
  8. 52
  9. 5.8
  10. 93
  11. 95
  12. 108
  13. 89
  14. 8.3
  15. 50
  16. 17
  17. 6.6
  18. 74
  19. 9.5
  20. 40
  21. 8.4
  22. 4.6
  23. 7.1
  24. 80
  25. 15
  26. 19
  27. 5.9
  28. 72
  29. 83
  30. 8.6
  31. 23
  32. 34
  33. 56
  34. 8.5
  35. 6.9
  36. 5.6
  37. 52
  38. 35
  39. 65
  40. 9.1

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