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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 312 · 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 1256 ÷ 38? (a) 3100 (b) 31 (c) 310
  2. 2.Best estimate of 2915 ÷ 64? (a) 490 (b) 49 (c) 4900
  3. 3.Best estimate of 6031 ÷ 89? (a) 67 (b) 670 (c) 6700
  4. 4.Best estimate of 3009 ÷ 58? (a) 50 (b) 500 (c) 5000
  5. 5.Best estimate of 2120 ÷ 83? (a) 2700 (b) 270 (c) 27
  6. 6.√23 to 1 decimal place? (a) 4.9 (b) 5.0 (c) 5.1 (d) 4.8
  7. 7.Best estimate of 5116 ÷ 67? (a) 730 (b) 7300 (c) 73
  8. 8.√45 to 1 decimal place? (a) 7.0 (b) 6.9 (c) 6.7 (d) 6.8
  9. 9.√66 to 1 decimal place? (a) 7.8 (b) 8.0 (c) 7.9 (d) 8.1
  10. 10.Best estimate of 3319 ÷ 53? (a) 660 (b) 6600 (c) 66
  11. 11.Best estimate of 5693 ÷ 64? (a) 95 (b) 950 (c) 9500
  12. 12.√83 to 1 decimal place? (a) 8.9 (b) 8.8 (c) 9.0 (d) 9.1
  13. 13.Best estimate of 4214 ÷ 46? (a) 8400 (b) 840 (c) 84
  14. 14.√94 to 1 decimal place? (a) 9.9 (b) 9.8 (c) 9.7 (d) 10.0
  15. 15.Best estimate of 2905 ÷ 31? (a) 9700 (b) 970 (c) 97
  16. 16.Best estimate of 3988 ÷ 71? (a) 5700 (b) 570 (c) 57
  17. 17.√42 to 1 decimal place? (a) 6.7 (b) 6.6 (c) 6.5 (d) 6.8
  18. 18.Best estimate of 568 ÷ 42? (a) 14 (b) 140 (c) 1400
  19. 19.√72 to 1 decimal place? (a) 8.8 (b) 8.7 (c) 8.5 (d) 8.6
  20. 20.√24 to 1 decimal place? (a) 4.9 (b) 4.8 (c) 4.6 (d) 4.7
  21. 21.√22 to 1 decimal place? (a) 4.5 (b) 4.7 (c) 4.6 (d) 4.4
  22. 22.√74 to 1 decimal place? (a) 8.9 (b) 8.8 (c) 8.6 (d) 8.7
  23. 23.Best estimate of 877 ÷ 56? (a) 15 (b) 1500 (c) 150
  24. 24.√96 to 1 decimal place? (a) 9.8 (b) 9.5 (c) 9.7 (d) 9.6
  25. 25.√41 to 1 decimal place? (a) 6.5 (b) 6.6 (c) 6.7 (d) 6.4
  26. 26.√75 to 1 decimal place? (a) 8.5 (b) 8.6 (c) 8.8 (d) 8.7
  27. 27.Best estimate of 3022 ÷ 61? (a) 500 (b) 5000 (c) 50
  28. 28.Best estimate of 2218 ÷ 62? (a) 37 (b) 370 (c) 3700
  29. 29.√62 to 1 decimal place? (a) 8.0 (b) 7.9 (c) 8.1 (d) 7.8
  30. 30.Best estimate of 2844 ÷ 87? (a) 320 (b) 3200 (c) 32
  31. 31.Best estimate of 1364 ÷ 26? (a) 45 (b) 450 (c) 4500
  32. 32.Best estimate of 4763 ÷ 61? (a) 7900 (b) 79 (c) 790
  33. 33.Best estimate of 3026 ÷ 54? (a) 61 (b) 6100 (c) 610
  34. 34.Best estimate of 1846 ÷ 34? (a) 62 (b) 6200 (c) 620
  35. 35.Best estimate of 853 ÷ 52? (a) 17 (b) 1700 (c) 170
  36. 36.Best estimate of 798 ÷ 56? (a) 1300 (b) 130 (c) 13
  37. 37.Best estimate of 1138 ÷ 27? (a) 380 (b) 38 (c) 3800
  38. 38.Best estimate of 6083 ÷ 73? (a) 8700 (b) 870 (c) 87
  39. 39.Best estimate of 2785 ÷ 62? (a) 460 (b) 4600 (c) 46
  40. 40.√77 to 1 decimal place? (a) 8.6 (b) 8.7 (c) 8.8 (d) 8.5

Answer key

  1. 31
  2. 49
  3. 67
  4. 50
  5. 27
  6. 4.8
  7. 73
  8. 6.7
  9. 8.1
  10. 66
  11. 95
  12. 9.1
  13. 84
  14. 9.7
  15. 97
  16. 57
  17. 6.5
  18. 14
  19. 8.5
  20. 4.9
  21. 4.7
  22. 8.6
  23. 15
  24. 9.8
  25. 6.4
  26. 8.7
  27. 50
  28. 37
  29. 7.9
  30. 32
  31. 45
  32. 79
  33. 61
  34. 62
  35. 17
  36. 13
  37. 38
  38. 87
  39. 46
  40. 8.8

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