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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 855 · 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 1707 ÷ 23? (a) 85 (b) 8500 (c) 850
  2. 2.Best estimate of 1374 ÷ 72? (a) 20 (b) 200 (c) 2000
  3. 3.Best estimate of 1237 ÷ 72? (a) 18 (b) 1800 (c) 180
  4. 4.√30 to 1 decimal place? (a) 5.8 (b) 5.5 (c) 5.6 (d) 5.7
  5. 5.Best estimate of 5089 ÷ 56? (a) 8500 (b) 850 (c) 85
  6. 6.Best estimate of 681 ÷ 42? (a) 1700 (b) 170 (c) 17
  7. 7.√84 to 1 decimal place? (a) 9.2 (b) 9.3 (c) 9.5 (d) 9.4
  8. 8.√71 to 1 decimal place? (a) 8.3 (b) 8.2 (c) 8.5 (d) 8.4
  9. 9.Best estimate of 1104 ÷ 77? (a) 140 (b) 1400 (c) 14
  10. 10.Best estimate of 3997 ÷ 61? (a) 670 (b) 67 (c) 6700
  11. 11.√80 to 1 decimal place? (a) 9.0 (b) 9.1 (c) 8.9 (d) 8.8
  12. 12.√87 to 1 decimal place? (a) 9.2 (b) 9.5 (c) 9.3 (d) 9.4
  13. 13.Best estimate of 2553 ÷ 36? (a) 640 (b) 64 (c) 6400
  14. 14.√23 to 1 decimal place? (a) 4.9 (b) 4.7 (c) 4.8 (d) 4.6
  15. 15.√85 to 1 decimal place? (a) 9.3 (b) 9.0 (c) 9.1 (d) 9.2
  16. 16.√34 to 1 decimal place? (a) 6.1 (b) 5.9 (c) 6.0 (d) 5.8
  17. 17.√20 to 1 decimal place? (a) 4.4 (b) 4.7 (c) 4.5 (d) 4.6
  18. 18.√70 to 1 decimal place? (a) 8.5 (b) 8.4 (c) 8.3 (d) 8.6
  19. 19.√26 to 1 decimal place? (a) 5.0 (b) 5.3 (c) 5.1 (d) 5.2
  20. 20.√50 to 1 decimal place? (a) 7.2 (b) 7.1 (c) 7.3 (d) 7.4
  21. 21.√51 to 1 decimal place? (a) 7.2 (b) 7.4 (c) 7.1 (d) 7.3
  22. 22.Best estimate of 4155 ÷ 58? (a) 690 (b) 69 (c) 6900
  23. 23.Best estimate of 2352 ÷ 37? (a) 5900 (b) 590 (c) 59
  24. 24.Best estimate of 6486 ÷ 79? (a) 8100 (b) 81 (c) 810
  25. 25.Best estimate of 3149 ÷ 86? (a) 3500 (b) 35 (c) 350
  26. 26.Best estimate of 5038 ÷ 79? (a) 63 (b) 630 (c) 6300
  27. 27.√42 to 1 decimal place? (a) 6.8 (b) 6.6 (c) 6.7 (d) 6.5
  28. 28.Best estimate of 4015 ÷ 42? (a) 100 (b) 1000 (c) 10000
  29. 29.Best estimate of 1644 ÷ 39? (a) 41 (b) 410 (c) 4100
  30. 30.Best estimate of 1165 ÷ 86? (a) 13 (b) 1300 (c) 130
  31. 31.√37 to 1 decimal place? (a) 6.1 (b) 6.2 (c) 6.3 (d) 6.4
  32. 32.Best estimate of 922 ÷ 37? (a) 23 (b) 2300 (c) 230
  33. 33.√40 to 1 decimal place? (a) 6.2 (b) 6.4 (c) 6.1 (d) 6.3
  34. 34.Best estimate of 2673 ÷ 72? (a) 3800 (b) 38 (c) 380
  35. 35.Best estimate of 746 ÷ 46? (a) 1500 (b) 150 (c) 15
  36. 36.Best estimate of 1099 ÷ 36? (a) 27 (b) 270 (c) 2700
  37. 37.Best estimate of 4056 ÷ 46? (a) 810 (b) 8100 (c) 81
  38. 38.Best estimate of 1745 ÷ 51? (a) 3500 (b) 350 (c) 35
  39. 39.√82 to 1 decimal place? (a) 9.1 (b) 8.8 (c) 9.0 (d) 8.9
  40. 40.Best estimate of 6944 ÷ 73? (a) 99 (b) 9900 (c) 990

Answer key

  1. 85
  2. 20
  3. 18
  4. 5.5
  5. 85
  6. 17
  7. 9.2
  8. 8.4
  9. 14
  10. 67
  11. 8.9
  12. 9.3
  13. 64
  14. 4.8
  15. 9.2
  16. 5.8
  17. 4.5
  18. 8.4
  19. 5.1
  20. 7.1
  21. 7.1
  22. 69
  23. 59
  24. 81
  25. 35
  26. 63
  27. 6.5
  28. 100
  29. 41
  30. 13
  31. 6.1
  32. 23
  33. 6.3
  34. 38
  35. 15
  36. 27
  37. 81
  38. 35
  39. 9.1
  40. 99

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