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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 169 · 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 909 ÷ 29? (a) 30 (b) 3000 (c) 300
  2. 2.Best estimate of 2646 ÷ 34? (a) 8800 (b) 880 (c) 88
  3. 3.√45 to 1 decimal place? (a) 6.8 (b) 6.6 (c) 6.7 (d) 6.5
  4. 4.Best estimate of 1498 ÷ 46? (a) 300 (b) 30 (c) 3000
  5. 5.Best estimate of 5610 ÷ 89? (a) 6200 (b) 620 (c) 62
  6. 6.Best estimate of 2779 ÷ 62? (a) 4600 (b) 46 (c) 460
  7. 7.√84 to 1 decimal place? (a) 9.4 (b) 9.3 (c) 9.5 (d) 9.2
  8. 8.Best estimate of 2804 ÷ 31? (a) 930 (b) 93 (c) 9300
  9. 9.Best estimate of 1698 ÷ 48? (a) 3400 (b) 340 (c) 34
  10. 10.Best estimate of 5972 ÷ 68? (a) 85 (b) 8500 (c) 850
  11. 11.√42 to 1 decimal place? (a) 6.7 (b) 6.6 (c) 6.5 (d) 6.8
  12. 12.√58 to 1 decimal place? (a) 7.6 (b) 7.5 (c) 7.7 (d) 7.4
  13. 13.√37 to 1 decimal place? (a) 6.2 (b) 6.1 (c) 6.3 (d) 6.4
  14. 14.Best estimate of 5718 ÷ 76? (a) 710 (b) 71 (c) 7100
  15. 15.Best estimate of 6325 ÷ 68? (a) 90 (b) 9000 (c) 900
  16. 16.Best estimate of 403 ÷ 29? (a) 13 (b) 1300 (c) 130
  17. 17.√30 to 1 decimal place? (a) 5.8 (b) 5.7 (c) 5.5 (d) 5.6
  18. 18.√41 to 1 decimal place? (a) 6.5 (b) 6.6 (c) 6.7 (d) 6.4
  19. 19.Best estimate of 1284 ÷ 24? (a) 6400 (b) 640 (c) 64
  20. 20.√44 to 1 decimal place? (a) 6.9 (b) 6.8 (c) 6.7 (d) 6.6
  21. 21.Best estimate of 1383 ÷ 73? (a) 20 (b) 200 (c) 2000
  22. 22.Best estimate of 1582 ÷ 87? (a) 180 (b) 1800 (c) 18
  23. 23.Best estimate of 5349 ÷ 82? (a) 67 (b) 670 (c) 6700
  24. 24.√35 to 1 decimal place? (a) 6.1 (b) 6.0 (c) 5.8 (d) 5.9
  25. 25.Best estimate of 6763 ÷ 74? (a) 9700 (b) 97 (c) 970
  26. 26.√22 to 1 decimal place? (a) 4.5 (b) 4.8 (c) 4.6 (d) 4.7
  27. 27.√70 to 1 decimal place? (a) 8.6 (b) 8.5 (c) 8.7 (d) 8.4
  28. 28.Best estimate of 873 ÷ 38? (a) 2200 (b) 220 (c) 22
  29. 29.√98 to 1 decimal place? (a) 10.0 (b) 9.9 (c) 10.1 (d) 9.8
  30. 30.Best estimate of 3925 ÷ 53? (a) 79 (b) 790 (c) 7900
  31. 31.√75 to 1 decimal place? (a) 8.8 (b) 8.6 (c) 8.7 (d) 8.5
  32. 32.√71 to 1 decimal place? (a) 8.5 (b) 8.3 (c) 8.4 (d) 8.2
  33. 33.Best estimate of 4599 ÷ 73? (a) 660 (b) 6600 (c) 66
  34. 34.Best estimate of 5146 ÷ 57? (a) 8600 (b) 860 (c) 86
  35. 35.Best estimate of 5836 ÷ 71? (a) 8300 (b) 83 (c) 830
  36. 36.√92 to 1 decimal place? (a) 9.8 (b) 9.7 (c) 9.6 (d) 9.9
  37. 37.√21 to 1 decimal place? (a) 4.9 (b) 4.8 (c) 4.7 (d) 4.6
  38. 38.√74 to 1 decimal place? (a) 8.4 (b) 8.6 (c) 8.5 (d) 8.7
  39. 39.√43 to 1 decimal place? (a) 6.4 (b) 6.6 (c) 6.7 (d) 6.5
  40. 40.Best estimate of 1309 ÷ 36? (a) 3300 (b) 330 (c) 33

Answer key

  1. 30
  2. 88
  3. 6.7
  4. 30
  5. 62
  6. 46
  7. 9.2
  8. 93
  9. 34
  10. 85
  11. 6.5
  12. 7.6
  13. 6.1
  14. 71
  15. 90
  16. 13
  17. 5.5
  18. 6.4
  19. 64
  20. 6.6
  21. 20
  22. 18
  23. 67
  24. 5.9
  25. 97
  26. 4.7
  27. 8.4
  28. 22
  29. 9.9
  30. 79
  31. 8.7
  32. 8.4
  33. 66
  34. 86
  35. 83
  36. 9.6
  37. 4.6
  38. 8.6
  39. 6.6
  40. 33

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