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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 84 · 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 2689 ÷ 79? (a) 3400 (b) 34 (c) 340
  2. 2.√31 to 1 decimal place? (a) 5.9 (b) 5.7 (c) 5.6 (d) 5.8
  3. 3.Best estimate of 2102 ÷ 22? (a) 10500 (b) 1050 (c) 105
  4. 4.Best estimate of 2559 ÷ 72? (a) 370 (b) 37 (c) 3700
  5. 5.Best estimate of 3344 ÷ 53? (a) 67 (b) 670 (c) 6700
  6. 6.√89 to 1 decimal place? (a) 9.4 (b) 9.5 (c) 9.6 (d) 9.7
  7. 7.√34 to 1 decimal place? (a) 5.7 (b) 5.9 (c) 5.8 (d) 5.6
  8. 8.√65 to 1 decimal place? (a) 8.1 (b) 8.0 (c) 7.9 (d) 8.2
  9. 9.Best estimate of 1753 ÷ 89? (a) 1900 (b) 190 (c) 19
  10. 10.√37 to 1 decimal place? (a) 6.2 (b) 6.1 (c) 6.3 (d) 6.4
  11. 11.Best estimate of 5318 ÷ 64? (a) 89 (b) 8900 (c) 890
  12. 12.Best estimate of 1350 ÷ 54? (a) 2700 (b) 270 (c) 27
  13. 13.Best estimate of 1353 ÷ 38? (a) 3400 (b) 34 (c) 340
  14. 14.√24 to 1 decimal place? (a) 4.9 (b) 5.1 (c) 5.2 (d) 5.0
  15. 15.√23 to 1 decimal place? (a) 4.8 (b) 5.1 (c) 4.9 (d) 5.0
  16. 16.√53 to 1 decimal place? (a) 7.3 (b) 7.2 (c) 7.4 (d) 7.1
  17. 17.Best estimate of 3941 ÷ 42? (a) 990 (b) 9900 (c) 99
  18. 18.Best estimate of 1941 ÷ 42? (a) 49 (b) 4900 (c) 490
  19. 19.√27 to 1 decimal place? (a) 5.1 (b) 5.3 (c) 5.4 (d) 5.2
  20. 20.Best estimate of 1438 ÷ 24? (a) 72 (b) 720 (c) 7200
  21. 21.√98 to 1 decimal place? (a) 10.1 (b) 10.0 (c) 9.9 (d) 10.2
  22. 22.Best estimate of 4623 ÷ 76? (a) 5800 (b) 58 (c) 580
  23. 23.Best estimate of 1264 ÷ 82? (a) 16 (b) 160 (c) 1600
  24. 24.√32 to 1 decimal place? (a) 5.5 (b) 5.7 (c) 5.8 (d) 5.6
  25. 25.Best estimate of 5107 ÷ 58? (a) 85 (b) 850 (c) 8500
  26. 26.√82 to 1 decimal place? (a) 9.3 (b) 9.4 (c) 9.2 (d) 9.1
  27. 27.√42 to 1 decimal place? (a) 6.5 (b) 6.3 (c) 6.4 (d) 6.2
  28. 28.√61 to 1 decimal place? (a) 7.8 (b) 7.9 (c) 7.7 (d) 7.6
  29. 29.Best estimate of 4856 ÷ 84? (a) 6100 (b) 61 (c) 610
  30. 30.√84 to 1 decimal place? (a) 8.9 (b) 9.0 (c) 9.1 (d) 9.2
  31. 31.√26 to 1 decimal place? (a) 5.3 (b) 5.2 (c) 5.4 (d) 5.1
  32. 32.√92 to 1 decimal place? (a) 9.7 (b) 9.8 (c) 9.6 (d) 9.5
  33. 33.Best estimate of 1706 ÷ 28? (a) 570 (b) 5700 (c) 57
  34. 34.Best estimate of 1409 ÷ 27? (a) 470 (b) 4700 (c) 47
  35. 35.Best estimate of 6577 ÷ 73? (a) 9400 (b) 940 (c) 94
  36. 36.Best estimate of 4529 ÷ 58? (a) 7500 (b) 750 (c) 75
  37. 37.Best estimate of 1378 ÷ 44? (a) 34 (b) 3400 (c) 340
  38. 38.Best estimate of 2449 ÷ 56? (a) 41 (b) 410 (c) 4100
  39. 39.√56 to 1 decimal place? (a) 7.5 (b) 7.6 (c) 7.4 (d) 7.7
  40. 40.√41 to 1 decimal place? (a) 6.7 (b) 6.4 (c) 6.6 (d) 6.5

Answer key

  1. 34
  2. 5.6
  3. 105
  4. 37
  5. 67
  6. 9.4
  7. 5.8
  8. 8.1
  9. 19
  10. 6.1
  11. 89
  12. 27
  13. 34
  14. 4.9
  15. 4.8
  16. 7.3
  17. 99
  18. 49
  19. 5.2
  20. 72
  21. 9.9
  22. 58
  23. 16
  24. 5.7
  25. 85
  26. 9.1
  27. 6.5
  28. 7.8
  29. 61
  30. 9.2
  31. 5.1
  32. 9.6
  33. 57
  34. 47
  35. 94
  36. 75
  37. 34
  38. 41
  39. 7.5
  40. 6.4

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