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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 214 · 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 1839 ÷ 27? (a) 61 (b) 6100 (c) 610
  2. 2.Best estimate of 626 ÷ 29? (a) 210 (b) 2100 (c) 21
  3. 3.√24 to 1 decimal place? (a) 4.9 (b) 5.1 (c) 4.8 (d) 5.0
  4. 4.Best estimate of 3789 ÷ 57? (a) 63 (b) 6300 (c) 630
  5. 5.Best estimate of 2927 ÷ 72? (a) 420 (b) 4200 (c) 42
  6. 6.√82 to 1 decimal place? (a) 9.1 (b) 8.9 (c) 9.0 (d) 9.2
  7. 7.Best estimate of 5370 ÷ 66? (a) 77 (b) 770 (c) 7700
  8. 8.√29 to 1 decimal place? (a) 5.2 (b) 5.4 (c) 5.1 (d) 5.3
  9. 9.Best estimate of 5054 ÷ 56? (a) 840 (b) 84 (c) 8400
  10. 10.√65 to 1 decimal place? (a) 8.1 (b) 7.9 (c) 8.2 (d) 8.0
  11. 11.Best estimate of 5880 ÷ 74? (a) 8400 (b) 840 (c) 84
  12. 12.√88 to 1 decimal place? (a) 9.2 (b) 9.4 (c) 9.3 (d) 9.1
  13. 13.Best estimate of 2093 ÷ 64? (a) 350 (b) 35 (c) 3500
  14. 14.√22 to 1 decimal place? (a) 4.9 (b) 5.0 (c) 4.7 (d) 4.8
  15. 15.Best estimate of 6846 ÷ 73? (a) 98 (b) 980 (c) 9800
  16. 16.Best estimate of 5196 ÷ 63? (a) 8700 (b) 870 (c) 87
  17. 17.√32 to 1 decimal place? (a) 5.6 (b) 5.9 (c) 5.7 (d) 5.8
  18. 18.√58 to 1 decimal place? (a) 7.8 (b) 7.5 (c) 7.6 (d) 7.7
  19. 19.Best estimate of 1837 ÷ 24? (a) 92 (b) 9200 (c) 920
  20. 20.Best estimate of 5857 ÷ 74? (a) 840 (b) 8400 (c) 84
  21. 21.√45 to 1 decimal place? (a) 6.4 (b) 6.7 (c) 6.6 (d) 6.5
  22. 22.√92 to 1 decimal place? (a) 9.8 (b) 9.7 (c) 9.5 (d) 9.6
  23. 23.Best estimate of 3239 ÷ 71? (a) 4600 (b) 46 (c) 460
  24. 24.Best estimate of 3694 ÷ 49? (a) 7400 (b) 740 (c) 74
  25. 25.√46 to 1 decimal place? (a) 6.8 (b) 6.9 (c) 7.1 (d) 7.0
  26. 26.Best estimate of 2523 ÷ 37? (a) 630 (b) 6300 (c) 63
  27. 27.Best estimate of 1710 ÷ 46? (a) 340 (b) 34 (c) 3400
  28. 28.Best estimate of 7715 ÷ 84? (a) 9600 (b) 960 (c) 96
  29. 29.√30 to 1 decimal place? (a) 5.3 (b) 5.5 (c) 5.4 (d) 5.6
  30. 30.√51 to 1 decimal place? (a) 7.1 (b) 7.2 (c) 7.3 (d) 7.0
  31. 31.√40 to 1 decimal place? (a) 6.3 (b) 6.4 (c) 6.5 (d) 6.2
  32. 32.Best estimate of 6033 ÷ 84? (a) 75 (b) 750 (c) 7500
  33. 33.√34 to 1 decimal place? (a) 5.7 (b) 5.8 (c) 5.9 (d) 5.6
  34. 34.Best estimate of 1366 ÷ 69? (a) 2000 (b) 200 (c) 20
  35. 35.Best estimate of 3714 ÷ 46? (a) 740 (b) 7400 (c) 74
  36. 36.Best estimate of 4253 ÷ 53? (a) 85 (b) 850 (c) 8500
  37. 37.Best estimate of 683 ÷ 21? (a) 34 (b) 340 (c) 3400
  38. 38.Best estimate of 2613 ÷ 88? (a) 2900 (b) 290 (c) 29
  39. 39.√27 to 1 decimal place? (a) 4.9 (b) 5.0 (c) 5.2 (d) 5.1
  40. 40.√86 to 1 decimal place? (a) 9.5 (b) 9.3 (c) 9.4 (d) 9.6

Answer key

  1. 61
  2. 21
  3. 4.9
  4. 63
  5. 42
  6. 9.1
  7. 77
  8. 5.4
  9. 84
  10. 8.1
  11. 84
  12. 9.4
  13. 35
  14. 4.7
  15. 98
  16. 87
  17. 5.7
  18. 7.6
  19. 92
  20. 84
  21. 6.7
  22. 9.6
  23. 46
  24. 74
  25. 6.8
  26. 63
  27. 34
  28. 96
  29. 5.5
  30. 7.1
  31. 6.3
  32. 75
  33. 5.8
  34. 20
  35. 74
  36. 85
  37. 34
  38. 29
  39. 5.2
  40. 9.3

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