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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 108 · 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 3959 ÷ 42? (a) 99 (b) 9900 (c) 990
  2. 2.√59 to 1 decimal place? (a) 7.8 (b) 7.9 (c) 7.6 (d) 7.7
  3. 3.Best estimate of 2100 ÷ 34? (a) 700 (b) 7000 (c) 70
  4. 4.Best estimate of 3384 ÷ 46? (a) 6800 (b) 680 (c) 68
  5. 5.Best estimate of 1272 ÷ 34? (a) 42 (b) 420 (c) 4200
  6. 6.√37 to 1 decimal place? (a) 5.9 (b) 6.0 (c) 6.1 (d) 6.2
  7. 7.Best estimate of 8054 ÷ 89? (a) 890 (b) 8900 (c) 89
  8. 8.Best estimate of 3683 ÷ 56? (a) 610 (b) 61 (c) 6100
  9. 9.√27 to 1 decimal place? (a) 5.3 (b) 5.4 (c) 5.2 (d) 5.1
  10. 10.√82 to 1 decimal place? (a) 9.2 (b) 9.0 (c) 9.1 (d) 9.3
  11. 11.√21 to 1 decimal place? (a) 4.4 (b) 4.3 (c) 4.5 (d) 4.6
  12. 12.Best estimate of 924 ÷ 36? (a) 230 (b) 2300 (c) 23
  13. 13.Best estimate of 485 ÷ 33? (a) 1600 (b) 16 (c) 160
  14. 14.√43 to 1 decimal place? (a) 6.8 (b) 6.9 (c) 6.7 (d) 6.6
  15. 15.√28 to 1 decimal place? (a) 5.6 (b) 5.3 (c) 5.4 (d) 5.5
  16. 16.√50 to 1 decimal place? (a) 6.9 (b) 7.1 (c) 7.2 (d) 7.0
  17. 17.√22 to 1 decimal place? (a) 4.5 (b) 4.7 (c) 4.6 (d) 4.8
  18. 18.√66 to 1 decimal place? (a) 8.3 (b) 8.1 (c) 8.2 (d) 8.4
  19. 19.Best estimate of 2355 ÷ 83? (a) 290 (b) 29 (c) 2900
  20. 20.Best estimate of 1285 ÷ 62? (a) 2100 (b) 21 (c) 210
  21. 21.√32 to 1 decimal place? (a) 5.6 (b) 5.4 (c) 5.7 (d) 5.5
  22. 22.Best estimate of 2284 ÷ 78? (a) 2900 (b) 290 (c) 29
  23. 23.Best estimate of 6109 ÷ 72? (a) 8700 (b) 87 (c) 870
  24. 24.Best estimate of 989 ÷ 29? (a) 330 (b) 3300 (c) 33
  25. 25.√87 to 1 decimal place? (a) 9.6 (b) 9.5 (c) 9.3 (d) 9.4
  26. 26.Best estimate of 2565 ÷ 86? (a) 2900 (b) 29 (c) 290
  27. 27.Best estimate of 1688 ÷ 34? (a) 560 (b) 56 (c) 5600
  28. 28.Best estimate of 3852 ÷ 51? (a) 77 (b) 770 (c) 7700
  29. 29.Best estimate of 320 ÷ 24? (a) 160 (b) 16 (c) 1600
  30. 30.Best estimate of 5244 ÷ 76? (a) 66 (b) 6600 (c) 660
  31. 31.√46 to 1 decimal place? (a) 6.8 (b) 6.5 (c) 6.7 (d) 6.6
  32. 32.√40 to 1 decimal place? (a) 6.3 (b) 6.2 (c) 6.1 (d) 6.4
  33. 33.√20 to 1 decimal place? (a) 4.6 (b) 4.4 (c) 4.7 (d) 4.5
  34. 34.Best estimate of 5348 ÷ 56? (a) 8900 (b) 890 (c) 89
  35. 35.√61 to 1 decimal place? (a) 7.5 (b) 7.7 (c) 7.6 (d) 7.8
  36. 36.Best estimate of 1106 ÷ 53? (a) 2200 (b) 220 (c) 22
  37. 37.Best estimate of 4551 ÷ 59? (a) 76 (b) 7600 (c) 760
  38. 38.√98 to 1 decimal place? (a) 9.9 (b) 10.0 (c) 10.1 (d) 9.8
  39. 39.√24 to 1 decimal place? (a) 5.2 (b) 4.9 (c) 5.1 (d) 5.0
  40. 40.Best estimate of 7547 ÷ 83? (a) 94 (b) 9400 (c) 940

Answer key

  1. 99
  2. 7.7
  3. 70
  4. 68
  5. 42
  6. 6.1
  7. 89
  8. 61
  9. 5.2
  10. 9.1
  11. 4.6
  12. 23
  13. 16
  14. 6.6
  15. 5.3
  16. 7.1
  17. 4.7
  18. 8.1
  19. 29
  20. 21
  21. 5.7
  22. 29
  23. 87
  24. 33
  25. 9.3
  26. 29
  27. 56
  28. 77
  29. 16
  30. 66
  31. 6.8
  32. 6.3
  33. 4.5
  34. 89
  35. 7.8
  36. 22
  37. 76
  38. 9.9
  39. 4.9
  40. 94

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