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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 771 · 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.√47 to 1 decimal place? (a) 7.1 (b) 6.9 (c) 7.2 (d) 7.0
  2. 2.√84 to 1 decimal place? (a) 9.3 (b) 9.4 (c) 9.5 (d) 9.2
  3. 3.√55 to 1 decimal place? (a) 7.4 (b) 7.3 (c) 7.1 (d) 7.2
  4. 4.Best estimate of 4561 ÷ 61? (a) 760 (b) 7600 (c) 76
  5. 5.Best estimate of 1984 ÷ 77? (a) 250 (b) 2500 (c) 25
  6. 6.√58 to 1 decimal place? (a) 7.4 (b) 7.6 (c) 7.5 (d) 7.7
  7. 7.Best estimate of 2307 ÷ 68? (a) 3300 (b) 33 (c) 330
  8. 8.√22 to 1 decimal place? (a) 4.6 (b) 4.4 (c) 4.7 (d) 4.5
  9. 9.Best estimate of 2697 ÷ 84? (a) 3400 (b) 340 (c) 34
  10. 10.√61 to 1 decimal place? (a) 7.6 (b) 7.5 (c) 7.7 (d) 7.8
  11. 11.√63 to 1 decimal place? (a) 8.2 (b) 7.9 (c) 8.1 (d) 8.0
  12. 12.Best estimate of 1645 ÷ 38? (a) 410 (b) 41 (c) 4100
  13. 13.√26 to 1 decimal place? (a) 5.1 (b) 5.2 (c) 5.4 (d) 5.3
  14. 14.√52 to 1 decimal place? (a) 7.5 (b) 7.2 (c) 7.3 (d) 7.4
  15. 15.Best estimate of 441 ÷ 36? (a) 110 (b) 1100 (c) 11
  16. 16.√76 to 1 decimal place? (a) 8.6 (b) 8.7 (c) 8.8 (d) 8.5
  17. 17.√51 to 1 decimal place? (a) 7.1 (b) 7.2 (c) 7.4 (d) 7.3
  18. 18.Best estimate of 4503 ÷ 57? (a) 750 (b) 75 (c) 7500
  19. 19.√34 to 1 decimal place? (a) 5.8 (b) 5.9 (c) 5.7 (d) 6.0
  20. 20.Best estimate of 3455 ÷ 46? (a) 690 (b) 6900 (c) 69
  21. 21.Best estimate of 2521 ÷ 42? (a) 63 (b) 6300 (c) 630
  22. 22.√78 to 1 decimal place? (a) 8.7 (b) 8.8 (c) 8.6 (d) 8.9
  23. 23.Best estimate of 1524 ÷ 81? (a) 1900 (b) 190 (c) 19
  24. 24.√31 to 1 decimal place? (a) 5.6 (b) 5.4 (c) 5.5 (d) 5.3
  25. 25.√72 to 1 decimal place? (a) 8.6 (b) 8.5 (c) 8.7 (d) 8.8
  26. 26.Best estimate of 3389 ÷ 86? (a) 3800 (b) 38 (c) 380
  27. 27.Best estimate of 3259 ÷ 76? (a) 4100 (b) 41 (c) 410
  28. 28.Best estimate of 5939 ÷ 86? (a) 660 (b) 66 (c) 6600
  29. 29.Best estimate of 2831 ÷ 81? (a) 350 (b) 3500 (c) 35
  30. 30.Best estimate of 3337 ÷ 86? (a) 3700 (b) 37 (c) 370
  31. 31.Best estimate of 908 ÷ 58? (a) 1500 (b) 150 (c) 15
  32. 32.√44 to 1 decimal place? (a) 6.6 (b) 6.7 (c) 6.9 (d) 6.8
  33. 33.√92 to 1 decimal place? (a) 9.6 (b) 9.5 (c) 9.7 (d) 9.8
  34. 34.Best estimate of 1370 ÷ 56? (a) 230 (b) 23 (c) 2300
  35. 35.Best estimate of 2010 ÷ 82? (a) 2500 (b) 250 (c) 25
  36. 36.Best estimate of 4865 ÷ 67? (a) 7000 (b) 70 (c) 700
  37. 37.Best estimate of 3459 ÷ 37? (a) 860 (b) 86 (c) 8600
  38. 38.Best estimate of 6955 ÷ 79? (a) 870 (b) 8700 (c) 87
  39. 39.√89 to 1 decimal place? (a) 9.4 (b) 9.1 (c) 9.3 (d) 9.2
  40. 40.Best estimate of 1651 ÷ 82? (a) 2100 (b) 210 (c) 21

Answer key

  1. 6.9
  2. 9.2
  3. 7.4
  4. 76
  5. 25
  6. 7.6
  7. 33
  8. 4.7
  9. 34
  10. 7.8
  11. 7.9
  12. 41
  13. 5.1
  14. 7.2
  15. 11
  16. 8.7
  17. 7.1
  18. 75
  19. 5.8
  20. 69
  21. 63
  22. 8.8
  23. 19
  24. 5.6
  25. 8.5
  26. 38
  27. 41
  28. 66
  29. 35
  30. 37
  31. 15
  32. 6.6
  33. 9.6
  34. 23
  35. 25
  36. 70
  37. 86
  38. 87
  39. 9.4
  40. 21

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