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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 641 · 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.√75 to 1 decimal place? (a) 8.6 (b) 8.8 (c) 8.5 (d) 8.7
  2. 2.Best estimate of 1688 ÷ 56? (a) 2800 (b) 280 (c) 28
  3. 3.√65 to 1 decimal place? (a) 8.1 (b) 8.2 (c) 8.0 (d) 8.3
  4. 4.Best estimate of 1375 ÷ 44? (a) 3400 (b) 34 (c) 340
  5. 5.√88 to 1 decimal place? (a) 9.3 (b) 9.5 (c) 9.4 (d) 9.2
  6. 6.√78 to 1 decimal place? (a) 8.6 (b) 8.8 (c) 8.9 (d) 8.7
  7. 7.Best estimate of 1348 ÷ 22? (a) 6700 (b) 67 (c) 670
  8. 8.√63 to 1 decimal place? (a) 7.9 (b) 7.8 (c) 8.0 (d) 8.1
  9. 9.√35 to 1 decimal place? (a) 6.1 (b) 6.0 (c) 5.9 (d) 6.2
  10. 10.Best estimate of 305 ÷ 23? (a) 15 (b) 150 (c) 1500
  11. 11.Best estimate of 2888 ÷ 42? (a) 720 (b) 7200 (c) 72
  12. 12.Best estimate of 7163 ÷ 83? (a) 9000 (b) 90 (c) 900
  13. 13.√77 to 1 decimal place? (a) 8.8 (b) 8.7 (c) 8.6 (d) 8.5
  14. 14.√45 to 1 decimal place? (a) 6.5 (b) 6.6 (c) 6.4 (d) 6.7
  15. 15.√66 to 1 decimal place? (a) 8.4 (b) 8.1 (c) 8.2 (d) 8.3
  16. 16.Best estimate of 3941 ÷ 44? (a) 990 (b) 99 (c) 9900
  17. 17.√94 to 1 decimal place? (a) 9.6 (b) 9.8 (c) 9.5 (d) 9.7
  18. 18.√24 to 1 decimal place? (a) 5.1 (b) 5.0 (c) 5.2 (d) 4.9
  19. 19.Best estimate of 814 ÷ 29? (a) 2700 (b) 270 (c) 27
  20. 20.Best estimate of 5898 ÷ 72? (a) 84 (b) 840 (c) 8400
  21. 21.√42 to 1 decimal place? (a) 6.3 (b) 6.5 (c) 6.4 (d) 6.6
  22. 22.√44 to 1 decimal place? (a) 6.6 (b) 6.5 (c) 6.7 (d) 6.4
  23. 23.√58 to 1 decimal place? (a) 7.7 (b) 7.6 (c) 7.4 (d) 7.5
  24. 24.Best estimate of 5964 ÷ 71? (a) 85 (b) 850 (c) 8500
  25. 25.√62 to 1 decimal place? (a) 7.7 (b) 7.9 (c) 7.8 (d) 7.6
  26. 26.Best estimate of 3387 ÷ 62? (a) 56 (b) 560 (c) 5600
  27. 27.√72 to 1 decimal place? (a) 8.4 (b) 8.7 (c) 8.5 (d) 8.6
  28. 28.Best estimate of 5625 ÷ 77? (a) 700 (b) 7000 (c) 70
  29. 29.√55 to 1 decimal place? (a) 7.4 (b) 7.3 (c) 7.2 (d) 7.1
  30. 30.Best estimate of 1609 ÷ 26? (a) 540 (b) 5400 (c) 54
  31. 31.Best estimate of 5140 ÷ 68? (a) 730 (b) 7300 (c) 73
  32. 32.√56 to 1 decimal place? (a) 7.6 (b) 7.5 (c) 7.7 (d) 7.4
  33. 33.Best estimate of 4114 ÷ 71? (a) 590 (b) 59 (c) 5900
  34. 34.Best estimate of 7929 ÷ 86? (a) 880 (b) 88 (c) 8800
  35. 35.√82 to 1 decimal place? (a) 9.0 (b) 9.2 (c) 9.1 (d) 9.3
  36. 36.Best estimate of 2839 ÷ 66? (a) 410 (b) 41 (c) 4100
  37. 37.Best estimate of 2395 ÷ 36? (a) 60 (b) 600 (c) 6000
  38. 38.Best estimate of 1215 ÷ 62? (a) 200 (b) 2000 (c) 20
  39. 39.Best estimate of 866 ÷ 52? (a) 1700 (b) 17 (c) 170
  40. 40.Best estimate of 780 ÷ 26? (a) 26 (b) 260 (c) 2600

Answer key

  1. 8.7
  2. 28
  3. 8.1
  4. 34
  5. 9.4
  6. 8.8
  7. 67
  8. 7.9
  9. 5.9
  10. 15
  11. 72
  12. 90
  13. 8.8
  14. 6.7
  15. 8.1
  16. 99
  17. 9.7
  18. 4.9
  19. 27
  20. 84
  21. 6.5
  22. 6.6
  23. 7.6
  24. 85
  25. 7.9
  26. 56
  27. 8.5
  28. 70
  29. 7.4
  30. 54
  31. 73
  32. 7.5
  33. 59
  34. 88
  35. 9.1
  36. 41
  37. 60
  38. 20
  39. 17
  40. 26

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