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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 153 · 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 1399 ÷ 84? (a) 17 (b) 1700 (c) 170
  2. 2.Best estimate of 1182 ÷ 46? (a) 240 (b) 24 (c) 2400
  3. 3.Best estimate of 5873 ÷ 76? (a) 7300 (b) 730 (c) 73
  4. 4.Best estimate of 2219 ÷ 44? (a) 550 (b) 5500 (c) 55
  5. 5.√35 to 1 decimal place? (a) 5.9 (b) 5.6 (c) 5.7 (d) 5.8
  6. 6.Best estimate of 6562 ÷ 72? (a) 94 (b) 9400 (c) 940
  7. 7.Best estimate of 509 ÷ 24? (a) 250 (b) 2500 (c) 25
  8. 8.√65 to 1 decimal place? (a) 8.0 (b) 8.2 (c) 8.1 (d) 7.9
  9. 9.√53 to 1 decimal place? (a) 7.5 (b) 7.6 (c) 7.4 (d) 7.3
  10. 10.Best estimate of 4962 ÷ 62? (a) 83 (b) 8300 (c) 830
  11. 11.Best estimate of 1319 ÷ 22? (a) 660 (b) 6600 (c) 66
  12. 12.√44 to 1 decimal place? (a) 6.7 (b) 6.6 (c) 6.5 (d) 6.4
  13. 13.√82 to 1 decimal place? (a) 9.2 (b) 9.1 (c) 9.0 (d) 8.9
  14. 14.Best estimate of 1683 ÷ 52? (a) 340 (b) 34 (c) 3400
  15. 15.Best estimate of 1097 ÷ 81? (a) 140 (b) 1400 (c) 14
  16. 16.Best estimate of 5340 ÷ 74? (a) 7600 (b) 760 (c) 76
  17. 17.√38 to 1 decimal place? (a) 6.0 (b) 6.1 (c) 6.2 (d) 5.9
  18. 18.√40 to 1 decimal place? (a) 6.2 (b) 6.4 (c) 6.3 (d) 6.1
  19. 19.√87 to 1 decimal place? (a) 9.4 (b) 9.3 (c) 9.5 (d) 9.6
  20. 20.√61 to 1 decimal place? (a) 7.7 (b) 7.5 (c) 7.6 (d) 7.8
  21. 21.√31 to 1 decimal place? (a) 5.7 (b) 5.8 (c) 5.9 (d) 5.6
  22. 22.Best estimate of 4189 ÷ 61? (a) 700 (b) 70 (c) 7000
  23. 23.Best estimate of 610 ÷ 22? (a) 3100 (b) 310 (c) 31
  24. 24.Best estimate of 4312 ÷ 86? (a) 48 (b) 480 (c) 4800
  25. 25.Best estimate of 2210 ÷ 34? (a) 74 (b) 7400 (c) 740
  26. 26.√94 to 1 decimal place? (a) 9.9 (b) 9.7 (c) 9.8 (d) 9.6
  27. 27.√71 to 1 decimal place? (a) 8.2 (b) 8.3 (c) 8.4 (d) 8.1
  28. 28.Best estimate of 5985 ÷ 86? (a) 6700 (b) 670 (c) 67
  29. 29.Best estimate of 1420 ÷ 24? (a) 71 (b) 7100 (c) 710
  30. 30.Best estimate of 1707 ÷ 24? (a) 8500 (b) 85 (c) 850
  31. 31.Best estimate of 2395 ÷ 36? (a) 6000 (b) 600 (c) 60
  32. 32.Best estimate of 3953 ÷ 51? (a) 790 (b) 7900 (c) 79
  33. 33.√37 to 1 decimal place? (a) 5.9 (b) 6.1 (c) 5.8 (d) 6.0
  34. 34.√70 to 1 decimal place? (a) 8.2 (b) 8.4 (c) 8.1 (d) 8.3
  35. 35.Best estimate of 779 ÷ 46? (a) 160 (b) 1600 (c) 16
  36. 36.√51 to 1 decimal place? (a) 7.2 (b) 7.0 (c) 7.1 (d) 6.9
  37. 37.Best estimate of 5607 ÷ 66? (a) 8000 (b) 800 (c) 80
  38. 38.Best estimate of 1201 ÷ 26? (a) 4000 (b) 400 (c) 40
  39. 39.√98 to 1 decimal place? (a) 9.8 (b) 9.7 (c) 9.9 (d) 10.0
  40. 40.Best estimate of 2973 ÷ 42? (a) 7400 (b) 74 (c) 740

Answer key

  1. 17
  2. 24
  3. 73
  4. 55
  5. 5.9
  6. 94
  7. 25
  8. 8.1
  9. 7.3
  10. 83
  11. 66
  12. 6.6
  13. 9.1
  14. 34
  15. 14
  16. 76
  17. 6.2
  18. 6.3
  19. 9.3
  20. 7.8
  21. 5.6
  22. 70
  23. 31
  24. 48
  25. 74
  26. 9.7
  27. 8.4
  28. 67
  29. 71
  30. 85
  31. 60
  32. 79
  33. 6.1
  34. 8.4
  35. 16
  36. 7.1
  37. 80
  38. 40
  39. 9.9
  40. 74

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