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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 572 · 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 2967 ÷ 72? (a) 4200 (b) 420 (c) 42
  2. 2.Best estimate of 911 ÷ 58? (a) 150 (b) 15 (c) 1500
  3. 3.Best estimate of 3282 ÷ 86? (a) 3600 (b) 360 (c) 36
  4. 4.√69 to 1 decimal place? (a) 8.2 (b) 8.3 (c) 8.1 (d) 8.4
  5. 5.Best estimate of 7151 ÷ 82? (a) 890 (b) 89 (c) 8900
  6. 6.√61 to 1 decimal place? (a) 7.8 (b) 8.1 (c) 8.0 (d) 7.9
  7. 7.√87 to 1 decimal place? (a) 9.3 (b) 9.2 (c) 9.0 (d) 9.1
  8. 8.√47 to 1 decimal place? (a) 7.1 (b) 6.9 (c) 7.2 (d) 7.0
  9. 9.Best estimate of 2197 ÷ 23? (a) 1100 (b) 110 (c) 11000
  10. 10.Best estimate of 5189 ÷ 87? (a) 58 (b) 5800 (c) 580
  11. 11.√37 to 1 decimal place? (a) 6.0 (b) 6.1 (c) 5.9 (d) 6.2
  12. 12.√51 to 1 decimal place? (a) 7.1 (b) 7.0 (c) 6.9 (d) 7.2
  13. 13.√27 to 1 decimal place? (a) 5.2 (b) 5.4 (c) 5.3 (d) 5.1
  14. 14.√46 to 1 decimal place? (a) 6.6 (b) 6.8 (c) 6.7 (d) 6.5
  15. 15.Best estimate of 2850 ÷ 49? (a) 570 (b) 5700 (c) 57
  16. 16.Best estimate of 1030 ÷ 22? (a) 5200 (b) 520 (c) 52
  17. 17.√55 to 1 decimal place? (a) 7.4 (b) 7.3 (c) 7.1 (d) 7.2
  18. 18.√58 to 1 decimal place? (a) 7.7 (b) 7.6 (c) 7.8 (d) 7.5
  19. 19.√65 to 1 decimal place? (a) 8.1 (b) 8.2 (c) 8.3 (d) 8.0
  20. 20.Best estimate of 3106 ÷ 47? (a) 62 (b) 6200 (c) 620
  21. 21.Best estimate of 1124 ÷ 61? (a) 19 (b) 1900 (c) 190
  22. 22.Best estimate of 4024 ÷ 52? (a) 8000 (b) 80 (c) 800
  23. 23.Best estimate of 445 ÷ 37? (a) 110 (b) 11 (c) 1100
  24. 24.Best estimate of 5478 ÷ 77? (a) 6800 (b) 68 (c) 680
  25. 25.Best estimate of 1194 ÷ 29? (a) 400 (b) 4000 (c) 40
  26. 26.√71 to 1 decimal place? (a) 8.2 (b) 8.1 (c) 8.3 (d) 8.4
  27. 27.√90 to 1 decimal place? (a) 9.5 (b) 9.6 (c) 9.7 (d) 9.4
  28. 28.Best estimate of 3081 ÷ 42? (a) 77 (b) 770 (c) 7700
  29. 29.Best estimate of 2422 ÷ 68? (a) 35 (b) 3500 (c) 350
  30. 30.Best estimate of 938 ÷ 67? (a) 130 (b) 1300 (c) 13
  31. 31.Best estimate of 402 ÷ 28? (a) 130 (b) 13 (c) 1300
  32. 32.Best estimate of 4632 ÷ 62? (a) 7700 (b) 77 (c) 770
  33. 33.Best estimate of 2002 ÷ 24? (a) 100 (b) 1000 (c) 10000
  34. 34.Best estimate of 2907 ÷ 44? (a) 73 (b) 7300 (c) 730
  35. 35.Best estimate of 2101 ÷ 46? (a) 4200 (b) 42 (c) 420
  36. 36.Best estimate of 2937 ÷ 61? (a) 490 (b) 4900 (c) 49
  37. 37.√50 to 1 decimal place? (a) 7.3 (b) 7.2 (c) 7.4 (d) 7.1
  38. 38.Best estimate of 2688 ÷ 76? (a) 34 (b) 340 (c) 3400
  39. 39.Best estimate of 1438 ÷ 27? (a) 4800 (b) 48 (c) 480
  40. 40.√56 to 1 decimal place? (a) 7.5 (b) 7.6 (c) 7.8 (d) 7.7

Answer key

  1. 42
  2. 15
  3. 36
  4. 8.3
  5. 89
  6. 7.8
  7. 9.3
  8. 6.9
  9. 110
  10. 58
  11. 6.1
  12. 7.1
  13. 5.2
  14. 6.8
  15. 57
  16. 52
  17. 7.4
  18. 7.6
  19. 8.1
  20. 62
  21. 19
  22. 80
  23. 11
  24. 68
  25. 40
  26. 8.4
  27. 9.5
  28. 77
  29. 35
  30. 13
  31. 13
  32. 77
  33. 100
  34. 73
  35. 42
  36. 49
  37. 7.1
  38. 34
  39. 48
  40. 7.5

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