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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 635 · 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 4005 ÷ 42? (a) 1000 (b) 10000 (c) 100
  2. 2.√98 to 1 decimal place? (a) 9.8 (b) 9.9 (c) 9.6 (d) 9.7
  3. 3.Best estimate of 1625 ÷ 27? (a) 540 (b) 5400 (c) 54
  4. 4.Best estimate of 592 ÷ 43? (a) 150 (b) 1500 (c) 15
  5. 5.√26 to 1 decimal place? (a) 5.0 (b) 5.2 (c) 5.1 (d) 4.9
  6. 6.Best estimate of 1035 ÷ 36? (a) 2600 (b) 260 (c) 26
  7. 7.√74 to 1 decimal place? (a) 8.7 (b) 8.8 (c) 8.6 (d) 8.9
  8. 8.Best estimate of 2549 ÷ 34? (a) 850 (b) 85 (c) 8500
  9. 9.Best estimate of 3267 ÷ 86? (a) 3600 (b) 36 (c) 360
  10. 10.Best estimate of 4685 ÷ 51? (a) 940 (b) 9400 (c) 94
  11. 11.√62 to 1 decimal place? (a) 8.0 (b) 7.9 (c) 7.8 (d) 8.1
  12. 12.Best estimate of 4161 ÷ 56? (a) 6900 (b) 690 (c) 69
  13. 13.√53 to 1 decimal place? (a) 7.4 (b) 7.5 (c) 7.6 (d) 7.3
  14. 14.Best estimate of 4799 ÷ 72? (a) 690 (b) 6900 (c) 69
  15. 15.√85 to 1 decimal place? (a) 9.3 (b) 9.2 (c) 9.1 (d) 9.0
  16. 16.Best estimate of 1297 ÷ 58? (a) 22 (b) 2200 (c) 220
  17. 17.Best estimate of 1708 ÷ 24? (a) 85 (b) 8500 (c) 850
  18. 18.Best estimate of 1452 ÷ 23? (a) 730 (b) 73 (c) 7300
  19. 19.√61 to 1 decimal place? (a) 7.6 (b) 7.8 (c) 7.7 (d) 7.9
  20. 20.√71 to 1 decimal place? (a) 8.5 (b) 8.4 (c) 8.6 (d) 8.7
  21. 21.√92 to 1 decimal place? (a) 9.3 (b) 9.6 (c) 9.4 (d) 9.5
  22. 22.√86 to 1 decimal place? (a) 9.3 (b) 9.4 (c) 9.5 (d) 9.2
  23. 23.√56 to 1 decimal place? (a) 7.6 (b) 7.4 (c) 7.5 (d) 7.7
  24. 24.Best estimate of 1506 ÷ 36? (a) 3800 (b) 380 (c) 38
  25. 25.Best estimate of 5112 ÷ 63? (a) 850 (b) 8500 (c) 85
  26. 26.Best estimate of 2816 ÷ 67? (a) 40 (b) 400 (c) 4000
  27. 27.√40 to 1 decimal place? (a) 6.2 (b) 6.3 (c) 6.1 (d) 6.4
  28. 28.Best estimate of 2284 ÷ 28? (a) 760 (b) 7600 (c) 76
  29. 29.Best estimate of 4901 ÷ 76? (a) 61 (b) 610 (c) 6100
  30. 30.√38 to 1 decimal place? (a) 6.2 (b) 5.9 (c) 6.0 (d) 6.1
  31. 31.Best estimate of 1930 ÷ 29? (a) 640 (b) 6400 (c) 64
  32. 32.Best estimate of 2163 ÷ 29? (a) 72 (b) 720 (c) 7200
  33. 33.√47 to 1 decimal place? (a) 7.1 (b) 7.0 (c) 6.9 (d) 7.2
  34. 34.√31 to 1 decimal place? (a) 5.6 (b) 5.3 (c) 5.4 (d) 5.5
  35. 35.Best estimate of 2158 ÷ 78? (a) 2700 (b) 270 (c) 27
  36. 36.Best estimate of 4500 ÷ 72? (a) 6400 (b) 640 (c) 64
  37. 37.Best estimate of 5085 ÷ 62? (a) 8500 (b) 85 (c) 850
  38. 38.Best estimate of 3599 ÷ 64? (a) 6000 (b) 60 (c) 600
  39. 39.√82 to 1 decimal place? (a) 9.3 (b) 9.2 (c) 9.1 (d) 9.0
  40. 40.√67 to 1 decimal place? (a) 8.0 (b) 8.1 (c) 8.2 (d) 8.3

Answer key

  1. 100
  2. 9.9
  3. 54
  4. 15
  5. 5.1
  6. 26
  7. 8.6
  8. 85
  9. 36
  10. 94
  11. 7.9
  12. 69
  13. 7.3
  14. 69
  15. 9.2
  16. 22
  17. 85
  18. 73
  19. 7.8
  20. 8.4
  21. 9.6
  22. 9.3
  23. 7.5
  24. 38
  25. 85
  26. 40
  27. 6.3
  28. 76
  29. 61
  30. 6.2
  31. 64
  32. 72
  33. 6.9
  34. 5.6
  35. 27
  36. 64
  37. 85
  38. 60
  39. 9.1
  40. 8.2

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