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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 878 · 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 1956 ÷ 81? (a) 2400 (b) 24 (c) 240
  2. 2.Best estimate of 2112 ÷ 32? (a) 700 (b) 7000 (c) 70
  3. 3.√56 to 1 decimal place? (a) 7.5 (b) 7.7 (c) 7.6 (d) 7.8
  4. 4.√50 to 1 decimal place? (a) 7.2 (b) 7.1 (c) 7.3 (d) 7.0
  5. 5.√23 to 1 decimal place? (a) 4.6 (b) 4.8 (c) 4.5 (d) 4.7
  6. 6.√41 to 1 decimal place? (a) 6.5 (b) 6.6 (c) 6.7 (d) 6.4
  7. 7.√71 to 1 decimal place? (a) 8.4 (b) 8.3 (c) 8.5 (d) 8.6
  8. 8.Best estimate of 2199 ÷ 33? (a) 7300 (b) 730 (c) 73
  9. 9.Best estimate of 2609 ÷ 66? (a) 3700 (b) 37 (c) 370
  10. 10.Best estimate of 4106 ÷ 89? (a) 460 (b) 46 (c) 4600
  11. 11.√74 to 1 decimal place? (a) 8.9 (b) 8.7 (c) 8.6 (d) 8.8
  12. 12.Best estimate of 1864 ÷ 64? (a) 310 (b) 3100 (c) 31
  13. 13.√84 to 1 decimal place? (a) 9.2 (b) 9.1 (c) 9.0 (d) 8.9
  14. 14.Best estimate of 5029 ÷ 66? (a) 72 (b) 7200 (c) 720
  15. 15.√61 to 1 decimal place? (a) 7.8 (b) 8.0 (c) 7.9 (d) 8.1
  16. 16.Best estimate of 1081 ÷ 23? (a) 54 (b) 5400 (c) 540
  17. 17.√80 to 1 decimal place? (a) 8.9 (b) 9.0 (c) 9.1 (d) 9.2
  18. 18.√31 to 1 decimal place? (a) 5.5 (b) 5.6 (c) 5.4 (d) 5.7
  19. 19.√55 to 1 decimal place? (a) 7.3 (b) 7.4 (c) 7.1 (d) 7.2
  20. 20.√98 to 1 decimal place? (a) 9.9 (b) 9.8 (c) 10.0 (d) 9.7
  21. 21.Best estimate of 2189 ÷ 82? (a) 270 (b) 27 (c) 2700
  22. 22.Best estimate of 5464 ÷ 81? (a) 6800 (b) 68 (c) 680
  23. 23.Best estimate of 3459 ÷ 54? (a) 69 (b) 6900 (c) 690
  24. 24.√26 to 1 decimal place? (a) 5.2 (b) 5.4 (c) 5.3 (d) 5.1
  25. 25.√75 to 1 decimal place? (a) 8.7 (b) 8.5 (c) 8.6 (d) 8.4
  26. 26.Best estimate of 1817 ÷ 37? (a) 4500 (b) 45 (c) 450
  27. 27.Best estimate of 3882 ÷ 47? (a) 78 (b) 780 (c) 7800
  28. 28.Best estimate of 2369 ÷ 26? (a) 79 (b) 7900 (c) 790
  29. 29.√34 to 1 decimal place? (a) 5.8 (b) 5.9 (c) 6.0 (d) 5.7
  30. 30.Best estimate of 2411 ÷ 32? (a) 80 (b) 8000 (c) 800
  31. 31.Best estimate of 4339 ÷ 61? (a) 720 (b) 72 (c) 7200
  32. 32.Best estimate of 6490 ÷ 87? (a) 7200 (b) 720 (c) 72
  33. 33.√22 to 1 decimal place? (a) 4.8 (b) 4.7 (c) 4.9 (d) 4.6
  34. 34.√30 to 1 decimal place? (a) 5.3 (b) 5.4 (c) 5.2 (d) 5.5
  35. 35.Best estimate of 4518 ÷ 74? (a) 650 (b) 65 (c) 6500
  36. 36.Best estimate of 1748 ÷ 38? (a) 4400 (b) 44 (c) 440
  37. 37.Best estimate of 5424 ÷ 69? (a) 77 (b) 770 (c) 7700
  38. 38.Best estimate of 2980 ÷ 63? (a) 500 (b) 5000 (c) 50
  39. 39.√90 to 1 decimal place? (a) 9.8 (b) 9.5 (c) 9.6 (d) 9.7
  40. 40.√92 to 1 decimal place? (a) 9.7 (b) 9.8 (c) 9.9 (d) 9.6

Answer key

  1. 24
  2. 70
  3. 7.5
  4. 7.1
  5. 4.8
  6. 6.4
  7. 8.4
  8. 73
  9. 37
  10. 46
  11. 8.6
  12. 31
  13. 9.2
  14. 72
  15. 7.8
  16. 54
  17. 8.9
  18. 5.6
  19. 7.4
  20. 9.9
  21. 27
  22. 68
  23. 69
  24. 5.1
  25. 8.7
  26. 45
  27. 78
  28. 79
  29. 5.8
  30. 80
  31. 72
  32. 72
  33. 4.7
  34. 5.5
  35. 65
  36. 44
  37. 77
  38. 50
  39. 9.5
  40. 9.6

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