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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 77 · 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 4803 ÷ 52? (a) 960 (b) 9600 (c) 96
  2. 2.Best estimate of 5205 ÷ 84? (a) 65 (b) 6500 (c) 650
  3. 3.√37 to 1 decimal place? (a) 6.2 (b) 6.0 (c) 6.3 (d) 6.1
  4. 4.Best estimate of 1868 ÷ 24? (a) 9300 (b) 930 (c) 93
  5. 5.Best estimate of 1711 ÷ 37? (a) 4300 (b) 43 (c) 430
  6. 6.√52 to 1 decimal place? (a) 7.0 (b) 7.1 (c) 7.3 (d) 7.2
  7. 7.Best estimate of 5815 ÷ 78? (a) 7300 (b) 73 (c) 730
  8. 8.Best estimate of 3684 ÷ 51? (a) 7400 (b) 74 (c) 740
  9. 9.√62 to 1 decimal place? (a) 7.7 (b) 7.8 (c) 7.9 (d) 7.6
  10. 10.Best estimate of 1863 ÷ 63? (a) 31 (b) 3100 (c) 310
  11. 11.Best estimate of 1552 ÷ 27? (a) 5200 (b) 52 (c) 520
  12. 12.√44 to 1 decimal place? (a) 6.4 (b) 6.6 (c) 6.3 (d) 6.5
  13. 13.√55 to 1 decimal place? (a) 7.2 (b) 7.3 (c) 7.4 (d) 7.5
  14. 14.√80 to 1 decimal place? (a) 8.8 (b) 8.7 (c) 8.9 (d) 9.0
  15. 15.Best estimate of 1873 ÷ 52? (a) 370 (b) 37 (c) 3700
  16. 16.Best estimate of 3008 ÷ 51? (a) 60 (b) 6000 (c) 600
  17. 17.Best estimate of 4071 ÷ 62? (a) 680 (b) 6800 (c) 68
  18. 18.Best estimate of 2788 ÷ 54? (a) 560 (b) 56 (c) 5600
  19. 19.√20 to 1 decimal place? (a) 4.7 (b) 4.8 (c) 4.6 (d) 4.5
  20. 20.√88 to 1 decimal place? (a) 9.4 (b) 9.1 (c) 9.3 (d) 9.2
  21. 21.√70 to 1 decimal place? (a) 8.3 (b) 8.4 (c) 8.2 (d) 8.5
  22. 22.√31 to 1 decimal place? (a) 5.3 (b) 5.4 (c) 5.5 (d) 5.6
  23. 23.√23 to 1 decimal place? (a) 4.9 (b) 4.8 (c) 5.0 (d) 4.7
  24. 24.Best estimate of 2462 ÷ 72? (a) 35 (b) 3500 (c) 350
  25. 25.√72 to 1 decimal place? (a) 8.5 (b) 8.3 (c) 8.4 (d) 8.6
  26. 26.Best estimate of 3432 ÷ 61? (a) 570 (b) 57 (c) 5700
  27. 27.√78 to 1 decimal place? (a) 9.0 (b) 8.8 (c) 8.7 (d) 8.9
  28. 28.Best estimate of 1047 ÷ 21? (a) 5200 (b) 52 (c) 520
  29. 29.√32 to 1 decimal place? (a) 6.0 (b) 5.9 (c) 5.8 (d) 5.7
  30. 30.Best estimate of 2031 ÷ 29? (a) 68 (b) 6800 (c) 680
  31. 31.Best estimate of 6316 ÷ 77? (a) 790 (b) 79 (c) 7900
  32. 32.Best estimate of 1687 ÷ 52? (a) 34 (b) 340 (c) 3400
  33. 33.Best estimate of 1891 ÷ 61? (a) 32 (b) 3200 (c) 320
  34. 34.Best estimate of 1949 ÷ 26? (a) 650 (b) 6500 (c) 65
  35. 35.Best estimate of 2477 ÷ 26? (a) 83 (b) 8300 (c) 830
  36. 36.Best estimate of 2299 ÷ 72? (a) 330 (b) 33 (c) 3300
  37. 37.Best estimate of 2761 ÷ 32? (a) 92 (b) 920 (c) 9200
  38. 38.Best estimate of 4646 ÷ 79? (a) 580 (b) 5800 (c) 58
  39. 39.√65 to 1 decimal place? (a) 8.4 (b) 8.3 (c) 8.1 (d) 8.2
  40. 40.√26 to 1 decimal place? (a) 5.0 (b) 5.3 (c) 5.1 (d) 5.2

Answer key

  1. 96
  2. 65
  3. 6.1
  4. 93
  5. 43
  6. 7.2
  7. 73
  8. 74
  9. 7.9
  10. 31
  11. 52
  12. 6.6
  13. 7.4
  14. 8.9
  15. 37
  16. 60
  17. 68
  18. 56
  19. 4.5
  20. 9.4
  21. 8.4
  22. 5.6
  23. 4.8
  24. 35
  25. 8.5
  26. 57
  27. 8.8
  28. 52
  29. 5.7
  30. 68
  31. 79
  32. 34
  33. 32
  34. 65
  35. 83
  36. 33
  37. 92
  38. 58
  39. 8.1
  40. 5.1

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