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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 270 · 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 1989 ÷ 39? (a) 500 (b) 5000 (c) 50
  2. 2.Best estimate of 4266 ÷ 64? (a) 7100 (b) 71 (c) 710
  3. 3.√22 to 1 decimal place? (a) 4.9 (b) 4.8 (c) 5.0 (d) 4.7
  4. 4.Best estimate of 6091 ÷ 84? (a) 7600 (b) 76 (c) 760
  5. 5.√89 to 1 decimal place? (a) 9.5 (b) 9.4 (c) 9.3 (d) 9.2
  6. 6.Best estimate of 1380 ÷ 26? (a) 460 (b) 4600 (c) 46
  7. 7.√98 to 1 decimal place? (a) 9.9 (b) 9.8 (c) 9.7 (d) 9.6
  8. 8.√61 to 1 decimal place? (a) 7.9 (b) 7.7 (c) 7.6 (d) 7.8
  9. 9.Best estimate of 2869 ÷ 76? (a) 36 (b) 3600 (c) 360
  10. 10.Best estimate of 4358 ÷ 73? (a) 620 (b) 62 (c) 6200
  11. 11.√65 to 1 decimal place? (a) 8.2 (b) 8.1 (c) 8.4 (d) 8.3
  12. 12.Best estimate of 4298 ÷ 51? (a) 860 (b) 8600 (c) 86
  13. 13.√52 to 1 decimal place? (a) 7.3 (b) 7.2 (c) 7.4 (d) 7.1
  14. 14.Best estimate of 1656 ÷ 22? (a) 83 (b) 830 (c) 8300
  15. 15.Best estimate of 1013 ÷ 83? (a) 1300 (b) 130 (c) 13
  16. 16.Best estimate of 655 ÷ 49? (a) 1300 (b) 130 (c) 13
  17. 17.√71 to 1 decimal place? (a) 8.7 (b) 8.4 (c) 8.5 (d) 8.6
  18. 18.Best estimate of 2010 ÷ 26? (a) 67 (b) 6700 (c) 670
  19. 19.√21 to 1 decimal place? (a) 4.4 (b) 4.7 (c) 4.6 (d) 4.5
  20. 20.Best estimate of 3666 ÷ 67? (a) 52 (b) 5200 (c) 520
  21. 21.√92 to 1 decimal place? (a) 9.7 (b) 9.8 (c) 9.9 (d) 9.6
  22. 22.Best estimate of 5633 ÷ 79? (a) 7000 (b) 70 (c) 700
  23. 23.Best estimate of 3647 ÷ 76? (a) 4600 (b) 46 (c) 460
  24. 24.√85 to 1 decimal place? (a) 9.4 (b) 9.2 (c) 9.3 (d) 9.5
  25. 25.√74 to 1 decimal place? (a) 8.6 (b) 8.7 (c) 8.4 (d) 8.5
  26. 26.√59 to 1 decimal place? (a) 7.8 (b) 7.9 (c) 7.7 (d) 7.6
  27. 27.Best estimate of 851 ÷ 22? (a) 4300 (b) 430 (c) 43
  28. 28.Best estimate of 2132 ÷ 82? (a) 2700 (b) 27 (c) 270
  29. 29.Best estimate of 4329 ÷ 56? (a) 720 (b) 72 (c) 7200
  30. 30.√50 to 1 decimal place? (a) 7.1 (b) 7.2 (c) 7.3 (d) 7.0
  31. 31.Best estimate of 971 ÷ 41? (a) 2400 (b) 240 (c) 24
  32. 32.Best estimate of 4526 ÷ 82? (a) 570 (b) 57 (c) 5700
  33. 33.Best estimate of 8000 ÷ 84? (a) 10000 (b) 100 (c) 1000
  34. 34.√44 to 1 decimal place? (a) 6.4 (b) 6.5 (c) 6.3 (d) 6.6
  35. 35.√26 to 1 decimal place? (a) 5.1 (b) 5.3 (c) 5.0 (d) 5.2
  36. 36.√35 to 1 decimal place? (a) 5.8 (b) 5.9 (c) 6.1 (d) 6.0
  37. 37.Best estimate of 1015 ÷ 28? (a) 340 (b) 34 (c) 3400
  38. 38.Best estimate of 4699 ÷ 62? (a) 780 (b) 7800 (c) 78
  39. 39.Best estimate of 1171 ÷ 72? (a) 170 (b) 1700 (c) 17
  40. 40.Best estimate of 2204 ÷ 28? (a) 7300 (b) 73 (c) 730

Answer key

  1. 50
  2. 71
  3. 4.7
  4. 76
  5. 9.4
  6. 46
  7. 9.9
  8. 7.8
  9. 36
  10. 62
  11. 8.1
  12. 86
  13. 7.2
  14. 83
  15. 13
  16. 13
  17. 8.4
  18. 67
  19. 4.6
  20. 52
  21. 9.6
  22. 70
  23. 46
  24. 9.2
  25. 8.6
  26. 7.7
  27. 43
  28. 27
  29. 72
  30. 7.1
  31. 24
  32. 57
  33. 100
  34. 6.6
  35. 5.1
  36. 5.9
  37. 34
  38. 78
  39. 17
  40. 73

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