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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 155 · 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 2726 ÷ 86? (a) 3000 (b) 300 (c) 30
  2. 2.Best estimate of 4697 ÷ 62? (a) 780 (b) 7800 (c) 78
  3. 3.√67 to 1 decimal place? (a) 8.1 (b) 8.0 (c) 8.3 (d) 8.2
  4. 4.Best estimate of 2940 ÷ 61? (a) 4900 (b) 49 (c) 490
  5. 5.√30 to 1 decimal place? (a) 5.6 (b) 5.7 (c) 5.5 (d) 5.4
  6. 6.Best estimate of 1308 ÷ 38? (a) 3300 (b) 33 (c) 330
  7. 7.√55 to 1 decimal place? (a) 7.7 (b) 7.6 (c) 7.4 (d) 7.5
  8. 8.Best estimate of 2574 ÷ 34? (a) 860 (b) 86 (c) 8600
  9. 9.√37 to 1 decimal place? (a) 6.0 (b) 5.9 (c) 6.2 (d) 6.1
  10. 10.√34 to 1 decimal place? (a) 5.6 (b) 5.9 (c) 5.7 (d) 5.8
  11. 11.Best estimate of 4033 ÷ 56? (a) 6700 (b) 670 (c) 67
  12. 12.√61 to 1 decimal place? (a) 8.0 (b) 7.7 (c) 7.8 (d) 7.9
  13. 13.Best estimate of 3972 ÷ 81? (a) 5000 (b) 50 (c) 500
  14. 14.√26 to 1 decimal place? (a) 4.8 (b) 5.1 (c) 4.9 (d) 5.0
  15. 15.Best estimate of 2310 ÷ 33? (a) 77 (b) 770 (c) 7700
  16. 16.√83 to 1 decimal place? (a) 9.2 (b) 8.9 (c) 9.0 (d) 9.1
  17. 17.Best estimate of 3930 ÷ 64? (a) 6600 (b) 66 (c) 660
  18. 18.Best estimate of 1851 ÷ 36? (a) 4600 (b) 46 (c) 460
  19. 19.Best estimate of 1688 ÷ 26? (a) 56 (b) 560 (c) 5600
  20. 20.Best estimate of 304 ÷ 21? (a) 150 (b) 15 (c) 1500
  21. 21.√24 to 1 decimal place? (a) 4.7 (b) 4.9 (c) 4.6 (d) 4.8
  22. 22.Best estimate of 4247 ÷ 68? (a) 61 (b) 610 (c) 6100
  23. 23.Best estimate of 445 ÷ 27? (a) 1500 (b) 150 (c) 15
  24. 24.Best estimate of 1552 ÷ 84? (a) 19 (b) 1900 (c) 190
  25. 25.√48 to 1 decimal place? (a) 6.7 (b) 6.9 (c) 6.8 (d) 6.6
  26. 26.√65 to 1 decimal place? (a) 8.1 (b) 8.2 (c) 8.3 (d) 8.0
  27. 27.√66 to 1 decimal place? (a) 7.9 (b) 8.0 (c) 8.1 (d) 8.2
  28. 28.Best estimate of 698 ÷ 38? (a) 17 (b) 170 (c) 1700
  29. 29.Best estimate of 1970 ÷ 86? (a) 22 (b) 220 (c) 2200
  30. 30.Best estimate of 2108 ÷ 52? (a) 420 (b) 42 (c) 4200
  31. 31.Best estimate of 3380 ÷ 36? (a) 850 (b) 8500 (c) 85
  32. 32.Best estimate of 1332 ÷ 26? (a) 44 (b) 440 (c) 4400
  33. 33.√90 to 1 decimal place? (a) 9.5 (b) 9.4 (c) 9.6 (d) 9.7
  34. 34.√38 to 1 decimal place? (a) 6.5 (b) 6.2 (c) 6.4 (d) 6.3
  35. 35.Best estimate of 4668 ÷ 64? (a) 780 (b) 7800 (c) 78
  36. 36.√31 to 1 decimal place? (a) 5.3 (b) 5.4 (c) 5.6 (d) 5.5
  37. 37.Best estimate of 4445 ÷ 79? (a) 560 (b) 5600 (c) 56
  38. 38.Best estimate of 4278 ÷ 67? (a) 61 (b) 610 (c) 6100
  39. 39.Best estimate of 1873 ÷ 21? (a) 940 (b) 94 (c) 9400
  40. 40.√98 to 1 decimal place? (a) 9.7 (b) 9.8 (c) 9.9 (d) 9.6

Answer key

  1. 30
  2. 78
  3. 8.2
  4. 49
  5. 5.5
  6. 33
  7. 7.4
  8. 86
  9. 6.1
  10. 5.8
  11. 67
  12. 7.8
  13. 50
  14. 5.1
  15. 77
  16. 9.1
  17. 66
  18. 46
  19. 56
  20. 15
  21. 4.9
  22. 61
  23. 15
  24. 19
  25. 6.9
  26. 8.1
  27. 8.1
  28. 17
  29. 22
  30. 42
  31. 85
  32. 44
  33. 9.5
  34. 6.2
  35. 78
  36. 5.6
  37. 56
  38. 61
  39. 94
  40. 9.9

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