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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 194 · 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 1384 ÷ 83? (a) 170 (b) 1700 (c) 17
  2. 2.Best estimate of 1970 ÷ 37? (a) 49 (b) 490 (c) 4900
  3. 3.Best estimate of 4899 ÷ 62? (a) 8200 (b) 82 (c) 820
  4. 4.Best estimate of 578 ÷ 26? (a) 1900 (b) 190 (c) 19
  5. 5.Best estimate of 2976 ÷ 77? (a) 370 (b) 3700 (c) 37
  6. 6.Best estimate of 2696 ÷ 86? (a) 3000 (b) 300 (c) 30
  7. 7.Best estimate of 4037 ÷ 67? (a) 58 (b) 580 (c) 5800
  8. 8.Best estimate of 3004 ÷ 38? (a) 7500 (b) 75 (c) 750
  9. 9.Best estimate of 2402 ÷ 54? (a) 4800 (b) 48 (c) 480
  10. 10.√78 to 1 decimal place? (a) 8.8 (b) 8.6 (c) 8.5 (d) 8.7
  11. 11.Best estimate of 1956 ÷ 26? (a) 6500 (b) 65 (c) 650
  12. 12.Best estimate of 1128 ÷ 66? (a) 1600 (b) 160 (c) 16
  13. 13.Best estimate of 2124 ÷ 58? (a) 3500 (b) 35 (c) 350
  14. 14.√61 to 1 decimal place? (a) 7.8 (b) 7.9 (c) 8.1 (d) 8.0
  15. 15.Best estimate of 3031 ÷ 56? (a) 510 (b) 5100 (c) 51
  16. 16.Best estimate of 1224 ÷ 56? (a) 2000 (b) 200 (c) 20
  17. 17.√59 to 1 decimal place? (a) 7.7 (b) 7.8 (c) 7.9 (d) 7.6
  18. 18.√48 to 1 decimal place? (a) 6.8 (b) 6.6 (c) 6.7 (d) 6.9
  19. 19.√37 to 1 decimal place? (a) 6.1 (b) 6.2 (c) 6.3 (d) 6.4
  20. 20.Best estimate of 4762 ÷ 54? (a) 950 (b) 9500 (c) 95
  21. 21.√82 to 1 decimal place? (a) 9.1 (b) 8.9 (c) 9.0 (d) 8.8
  22. 22.√70 to 1 decimal place? (a) 8.3 (b) 8.4 (c) 8.5 (d) 8.6
  23. 23.Best estimate of 4339 ÷ 78? (a) 54 (b) 540 (c) 5400
  24. 24.√30 to 1 decimal place? (a) 5.7 (b) 5.4 (c) 5.6 (d) 5.5
  25. 25.√74 to 1 decimal place? (a) 8.7 (b) 8.9 (c) 8.8 (d) 8.6
  26. 26.√21 to 1 decimal place? (a) 4.9 (b) 4.8 (c) 4.6 (d) 4.7
  27. 27.Best estimate of 3661 ÷ 54? (a) 730 (b) 73 (c) 7300
  28. 28.Best estimate of 3544 ÷ 76? (a) 4400 (b) 44 (c) 440
  29. 29.Best estimate of 1656 ÷ 52? (a) 330 (b) 3300 (c) 33
  30. 30.Best estimate of 1277 ÷ 22? (a) 640 (b) 6400 (c) 64
  31. 31.Best estimate of 4045 ÷ 57? (a) 67 (b) 6700 (c) 670
  32. 32.√83 to 1 decimal place? (a) 8.9 (b) 9.2 (c) 9.0 (d) 9.1
  33. 33.√79 to 1 decimal place? (a) 8.9 (b) 9.0 (c) 9.2 (d) 9.1
  34. 34.Best estimate of 1515 ÷ 72? (a) 2200 (b) 220 (c) 22
  35. 35.Best estimate of 4087 ÷ 82? (a) 51 (b) 5100 (c) 510
  36. 36.Best estimate of 6027 ÷ 64? (a) 100 (b) 1000 (c) 10000
  37. 37.√42 to 1 decimal place? (a) 6.6 (b) 6.5 (c) 6.8 (d) 6.7
  38. 38.√72 to 1 decimal place? (a) 8.7 (b) 8.4 (c) 8.6 (d) 8.5
  39. 39.√53 to 1 decimal place? (a) 7.2 (b) 7.1 (c) 7.3 (d) 7.4
  40. 40.Best estimate of 2025 ÷ 84? (a) 25 (b) 2500 (c) 250

Answer key

  1. 17
  2. 49
  3. 82
  4. 19
  5. 37
  6. 30
  7. 58
  8. 75
  9. 48
  10. 8.8
  11. 65
  12. 16
  13. 35
  14. 7.8
  15. 51
  16. 20
  17. 7.7
  18. 6.9
  19. 6.1
  20. 95
  21. 9.1
  22. 8.4
  23. 54
  24. 5.5
  25. 8.6
  26. 4.6
  27. 73
  28. 44
  29. 33
  30. 64
  31. 67
  32. 9.1
  33. 8.9
  34. 22
  35. 51
  36. 100
  37. 6.5
  38. 8.5
  39. 7.3
  40. 25

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