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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 777 · 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.√30 to 1 decimal place? (a) 5.3 (b) 5.2 (c) 5.5 (d) 5.4
  2. 2.Best estimate of 4883 ÷ 86? (a) 540 (b) 54 (c) 5400
  3. 3.√86 to 1 decimal place? (a) 9.3 (b) 9.2 (c) 9.4 (d) 9.1
  4. 4.√26 to 1 decimal place? (a) 4.8 (b) 4.9 (c) 5.1 (d) 5.0
  5. 5.√71 to 1 decimal place? (a) 8.2 (b) 8.4 (c) 8.1 (d) 8.3
  6. 6.√75 to 1 decimal place? (a) 8.7 (b) 8.5 (c) 8.4 (d) 8.6
  7. 7.Best estimate of 1037 ÷ 78? (a) 13 (b) 130 (c) 1300
  8. 8.Best estimate of 2256 ÷ 46? (a) 450 (b) 45 (c) 4500
  9. 9.Best estimate of 1287 ÷ 82? (a) 1600 (b) 160 (c) 16
  10. 10.√32 to 1 decimal place? (a) 5.4 (b) 5.7 (c) 5.5 (d) 5.6
  11. 11.Best estimate of 2316 ÷ 42? (a) 58 (b) 580 (c) 5800
  12. 12.Best estimate of 3110 ÷ 72? (a) 4400 (b) 440 (c) 44
  13. 13.Best estimate of 3441 ÷ 62? (a) 570 (b) 5700 (c) 57
  14. 14.Best estimate of 2472 ÷ 83? (a) 3100 (b) 310 (c) 31
  15. 15.Best estimate of 1544 ÷ 54? (a) 310 (b) 3100 (c) 31
  16. 16.Best estimate of 2108 ÷ 26? (a) 70 (b) 7000 (c) 700
  17. 17.Best estimate of 508 ÷ 21? (a) 2500 (b) 25 (c) 250
  18. 18.Best estimate of 4722 ÷ 68? (a) 670 (b) 67 (c) 6700
  19. 19.Best estimate of 576 ÷ 32? (a) 19 (b) 1900 (c) 190
  20. 20.√94 to 1 decimal place? (a) 10.0 (b) 9.7 (c) 9.8 (d) 9.9
  21. 21.√55 to 1 decimal place? (a) 7.6 (b) 7.3 (c) 7.5 (d) 7.4
  22. 22.√22 to 1 decimal place? (a) 5.0 (b) 4.9 (c) 4.7 (d) 4.8
  23. 23.Best estimate of 7829 ÷ 84? (a) 980 (b) 98 (c) 9800
  24. 24.Best estimate of 1991 ÷ 32? (a) 660 (b) 66 (c) 6600
  25. 25.Best estimate of 390 ÷ 26? (a) 130 (b) 13 (c) 1300
  26. 26.√83 to 1 decimal place? (a) 9.1 (b) 9.0 (c) 8.8 (d) 8.9
  27. 27.Best estimate of 1935 ÷ 37? (a) 48 (b) 4800 (c) 480
  28. 28.Best estimate of 1220 ÷ 22? (a) 610 (b) 6100 (c) 61
  29. 29.Best estimate of 1056 ÷ 32? (a) 35 (b) 350 (c) 3500
  30. 30.√31 to 1 decimal place? (a) 5.5 (b) 5.6 (c) 5.3 (d) 5.4
  31. 31.Best estimate of 2511 ÷ 53? (a) 50 (b) 500 (c) 5000
  32. 32.Best estimate of 1356 ÷ 34? (a) 4500 (b) 450 (c) 45
  33. 33.√78 to 1 decimal place? (a) 8.8 (b) 8.6 (c) 8.7 (d) 8.9
  34. 34.√46 to 1 decimal place? (a) 6.9 (b) 6.6 (c) 6.7 (d) 6.8
  35. 35.Best estimate of 4195 ÷ 76? (a) 52 (b) 5200 (c) 520
  36. 36.√50 to 1 decimal place? (a) 6.9 (b) 7.1 (c) 6.8 (d) 7.0
  37. 37.√61 to 1 decimal place? (a) 7.8 (b) 7.7 (c) 7.6 (d) 7.9
  38. 38.Best estimate of 1421 ÷ 47? (a) 280 (b) 2800 (c) 28
  39. 39.Best estimate of 2252 ÷ 46? (a) 4500 (b) 45 (c) 450
  40. 40.Best estimate of 3534 ÷ 87? (a) 39 (b) 390 (c) 3900

Answer key

  1. 5.5
  2. 54
  3. 9.3
  4. 5.1
  5. 8.4
  6. 8.7
  7. 13
  8. 45
  9. 16
  10. 5.7
  11. 58
  12. 44
  13. 57
  14. 31
  15. 31
  16. 70
  17. 25
  18. 67
  19. 19
  20. 9.7
  21. 7.4
  22. 4.7
  23. 98
  24. 66
  25. 13
  26. 9.1
  27. 48
  28. 61
  29. 35
  30. 5.6
  31. 50
  32. 45
  33. 8.8
  34. 6.8
  35. 52
  36. 7.1
  37. 7.8
  38. 28
  39. 45
  40. 39

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