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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 515 · 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.√45 to 1 decimal place? (a) 7.0 (b) 6.9 (c) 6.8 (d) 6.7
  2. 2.√40 to 1 decimal place? (a) 6.4 (b) 6.3 (c) 6.1 (d) 6.2
  3. 3.Best estimate of 4297 ÷ 89? (a) 4800 (b) 480 (c) 48
  4. 4.√74 to 1 decimal place? (a) 8.7 (b) 8.6 (c) 8.8 (d) 8.9
  5. 5.√79 to 1 decimal place? (a) 8.7 (b) 8.8 (c) 9.0 (d) 8.9
  6. 6.Best estimate of 554 ÷ 34? (a) 18 (b) 180 (c) 1800
  7. 7.Best estimate of 3810 ÷ 76? (a) 480 (b) 48 (c) 4800
  8. 8.√24 to 1 decimal place? (a) 5.0 (b) 4.8 (c) 4.9 (d) 4.7
  9. 9.√37 to 1 decimal place? (a) 6.2 (b) 6.3 (c) 6.4 (d) 6.1
  10. 10.√80 to 1 decimal place? (a) 8.9 (b) 8.6 (c) 8.7 (d) 8.8
  11. 11.Best estimate of 833 ÷ 46? (a) 17 (b) 170 (c) 1700
  12. 12.Best estimate of 722 ÷ 46? (a) 140 (b) 14 (c) 1400
  13. 13.Best estimate of 2073 ÷ 87? (a) 2300 (b) 230 (c) 23
  14. 14.Best estimate of 1985 ÷ 22? (a) 99 (b) 990 (c) 9900
  15. 15.Best estimate of 537 ÷ 39? (a) 130 (b) 13 (c) 1300
  16. 16.√20 to 1 decimal place? (a) 4.3 (b) 4.5 (c) 4.4 (d) 4.6
  17. 17.Best estimate of 2334 ÷ 44? (a) 5800 (b) 580 (c) 58
  18. 18.Best estimate of 4827 ÷ 56? (a) 800 (b) 8000 (c) 80
  19. 19.Best estimate of 4022 ÷ 46? (a) 8000 (b) 800 (c) 80
  20. 20.Best estimate of 481 ÷ 24? (a) 24 (b) 240 (c) 2400
  21. 21.Best estimate of 2482 ÷ 86? (a) 280 (b) 28 (c) 2800
  22. 22.Best estimate of 1846 ÷ 68? (a) 26 (b) 260 (c) 2600
  23. 23.√55 to 1 decimal place? (a) 7.5 (b) 7.6 (c) 7.4 (d) 7.7
  24. 24.√42 to 1 decimal place? (a) 6.6 (b) 6.5 (c) 6.4 (d) 6.3
  25. 25.Best estimate of 1731 ÷ 24? (a) 8700 (b) 870 (c) 87
  26. 26.√35 to 1 decimal place? (a) 6.1 (b) 5.9 (c) 5.8 (d) 6.0
  27. 27.Best estimate of 527 ÷ 28? (a) 1800 (b) 18 (c) 180
  28. 28.Best estimate of 4137 ÷ 61? (a) 690 (b) 6900 (c) 69
  29. 29.Best estimate of 501 ÷ 23? (a) 250 (b) 25 (c) 2500
  30. 30.√34 to 1 decimal place? (a) 5.7 (b) 5.9 (c) 6.0 (d) 5.8
  31. 31.Best estimate of 2349 ÷ 72? (a) 340 (b) 34 (c) 3400
  32. 32.Best estimate of 1879 ÷ 48? (a) 3800 (b) 38 (c) 380
  33. 33.Best estimate of 2022 ÷ 49? (a) 4000 (b) 40 (c) 400
  34. 34.Best estimate of 971 ÷ 24? (a) 4900 (b) 490 (c) 49
  35. 35.Best estimate of 4894 ÷ 86? (a) 5400 (b) 54 (c) 540
  36. 36.Best estimate of 4098 ÷ 57? (a) 680 (b) 6800 (c) 68
  37. 37.Best estimate of 1819 ÷ 34? (a) 6100 (b) 610 (c) 61
  38. 38.Best estimate of 1295 ÷ 66? (a) 1900 (b) 19 (c) 190
  39. 39.√75 to 1 decimal place? (a) 8.8 (b) 8.6 (c) 8.5 (d) 8.7
  40. 40.√31 to 1 decimal place? (a) 5.8 (b) 5.7 (c) 5.5 (d) 5.6

Answer key

  1. 6.7
  2. 6.3
  3. 48
  4. 8.6
  5. 8.9
  6. 18
  7. 48
  8. 4.9
  9. 6.1
  10. 8.9
  11. 17
  12. 14
  13. 23
  14. 99
  15. 13
  16. 4.5
  17. 58
  18. 80
  19. 80
  20. 24
  21. 28
  22. 26
  23. 7.4
  24. 6.5
  25. 87
  26. 5.9
  27. 18
  28. 69
  29. 25
  30. 5.8
  31. 34
  32. 38
  33. 40
  34. 49
  35. 54
  36. 68
  37. 61
  38. 19
  39. 8.7
  40. 5.6

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