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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 359 · 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 4973 ÷ 79? (a) 6200 (b) 620 (c) 62
  2. 2.Best estimate of 1558 ÷ 29? (a) 52 (b) 5200 (c) 520
  3. 3.√74 to 1 decimal place? (a) 8.8 (b) 8.7 (c) 8.6 (d) 8.5
  4. 4.Best estimate of 2971 ÷ 33? (a) 9900 (b) 99 (c) 990
  5. 5.Best estimate of 5916 ÷ 62? (a) 9900 (b) 99 (c) 990
  6. 6.Best estimate of 798 ÷ 32? (a) 2700 (b) 270 (c) 27
  7. 7.Best estimate of 340 ÷ 22? (a) 1700 (b) 170 (c) 17
  8. 8.√29 to 1 decimal place? (a) 5.4 (b) 5.7 (c) 5.5 (d) 5.6
  9. 9.√82 to 1 decimal place? (a) 8.8 (b) 8.9 (c) 9.0 (d) 9.1
  10. 10.√76 to 1 decimal place? (a) 8.7 (b) 8.5 (c) 8.6 (d) 8.8
  11. 11.√50 to 1 decimal place? (a) 6.8 (b) 6.9 (c) 7.0 (d) 7.1
  12. 12.√45 to 1 decimal place? (a) 6.7 (b) 6.6 (c) 6.8 (d) 6.9
  13. 13.√77 to 1 decimal place? (a) 8.8 (b) 8.7 (c) 8.9 (d) 9.0
  14. 14.√53 to 1 decimal place? (a) 7.2 (b) 7.3 (c) 7.1 (d) 7.4
  15. 15.Best estimate of 5883 ÷ 64? (a) 9800 (b) 980 (c) 98
  16. 16.√47 to 1 decimal place? (a) 6.6 (b) 6.9 (c) 6.7 (d) 6.8
  17. 17.√31 to 1 decimal place? (a) 5.7 (b) 5.4 (c) 5.6 (d) 5.5
  18. 18.Best estimate of 4401 ÷ 62? (a) 73 (b) 7300 (c) 730
  19. 19.Best estimate of 2614 ÷ 34? (a) 8700 (b) 87 (c) 870
  20. 20.Best estimate of 4714 ÷ 84? (a) 5900 (b) 590 (c) 59
  21. 21.Best estimate of 3201 ÷ 68? (a) 460 (b) 4600 (c) 46
  22. 22.√23 to 1 decimal place? (a) 4.5 (b) 4.6 (c) 4.8 (d) 4.7
  23. 23.Best estimate of 3519 ÷ 84? (a) 4400 (b) 440 (c) 44
  24. 24.Best estimate of 2353 ÷ 76? (a) 290 (b) 29 (c) 2900
  25. 25.Best estimate of 942 ÷ 26? (a) 31 (b) 310 (c) 3100
  26. 26.√59 to 1 decimal place? (a) 7.9 (b) 8.0 (c) 7.8 (d) 7.7
  27. 27.Best estimate of 3191 ÷ 34? (a) 1060 (b) 10600 (c) 106
  28. 28.√55 to 1 decimal place? (a) 7.5 (b) 7.4 (c) 7.2 (d) 7.3
  29. 29.√22 to 1 decimal place? (a) 4.6 (b) 4.5 (c) 4.7 (d) 4.8
  30. 30.√94 to 1 decimal place? (a) 10.0 (b) 9.8 (c) 9.7 (d) 9.9
  31. 31.Best estimate of 2621 ÷ 32? (a) 87 (b) 8700 (c) 870
  32. 32.Best estimate of 1089 ÷ 58? (a) 180 (b) 18 (c) 1800
  33. 33.Best estimate of 1286 ÷ 39? (a) 3200 (b) 320 (c) 32
  34. 34.√69 to 1 decimal place? (a) 8.4 (b) 8.1 (c) 8.3 (d) 8.2
  35. 35.Best estimate of 2141 ÷ 42? (a) 540 (b) 5400 (c) 54
  36. 36.√30 to 1 decimal place? (a) 5.5 (b) 5.7 (c) 5.8 (d) 5.6
  37. 37.Best estimate of 5492 ÷ 86? (a) 610 (b) 6100 (c) 61
  38. 38.Best estimate of 5981 ÷ 63? (a) 1000 (b) 10000 (c) 100
  39. 39.√89 to 1 decimal place? (a) 9.3 (b) 9.4 (c) 9.5 (d) 9.2
  40. 40.Best estimate of 2100 ÷ 29? (a) 70 (b) 7000 (c) 700

Answer key

  1. 62
  2. 52
  3. 8.6
  4. 99
  5. 99
  6. 27
  7. 17
  8. 5.4
  9. 9.1
  10. 8.7
  11. 7.1
  12. 6.7
  13. 8.8
  14. 7.3
  15. 98
  16. 6.9
  17. 5.6
  18. 73
  19. 87
  20. 59
  21. 46
  22. 4.8
  23. 44
  24. 29
  25. 31
  26. 7.7
  27. 106
  28. 7.4
  29. 4.7
  30. 9.7
  31. 87
  32. 18
  33. 32
  34. 8.3
  35. 54
  36. 5.5
  37. 61
  38. 100
  39. 9.4
  40. 70

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