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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 938 · 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.√76 to 1 decimal place? (a) 8.6 (b) 8.7 (c) 8.4 (d) 8.5
  2. 2.Best estimate of 691 ÷ 36? (a) 17 (b) 1700 (c) 170
  3. 3.√94 to 1 decimal place? (a) 9.5 (b) 9.7 (c) 9.6 (d) 9.4
  4. 4.√82 to 1 decimal place? (a) 9.1 (b) 8.9 (c) 9.0 (d) 9.2
  5. 5.Best estimate of 2430 ÷ 53? (a) 49 (b) 490 (c) 4900
  6. 6.√31 to 1 decimal place? (a) 5.6 (b) 5.7 (c) 5.5 (d) 5.4
  7. 7.Best estimate of 5253 ÷ 88? (a) 5800 (b) 58 (c) 580
  8. 8.Best estimate of 3049 ÷ 34? (a) 102 (b) 1020 (c) 10200
  9. 9.√80 to 1 decimal place? (a) 9.0 (b) 8.8 (c) 8.9 (d) 8.7
  10. 10.Best estimate of 722 ÷ 53? (a) 140 (b) 1400 (c) 14
  11. 11.√96 to 1 decimal place? (a) 9.9 (b) 9.7 (c) 9.6 (d) 9.8
  12. 12.Best estimate of 6079 ÷ 71? (a) 87 (b) 870 (c) 8700
  13. 13.Best estimate of 2812 ÷ 47? (a) 560 (b) 56 (c) 5600
  14. 14.Best estimate of 1582 ÷ 81? (a) 200 (b) 2000 (c) 20
  15. 15.Best estimate of 1795 ÷ 71? (a) 2600 (b) 260 (c) 26
  16. 16.√74 to 1 decimal place? (a) 8.6 (b) 8.5 (c) 8.7 (d) 8.4
  17. 17.√75 to 1 decimal place? (a) 8.6 (b) 8.7 (c) 8.5 (d) 8.8
  18. 18.√58 to 1 decimal place? (a) 7.5 (b) 7.4 (c) 7.6 (d) 7.7
  19. 19.√29 to 1 decimal place? (a) 5.3 (b) 5.2 (c) 5.1 (d) 5.4
  20. 20.Best estimate of 3677 ÷ 66? (a) 530 (b) 53 (c) 5300
  21. 21.√63 to 1 decimal place? (a) 7.8 (b) 7.9 (c) 7.7 (d) 8.0
  22. 22.√92 to 1 decimal place? (a) 9.5 (b) 9.7 (c) 9.6 (d) 9.8
  23. 23.Best estimate of 2112 ÷ 34? (a) 700 (b) 70 (c) 7000
  24. 24.Best estimate of 3712 ÷ 82? (a) 460 (b) 4600 (c) 46
  25. 25.√61 to 1 decimal place? (a) 7.9 (b) 7.7 (c) 7.8 (d) 8.0
  26. 26.Best estimate of 5624 ÷ 62? (a) 940 (b) 9400 (c) 94
  27. 27.√66 to 1 decimal place? (a) 8.3 (b) 8.2 (c) 8.4 (d) 8.1
  28. 28.Best estimate of 1832 ÷ 36? (a) 460 (b) 46 (c) 4600
  29. 29.Best estimate of 1789 ÷ 69? (a) 2600 (b) 260 (c) 26
  30. 30.√55 to 1 decimal place? (a) 7.5 (b) 7.4 (c) 7.2 (d) 7.3
  31. 31.Best estimate of 874 ÷ 37? (a) 2200 (b) 220 (c) 22
  32. 32.√90 to 1 decimal place? (a) 9.3 (b) 9.5 (c) 9.2 (d) 9.4
  33. 33.Best estimate of 2171 ÷ 42? (a) 5400 (b) 540 (c) 54
  34. 34.Best estimate of 2597 ÷ 42? (a) 650 (b) 6500 (c) 65
  35. 35.√21 to 1 decimal place? (a) 4.5 (b) 4.4 (c) 4.6 (d) 4.3
  36. 36.Best estimate of 3081 ÷ 72? (a) 440 (b) 44 (c) 4400
  37. 37.Best estimate of 800 ÷ 62? (a) 130 (b) 1300 (c) 13
  38. 38.Best estimate of 608 ÷ 44? (a) 1500 (b) 150 (c) 15
  39. 39.Best estimate of 1065 ÷ 32? (a) 3600 (b) 36 (c) 360
  40. 40.√62 to 1 decimal place? (a) 8.0 (b) 7.7 (c) 7.8 (d) 7.9

Answer key

  1. 8.7
  2. 17
  3. 9.7
  4. 9.1
  5. 49
  6. 5.6
  7. 58
  8. 102
  9. 8.9
  10. 14
  11. 9.8
  12. 87
  13. 56
  14. 20
  15. 26
  16. 8.6
  17. 8.7
  18. 7.6
  19. 5.4
  20. 53
  21. 7.9
  22. 9.6
  23. 70
  24. 46
  25. 7.8
  26. 94
  27. 8.1
  28. 46
  29. 26
  30. 7.4
  31. 22
  32. 9.5
  33. 54
  34. 65
  35. 4.6
  36. 44
  37. 13
  38. 15
  39. 36
  40. 7.9

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