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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 601 · 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.√32 to 1 decimal place? (a) 5.8 (b) 5.7 (c) 5.5 (d) 5.6
  2. 2.√98 to 1 decimal place? (a) 9.8 (b) 9.9 (c) 10.0 (d) 9.7
  3. 3.Best estimate of 1740 ÷ 38? (a) 440 (b) 4400 (c) 44
  4. 4.√83 to 1 decimal place? (a) 9.1 (b) 9.0 (c) 9.2 (d) 8.9
  5. 5.√69 to 1 decimal place? (a) 8.3 (b) 8.4 (c) 8.5 (d) 8.6
  6. 6.Best estimate of 2698 ÷ 34? (a) 9000 (b) 90 (c) 900
  7. 7.Best estimate of 5695 ÷ 86? (a) 6300 (b) 63 (c) 630
  8. 8.Best estimate of 3602 ÷ 74? (a) 510 (b) 5100 (c) 51
  9. 9.√92 to 1 decimal place? (a) 9.7 (b) 9.6 (c) 9.5 (d) 9.4
  10. 10.√27 to 1 decimal place? (a) 5.5 (b) 5.3 (c) 5.2 (d) 5.4
  11. 11.√38 to 1 decimal place? (a) 6.1 (b) 5.9 (c) 6.2 (d) 6.0
  12. 12.Best estimate of 3382 ÷ 53? (a) 6800 (b) 680 (c) 68
  13. 13.Best estimate of 1974 ÷ 41? (a) 49 (b) 490 (c) 4900
  14. 14.Best estimate of 4540 ÷ 54? (a) 910 (b) 9100 (c) 91
  15. 15.√65 to 1 decimal place? (a) 7.9 (b) 8.1 (c) 7.8 (d) 8.0
  16. 16.Best estimate of 868 ÷ 51? (a) 170 (b) 17 (c) 1700
  17. 17.√48 to 1 decimal place? (a) 6.8 (b) 6.9 (c) 6.7 (d) 7.0
  18. 18.Best estimate of 5684 ÷ 66? (a) 810 (b) 81 (c) 8100
  19. 19.√89 to 1 decimal place? (a) 9.5 (b) 9.3 (c) 9.2 (d) 9.4
  20. 20.Best estimate of 1269 ÷ 47? (a) 2500 (b) 250 (c) 25
  21. 21.√55 to 1 decimal place? (a) 7.2 (b) 7.3 (c) 7.5 (d) 7.4
  22. 22.√58 to 1 decimal place? (a) 7.4 (b) 7.3 (c) 7.5 (d) 7.6
  23. 23.Best estimate of 1805 ÷ 36? (a) 4500 (b) 45 (c) 450
  24. 24.√61 to 1 decimal place? (a) 7.8 (b) 7.7 (c) 7.6 (d) 7.5
  25. 25.√90 to 1 decimal place? (a) 9.5 (b) 9.4 (c) 9.6 (d) 9.7
  26. 26.√51 to 1 decimal place? (a) 7.2 (b) 7.4 (c) 7.1 (d) 7.3
  27. 27.√79 to 1 decimal place? (a) 9.0 (b) 9.1 (c) 8.9 (d) 8.8
  28. 28.√26 to 1 decimal place? (a) 5.2 (b) 5.4 (c) 5.1 (d) 5.3
  29. 29.√43 to 1 decimal place? (a) 6.7 (b) 6.9 (c) 6.8 (d) 6.6
  30. 30.Best estimate of 1611 ÷ 38? (a) 400 (b) 4000 (c) 40
  31. 31.Best estimate of 4807 ÷ 68? (a) 690 (b) 69 (c) 6900
  32. 32.Best estimate of 1747 ÷ 47? (a) 3500 (b) 350 (c) 35
  33. 33.√74 to 1 decimal place? (a) 8.8 (b) 8.5 (c) 8.6 (d) 8.7
  34. 34.√21 to 1 decimal place? (a) 4.8 (b) 4.7 (c) 4.5 (d) 4.6
  35. 35.√28 to 1 decimal place? (a) 5.5 (b) 5.4 (c) 5.3 (d) 5.6
  36. 36.Best estimate of 5729 ÷ 61? (a) 95 (b) 9500 (c) 950
  37. 37.Best estimate of 400 ÷ 23? (a) 20 (b) 2000 (c) 200
  38. 38.Best estimate of 480 ÷ 32? (a) 16 (b) 160 (c) 1600
  39. 39.Best estimate of 561 ÷ 43? (a) 14 (b) 140 (c) 1400
  40. 40.√45 to 1 decimal place? (a) 6.7 (b) 6.5 (c) 6.4 (d) 6.6

Answer key

  1. 5.7
  2. 9.9
  3. 44
  4. 9.1
  5. 8.3
  6. 90
  7. 63
  8. 51
  9. 9.6
  10. 5.2
  11. 6.2
  12. 68
  13. 49
  14. 91
  15. 8.1
  16. 17
  17. 6.9
  18. 81
  19. 9.4
  20. 25
  21. 7.4
  22. 7.6
  23. 45
  24. 7.8
  25. 9.5
  26. 7.1
  27. 8.9
  28. 5.1
  29. 6.6
  30. 40
  31. 69
  32. 35
  33. 8.6
  34. 4.6
  35. 5.3
  36. 95
  37. 20
  38. 16
  39. 14
  40. 6.7

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