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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 990 · 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 2411 ÷ 56? (a) 4000 (b) 40 (c) 400
  2. 2.Best estimate of 3186 ÷ 42? (a) 8000 (b) 80 (c) 800
  3. 3.Best estimate of 829 ÷ 26? (a) 2800 (b) 28 (c) 280
  4. 4.Best estimate of 4423 ÷ 66? (a) 63 (b) 6300 (c) 630
  5. 5.√77 to 1 decimal place? (a) 8.6 (b) 8.7 (c) 8.5 (d) 8.8
  6. 6.Best estimate of 1660 ÷ 52? (a) 3300 (b) 33 (c) 330
  7. 7.Best estimate of 4653 ÷ 83? (a) 580 (b) 5800 (c) 58
  8. 8.Best estimate of 434 ÷ 36? (a) 11 (b) 110 (c) 1100
  9. 9.Best estimate of 1201 ÷ 52? (a) 2400 (b) 24 (c) 240
  10. 10.√23 to 1 decimal place? (a) 4.8 (b) 4.9 (c) 5.0 (d) 5.1
  11. 11.Best estimate of 1833 ÷ 26? (a) 61 (b) 6100 (c) 610
  12. 12.√58 to 1 decimal place? (a) 7.7 (b) 7.8 (c) 7.6 (d) 7.9
  13. 13.Best estimate of 1367 ÷ 82? (a) 170 (b) 1700 (c) 17
  14. 14.√53 to 1 decimal place? (a) 7.6 (b) 7.5 (c) 7.3 (d) 7.4
  15. 15.√55 to 1 decimal place? (a) 7.5 (b) 7.4 (c) 7.6 (d) 7.3
  16. 16.√38 to 1 decimal place? (a) 6.4 (b) 6.2 (c) 6.3 (d) 6.5
  17. 17.√65 to 1 decimal place? (a) 8.4 (b) 8.1 (c) 8.2 (d) 8.3
  18. 18.√83 to 1 decimal place? (a) 9.1 (b) 8.9 (c) 8.8 (d) 9.0
  19. 19.Best estimate of 2029 ÷ 34? (a) 6800 (b) 680 (c) 68
  20. 20.Best estimate of 1105 ÷ 38? (a) 280 (b) 28 (c) 2800
  21. 21.Best estimate of 3013 ÷ 48? (a) 60 (b) 6000 (c) 600
  22. 22.√66 to 1 decimal place? (a) 8.0 (b) 8.3 (c) 8.2 (d) 8.1
  23. 23.Best estimate of 2026 ÷ 23? (a) 10100 (b) 1010 (c) 101
  24. 24.Best estimate of 3693 ÷ 42? (a) 920 (b) 9200 (c) 92
  25. 25.√71 to 1 decimal place? (a) 8.3 (b) 8.4 (c) 8.5 (d) 8.6
  26. 26.√30 to 1 decimal place? (a) 5.3 (b) 5.4 (c) 5.5 (d) 5.2
  27. 27.Best estimate of 6179 ÷ 76? (a) 770 (b) 77 (c) 7700
  28. 28.√59 to 1 decimal place? (a) 7.6 (b) 7.5 (c) 7.8 (d) 7.7
  29. 29.√72 to 1 decimal place? (a) 8.7 (b) 8.5 (c) 8.6 (d) 8.4
  30. 30.Best estimate of 2341 ÷ 26? (a) 7800 (b) 780 (c) 78
  31. 31.Best estimate of 1786 ÷ 61? (a) 3000 (b) 300 (c) 30
  32. 32.√78 to 1 decimal place? (a) 9.0 (b) 8.7 (c) 8.8 (d) 8.9
  33. 33.Best estimate of 1844 ÷ 32? (a) 61 (b) 6100 (c) 610
  34. 34.√61 to 1 decimal place? (a) 7.5 (b) 7.6 (c) 7.7 (d) 7.8
  35. 35.Best estimate of 2723 ÷ 53? (a) 540 (b) 5400 (c) 54
  36. 36.Best estimate of 1087 ÷ 28? (a) 3600 (b) 36 (c) 360
  37. 37.Best estimate of 1004 ÷ 52? (a) 20 (b) 2000 (c) 200
  38. 38.√98 to 1 decimal place? (a) 9.9 (b) 9.8 (c) 9.6 (d) 9.7
  39. 39.Best estimate of 1222 ÷ 64? (a) 20 (b) 2000 (c) 200
  40. 40.Best estimate of 4506 ÷ 82? (a) 56 (b) 5600 (c) 560

Answer key

  1. 40
  2. 80
  3. 28
  4. 63
  5. 8.8
  6. 33
  7. 58
  8. 11
  9. 24
  10. 4.8
  11. 61
  12. 7.6
  13. 17
  14. 7.3
  15. 7.4
  16. 6.2
  17. 8.1
  18. 9.1
  19. 68
  20. 28
  21. 60
  22. 8.1
  23. 101
  24. 92
  25. 8.4
  26. 5.5
  27. 77
  28. 7.7
  29. 8.5
  30. 78
  31. 30
  32. 8.8
  33. 61
  34. 7.8
  35. 54
  36. 36
  37. 20
  38. 9.9
  39. 20
  40. 56

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