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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 298 · 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 2211 ÷ 67? (a) 3200 (b) 32 (c) 320
  2. 2.Best estimate of 5790 ÷ 68? (a) 8300 (b) 83 (c) 830
  3. 3.√96 to 1 decimal place? (a) 9.9 (b) 9.8 (c) 9.6 (d) 9.7
  4. 4.Best estimate of 1428 ÷ 27? (a) 480 (b) 48 (c) 4800
  5. 5.Best estimate of 2054 ÷ 39? (a) 510 (b) 5100 (c) 51
  6. 6.√34 to 1 decimal place? (a) 5.8 (b) 5.6 (c) 5.7 (d) 5.9
  7. 7.Best estimate of 6648 ÷ 83? (a) 8300 (b) 83 (c) 830
  8. 8.√53 to 1 decimal place? (a) 7.3 (b) 7.4 (c) 7.6 (d) 7.5
  9. 9.Best estimate of 365 ÷ 24? (a) 18 (b) 180 (c) 1800
  10. 10.Best estimate of 4216 ÷ 66? (a) 6000 (b) 600 (c) 60
  11. 11.Best estimate of 7756 ÷ 82? (a) 970 (b) 9700 (c) 97
  12. 12.√74 to 1 decimal place? (a) 8.4 (b) 8.3 (c) 8.6 (d) 8.5
  13. 13.√23 to 1 decimal place? (a) 5.0 (b) 4.8 (c) 4.7 (d) 4.9
  14. 14.√82 to 1 decimal place? (a) 9.3 (b) 9.2 (c) 9.1 (d) 9.4
  15. 15.Best estimate of 2077 ÷ 77? (a) 26 (b) 2600 (c) 260
  16. 16.Best estimate of 6264 ÷ 81? (a) 780 (b) 7800 (c) 78
  17. 17.Best estimate of 5028 ÷ 86? (a) 560 (b) 5600 (c) 56
  18. 18.√40 to 1 decimal place? (a) 6.4 (b) 6.2 (c) 6.5 (d) 6.3
  19. 19.Best estimate of 4495 ÷ 62? (a) 75 (b) 750 (c) 7500
  20. 20.Best estimate of 4787 ÷ 66? (a) 68 (b) 680 (c) 6800
  21. 21.Best estimate of 1040 ÷ 21? (a) 520 (b) 5200 (c) 52
  22. 22.Best estimate of 3820 ÷ 66? (a) 5500 (b) 550 (c) 55
  23. 23.√27 to 1 decimal place? (a) 5.3 (b) 5.4 (c) 5.2 (d) 5.5
  24. 24.Best estimate of 1590 ÷ 62? (a) 27 (b) 2700 (c) 270
  25. 25.√92 to 1 decimal place? (a) 9.5 (b) 9.7 (c) 9.6 (d) 9.4
  26. 26.Best estimate of 2514 ÷ 31? (a) 8400 (b) 84 (c) 840
  27. 27.√21 to 1 decimal place? (a) 4.6 (b) 4.3 (c) 4.5 (d) 4.4
  28. 28.√80 to 1 decimal place? (a) 8.8 (b) 8.6 (c) 8.7 (d) 8.9
  29. 29.√26 to 1 decimal place? (a) 5.4 (b) 5.3 (c) 5.2 (d) 5.1
  30. 30.Best estimate of 1750 ÷ 26? (a) 580 (b) 58 (c) 5800
  31. 31.Best estimate of 4773 ÷ 89? (a) 530 (b) 5300 (c) 53
  32. 32.Best estimate of 2400 ÷ 89? (a) 2700 (b) 270 (c) 27
  33. 33.√43 to 1 decimal place? (a) 6.5 (b) 6.7 (c) 6.6 (d) 6.8
  34. 34.√85 to 1 decimal place? (a) 9.3 (b) 9.5 (c) 9.4 (d) 9.2
  35. 35.√84 to 1 decimal place? (a) 9.2 (b) 9.1 (c) 8.9 (d) 9.0
  36. 36.√67 to 1 decimal place? (a) 8.3 (b) 8.4 (c) 8.2 (d) 8.5
  37. 37.Best estimate of 1390 ÷ 66? (a) 20 (b) 2000 (c) 200
  38. 38.Best estimate of 5691 ÷ 71? (a) 8100 (b) 81 (c) 810
  39. 39.√78 to 1 decimal place? (a) 8.7 (b) 9.0 (c) 8.8 (d) 8.9
  40. 40.√55 to 1 decimal place? (a) 7.4 (b) 7.5 (c) 7.6 (d) 7.7

Answer key

  1. 32
  2. 83
  3. 9.8
  4. 48
  5. 51
  6. 5.8
  7. 83
  8. 7.3
  9. 18
  10. 60
  11. 97
  12. 8.6
  13. 4.8
  14. 9.1
  15. 26
  16. 78
  17. 56
  18. 6.3
  19. 75
  20. 68
  21. 52
  22. 55
  23. 5.2
  24. 27
  25. 9.6
  26. 84
  27. 4.6
  28. 8.9
  29. 5.1
  30. 58
  31. 53
  32. 27
  33. 6.6
  34. 9.2
  35. 9.2
  36. 8.2
  37. 20
  38. 81
  39. 8.8
  40. 7.4

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