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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 12 · 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 5155 ÷ 86? (a) 570 (b) 57 (c) 5700
  2. 2.Best estimate of 1214 ÷ 82? (a) 150 (b) 15 (c) 1500
  3. 3.Best estimate of 1660 ÷ 32? (a) 550 (b) 55 (c) 5500
  4. 4.Best estimate of 2038 ÷ 29? (a) 6800 (b) 680 (c) 68
  5. 5.√85 to 1 decimal place? (a) 9.3 (b) 9.5 (c) 9.4 (d) 9.2
  6. 6.√92 to 1 decimal place? (a) 9.5 (b) 9.6 (c) 9.4 (d) 9.7
  7. 7.√26 to 1 decimal place? (a) 4.9 (b) 5.0 (c) 5.1 (d) 5.2
  8. 8.Best estimate of 753 ÷ 47? (a) 150 (b) 1500 (c) 15
  9. 9.√65 to 1 decimal place? (a) 8.3 (b) 8.2 (c) 8.1 (d) 8.4
  10. 10.√27 to 1 decimal place? (a) 5.2 (b) 5.3 (c) 5.1 (d) 5.4
  11. 11.Best estimate of 1411 ÷ 26? (a) 47 (b) 4700 (c) 470
  12. 12.Best estimate of 4238 ÷ 77? (a) 5300 (b) 530 (c) 53
  13. 13.√74 to 1 decimal place? (a) 8.3 (b) 8.5 (c) 8.6 (d) 8.4
  14. 14.√34 to 1 decimal place? (a) 6.0 (b) 5.7 (c) 5.8 (d) 5.9
  15. 15.√48 to 1 decimal place? (a) 7.0 (b) 7.1 (c) 6.9 (d) 6.8
  16. 16.√61 to 1 decimal place? (a) 7.9 (b) 7.6 (c) 7.8 (d) 7.7
  17. 17.Best estimate of 2310 ÷ 37? (a) 5800 (b) 580 (c) 58
  18. 18.√76 to 1 decimal place? (a) 9.0 (b) 8.9 (c) 8.7 (d) 8.8
  19. 19.√37 to 1 decimal place? (a) 5.9 (b) 6.1 (c) 5.8 (d) 6.0
  20. 20.Best estimate of 2399 ÷ 29? (a) 800 (b) 8000 (c) 80
  21. 21.√70 to 1 decimal place? (a) 8.5 (b) 8.7 (c) 8.6 (d) 8.4
  22. 22.√21 to 1 decimal place? (a) 4.5 (b) 4.4 (c) 4.7 (d) 4.6
  23. 23.Best estimate of 1783 ÷ 76? (a) 2200 (b) 22 (c) 220
  24. 24.Best estimate of 1800 ÷ 77? (a) 230 (b) 23 (c) 2300
  25. 25.√32 to 1 decimal place? (a) 5.9 (b) 5.7 (c) 5.6 (d) 5.8
  26. 26.Best estimate of 3237 ÷ 34? (a) 108 (b) 10800 (c) 1080
  27. 27.Best estimate of 2388 ÷ 27? (a) 800 (b) 8000 (c) 80
  28. 28.√94 to 1 decimal place? (a) 9.6 (b) 9.4 (c) 9.5 (d) 9.7
  29. 29.Best estimate of 1921 ÷ 58? (a) 32 (b) 320 (c) 3200
  30. 30.Best estimate of 1757 ÷ 32? (a) 590 (b) 59 (c) 5900
  31. 31.Best estimate of 4602 ÷ 53? (a) 920 (b) 9200 (c) 92
  32. 32.Best estimate of 836 ÷ 51? (a) 17 (b) 170 (c) 1700
  33. 33.Best estimate of 4196 ÷ 62? (a) 700 (b) 70 (c) 7000
  34. 34.Best estimate of 3062 ÷ 62? (a) 51 (b) 510 (c) 5100
  35. 35.Best estimate of 1194 ÷ 51? (a) 24 (b) 2400 (c) 240
  36. 36.Best estimate of 2427 ÷ 56? (a) 4000 (b) 40 (c) 400
  37. 37.Best estimate of 4361 ÷ 63? (a) 7300 (b) 730 (c) 73
  38. 38.√82 to 1 decimal place? (a) 9.2 (b) 9.3 (c) 9.0 (d) 9.1
  39. 39.Best estimate of 1521 ÷ 32? (a) 5100 (b) 510 (c) 51
  40. 40.Best estimate of 6211 ÷ 81? (a) 780 (b) 78 (c) 7800

Answer key

  1. 57
  2. 15
  3. 55
  4. 68
  5. 9.2
  6. 9.6
  7. 5.1
  8. 15
  9. 8.1
  10. 5.2
  11. 47
  12. 53
  13. 8.6
  14. 5.8
  15. 6.9
  16. 7.8
  17. 58
  18. 8.7
  19. 6.1
  20. 80
  21. 8.4
  22. 4.6
  23. 22
  24. 23
  25. 5.7
  26. 108
  27. 80
  28. 9.7
  29. 32
  30. 59
  31. 92
  32. 17
  33. 70
  34. 51
  35. 24
  36. 40
  37. 73
  38. 9.1
  39. 51
  40. 78

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