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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 109 · 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.√53 to 1 decimal place? (a) 7.3 (b) 7.6 (c) 7.5 (d) 7.4
  2. 2.Best estimate of 3904 ÷ 46? (a) 7800 (b) 780 (c) 78
  3. 3.√88 to 1 decimal place? (a) 9.2 (b) 9.3 (c) 9.4 (d) 9.5
  4. 4.Best estimate of 2608 ÷ 29? (a) 8700 (b) 870 (c) 87
  5. 5.Best estimate of 3093 ÷ 87? (a) 3400 (b) 34 (c) 340
  6. 6.Best estimate of 1585 ÷ 88? (a) 18 (b) 180 (c) 1800
  7. 7.√40 to 1 decimal place? (a) 6.5 (b) 6.2 (c) 6.4 (d) 6.3
  8. 8.Best estimate of 5785 ÷ 83? (a) 72 (b) 7200 (c) 720
  9. 9.√69 to 1 decimal place? (a) 8.0 (b) 8.2 (c) 8.3 (d) 8.1
  10. 10.√28 to 1 decimal place? (a) 5.4 (b) 5.3 (c) 5.1 (d) 5.2
  11. 11.√61 to 1 decimal place? (a) 7.7 (b) 7.8 (c) 7.5 (d) 7.6
  12. 12.Best estimate of 819 ÷ 64? (a) 1400 (b) 14 (c) 140
  13. 13.Best estimate of 1626 ÷ 29? (a) 5400 (b) 54 (c) 540
  14. 14.√85 to 1 decimal place? (a) 9.1 (b) 8.9 (c) 9.2 (d) 9.0
  15. 15.Best estimate of 1124 ÷ 31? (a) 37 (b) 3700 (c) 370
  16. 16.√71 to 1 decimal place? (a) 8.4 (b) 8.2 (c) 8.5 (d) 8.3
  17. 17.Best estimate of 3355 ÷ 38? (a) 8400 (b) 840 (c) 84
  18. 18.√90 to 1 decimal place? (a) 9.5 (b) 9.3 (c) 9.4 (d) 9.2
  19. 19.Best estimate of 6668 ÷ 81? (a) 83 (b) 830 (c) 8300
  20. 20.Best estimate of 3011 ÷ 36? (a) 7500 (b) 750 (c) 75
  21. 21.√42 to 1 decimal place? (a) 6.8 (b) 6.6 (c) 6.7 (d) 6.5
  22. 22.Best estimate of 750 ÷ 24? (a) 3800 (b) 380 (c) 38
  23. 23.√89 to 1 decimal place? (a) 9.3 (b) 9.5 (c) 9.4 (d) 9.6
  24. 24.Best estimate of 2307 ÷ 72? (a) 3300 (b) 33 (c) 330
  25. 25.Best estimate of 2323 ÷ 46? (a) 4600 (b) 460 (c) 46
  26. 26.Best estimate of 5914 ÷ 87? (a) 66 (b) 660 (c) 6600
  27. 27.Best estimate of 2569 ÷ 73? (a) 3700 (b) 370 (c) 37
  28. 28.Best estimate of 1522 ÷ 56? (a) 25 (b) 250 (c) 2500
  29. 29.Best estimate of 1751 ÷ 56? (a) 29 (b) 290 (c) 2900
  30. 30.√46 to 1 decimal place? (a) 6.7 (b) 6.8 (c) 6.9 (d) 6.6
  31. 31.√51 to 1 decimal place? (a) 7.0 (b) 6.9 (c) 7.1 (d) 6.8
  32. 32.Best estimate of 2517 ÷ 41? (a) 63 (b) 6300 (c) 630
  33. 33.√92 to 1 decimal place? (a) 9.3 (b) 9.5 (c) 9.6 (d) 9.4
  34. 34.√20 to 1 decimal place? (a) 4.3 (b) 4.4 (c) 4.6 (d) 4.5
  35. 35.√83 to 1 decimal place? (a) 9.1 (b) 9.2 (c) 9.3 (d) 9.0
  36. 36.√37 to 1 decimal place? (a) 6.0 (b) 6.2 (c) 6.3 (d) 6.1
  37. 37.Best estimate of 2590 ÷ 78? (a) 320 (b) 3200 (c) 32
  38. 38.√35 to 1 decimal place? (a) 5.8 (b) 6.1 (c) 5.9 (d) 6.0
  39. 39.√58 to 1 decimal place? (a) 7.7 (b) 7.4 (c) 7.6 (d) 7.5
  40. 40.Best estimate of 4032 ÷ 49? (a) 81 (b) 8100 (c) 810

Answer key

  1. 7.3
  2. 78
  3. 9.4
  4. 87
  5. 34
  6. 18
  7. 6.3
  8. 72
  9. 8.3
  10. 5.3
  11. 7.8
  12. 14
  13. 54
  14. 9.2
  15. 37
  16. 8.4
  17. 84
  18. 9.5
  19. 83
  20. 75
  21. 6.5
  22. 38
  23. 9.4
  24. 33
  25. 46
  26. 66
  27. 37
  28. 25
  29. 29
  30. 6.8
  31. 7.1
  32. 63
  33. 9.6
  34. 4.5
  35. 9.1
  36. 6.1
  37. 32
  38. 5.9
  39. 7.6
  40. 81

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