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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 173 · 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.√42 to 1 decimal place? (a) 6.4 (b) 6.5 (c) 6.6 (d) 6.7
  2. 2.√96 to 1 decimal place? (a) 9.7 (b) 9.5 (c) 9.8 (d) 9.6
  3. 3.Best estimate of 2225 ÷ 41? (a) 5600 (b) 56 (c) 560
  4. 4.Best estimate of 7477 ÷ 86? (a) 83 (b) 830 (c) 8300
  5. 5.Best estimate of 2027 ÷ 46? (a) 41 (b) 410 (c) 4100
  6. 6.√26 to 1 decimal place? (a) 5.0 (b) 5.2 (c) 4.9 (d) 5.1
  7. 7.√31 to 1 decimal place? (a) 5.4 (b) 5.6 (c) 5.5 (d) 5.7
  8. 8.Best estimate of 2111 ÷ 73? (a) 300 (b) 30 (c) 3000
  9. 9.√71 to 1 decimal place? (a) 8.3 (b) 8.4 (c) 8.5 (d) 8.2
  10. 10.√87 to 1 decimal place? (a) 9.2 (b) 9.4 (c) 9.5 (d) 9.3
  11. 11.Best estimate of 1834 ÷ 38? (a) 460 (b) 46 (c) 4600
  12. 12.Best estimate of 863 ÷ 66? (a) 12 (b) 1200 (c) 120
  13. 13.Best estimate of 1862 ÷ 64? (a) 31 (b) 310 (c) 3100
  14. 14.√61 to 1 decimal place? (a) 7.8 (b) 8.0 (c) 7.9 (d) 8.1
  15. 15.√27 to 1 decimal place? (a) 5.0 (b) 5.2 (c) 5.1 (d) 4.9
  16. 16.Best estimate of 545 ÷ 32? (a) 1800 (b) 18 (c) 180
  17. 17.Best estimate of 1642 ÷ 43? (a) 4100 (b) 410 (c) 41
  18. 18.Best estimate of 2488 ÷ 42? (a) 620 (b) 6200 (c) 62
  19. 19.√94 to 1 decimal place? (a) 9.8 (b) 9.7 (c) 9.6 (d) 9.9
  20. 20.Best estimate of 2306 ÷ 52? (a) 460 (b) 4600 (c) 46
  21. 21.√30 to 1 decimal place? (a) 5.7 (b) 5.6 (c) 5.5 (d) 5.4
  22. 22.Best estimate of 1333 ÷ 61? (a) 2200 (b) 22 (c) 220
  23. 23.√85 to 1 decimal place? (a) 9.5 (b) 9.4 (c) 9.3 (d) 9.2
  24. 24.Best estimate of 3130 ÷ 54? (a) 630 (b) 63 (c) 6300
  25. 25.√79 to 1 decimal place? (a) 8.8 (b) 8.9 (c) 9.1 (d) 9.0
  26. 26.Best estimate of 1482 ÷ 32? (a) 4900 (b) 490 (c) 49
  27. 27.√90 to 1 decimal place? (a) 9.7 (b) 9.5 (c) 9.4 (d) 9.6
  28. 28.Best estimate of 6106 ÷ 86? (a) 6800 (b) 68 (c) 680
  29. 29.Best estimate of 1575 ÷ 81? (a) 20 (b) 2000 (c) 200
  30. 30.Best estimate of 4403 ÷ 49? (a) 880 (b) 88 (c) 8800
  31. 31.Best estimate of 1309 ÷ 53? (a) 2600 (b) 260 (c) 26
  32. 32.Best estimate of 682 ÷ 46? (a) 14 (b) 1400 (c) 140
  33. 33.√35 to 1 decimal place? (a) 5.9 (b) 5.7 (c) 5.6 (d) 5.8
  34. 34.√50 to 1 decimal place? (a) 7.3 (b) 7.1 (c) 7.2 (d) 7.0
  35. 35.√58 to 1 decimal place? (a) 7.7 (b) 7.8 (c) 7.6 (d) 7.9
  36. 36.√55 to 1 decimal place? (a) 7.7 (b) 7.4 (c) 7.5 (d) 7.6
  37. 37.√92 to 1 decimal place? (a) 9.4 (b) 9.5 (c) 9.3 (d) 9.6
  38. 38.Best estimate of 3759 ÷ 67? (a) 540 (b) 54 (c) 5400
  39. 39.Best estimate of 2529 ÷ 44? (a) 630 (b) 63 (c) 6300
  40. 40.Best estimate of 6689 ÷ 83? (a) 840 (b) 84 (c) 8400

Answer key

  1. 6.5
  2. 9.8
  3. 56
  4. 83
  5. 41
  6. 5.1
  7. 5.6
  8. 30
  9. 8.4
  10. 9.3
  11. 46
  12. 12
  13. 31
  14. 7.8
  15. 5.2
  16. 18
  17. 41
  18. 62
  19. 9.7
  20. 46
  21. 5.5
  22. 22
  23. 9.2
  24. 63
  25. 8.9
  26. 49
  27. 9.5
  28. 68
  29. 20
  30. 88
  31. 26
  32. 14
  33. 5.9
  34. 7.1
  35. 7.6
  36. 7.4
  37. 9.6
  38. 54
  39. 63
  40. 84

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