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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 174 · 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.√67 to 1 decimal place? (a) 8.3 (b) 8.4 (c) 8.2 (d) 8.1
  2. 2.Best estimate of 3998 ÷ 66? (a) 570 (b) 57 (c) 5700
  3. 3.Best estimate of 4326 ÷ 51? (a) 87 (b) 8700 (c) 870
  4. 4.√75 to 1 decimal place? (a) 8.6 (b) 8.7 (c) 8.8 (d) 8.9
  5. 5.√40 to 1 decimal place? (a) 6.1 (b) 6.3 (c) 6.2 (d) 6.4
  6. 6.√21 to 1 decimal place? (a) 4.6 (b) 4.4 (c) 4.5 (d) 4.3
  7. 7.Best estimate of 3700 ÷ 72? (a) 5300 (b) 53 (c) 530
  8. 8.Best estimate of 1129 ÷ 66? (a) 16 (b) 1600 (c) 160
  9. 9.Best estimate of 2871 ÷ 49? (a) 57 (b) 570 (c) 5700
  10. 10.√86 to 1 decimal place? (a) 9.3 (b) 9.4 (c) 9.5 (d) 9.2
  11. 11.√92 to 1 decimal place? (a) 9.7 (b) 9.9 (c) 9.8 (d) 9.6
  12. 12.Best estimate of 934 ÷ 44? (a) 2300 (b) 23 (c) 230
  13. 13.Best estimate of 648 ÷ 36? (a) 160 (b) 16 (c) 1600
  14. 14.√50 to 1 decimal place? (a) 7.1 (b) 6.9 (c) 6.8 (d) 7.0
  15. 15.Best estimate of 2358 ÷ 56? (a) 39 (b) 3900 (c) 390
  16. 16.√24 to 1 decimal place? (a) 4.9 (b) 5.1 (c) 5.0 (d) 4.8
  17. 17.Best estimate of 1439 ÷ 49? (a) 2900 (b) 29 (c) 290
  18. 18.Best estimate of 663 ÷ 44? (a) 170 (b) 17 (c) 1700
  19. 19.√45 to 1 decimal place? (a) 6.8 (b) 6.7 (c) 6.5 (d) 6.6
  20. 20.Best estimate of 1017 ÷ 72? (a) 1500 (b) 15 (c) 150
  21. 21.√26 to 1 decimal place? (a) 5.3 (b) 5.2 (c) 5.1 (d) 5.4
  22. 22.Best estimate of 4345 ÷ 56? (a) 7200 (b) 720 (c) 72
  23. 23.√58 to 1 decimal place? (a) 7.8 (b) 7.9 (c) 7.6 (d) 7.7
  24. 24.Best estimate of 3614 ÷ 52? (a) 7200 (b) 72 (c) 720
  25. 25.√52 to 1 decimal place? (a) 7.2 (b) 7.4 (c) 7.5 (d) 7.3
  26. 26.Best estimate of 2074 ÷ 32? (a) 69 (b) 6900 (c) 690
  27. 27.Best estimate of 4472 ÷ 72? (a) 6400 (b) 640 (c) 64
  28. 28.√47 to 1 decimal place? (a) 6.7 (b) 7.0 (c) 6.9 (d) 6.8
  29. 29.√90 to 1 decimal place? (a) 9.5 (b) 9.7 (c) 9.6 (d) 9.8
  30. 30.Best estimate of 4423 ÷ 58? (a) 74 (b) 7400 (c) 740
  31. 31.√42 to 1 decimal place? (a) 6.4 (b) 6.2 (c) 6.3 (d) 6.5
  32. 32.Best estimate of 1385 ÷ 59? (a) 23 (b) 2300 (c) 230
  33. 33.Best estimate of 5390 ÷ 89? (a) 600 (b) 6000 (c) 60
  34. 34.√65 to 1 decimal place? (a) 8.2 (b) 8.3 (c) 8.1 (d) 8.0
  35. 35.√88 to 1 decimal place? (a) 9.5 (b) 9.7 (c) 9.6 (d) 9.4
  36. 36.√72 to 1 decimal place? (a) 8.6 (b) 8.7 (c) 8.5 (d) 8.8
  37. 37.Best estimate of 421 ÷ 26? (a) 140 (b) 14 (c) 1400
  38. 38.Best estimate of 2377 ÷ 32? (a) 790 (b) 7900 (c) 79
  39. 39.Best estimate of 4400 ÷ 67? (a) 63 (b) 630 (c) 6300
  40. 40.Best estimate of 1726 ÷ 56? (a) 29 (b) 290 (c) 2900

Answer key

  1. 8.2
  2. 57
  3. 87
  4. 8.7
  5. 6.3
  6. 4.6
  7. 53
  8. 16
  9. 57
  10. 9.3
  11. 9.6
  12. 23
  13. 16
  14. 7.1
  15. 39
  16. 4.9
  17. 29
  18. 17
  19. 6.7
  20. 15
  21. 5.1
  22. 72
  23. 7.6
  24. 72
  25. 7.2
  26. 69
  27. 64
  28. 6.9
  29. 9.5
  30. 74
  31. 6.5
  32. 23
  33. 60
  34. 8.1
  35. 9.4
  36. 8.5
  37. 14
  38. 79
  39. 63
  40. 29

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