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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 185 · 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 1371 ÷ 84? (a) 170 (b) 17 (c) 1700
  2. 2.√75 to 1 decimal place? (a) 8.5 (b) 8.4 (c) 8.6 (d) 8.7
  3. 3.√51 to 1 decimal place? (a) 7.1 (b) 7.0 (c) 6.9 (d) 7.2
  4. 4.Best estimate of 1247 ÷ 21? (a) 620 (b) 62 (c) 6200
  5. 5.Best estimate of 682 ÷ 36? (a) 1700 (b) 17 (c) 170
  6. 6.√35 to 1 decimal place? (a) 6.2 (b) 6.0 (c) 6.1 (d) 5.9
  7. 7.√89 to 1 decimal place? (a) 9.3 (b) 9.4 (c) 9.1 (d) 9.2
  8. 8.√40 to 1 decimal place? (a) 6.3 (b) 6.5 (c) 6.6 (d) 6.4
  9. 9.Best estimate of 1350 ÷ 64? (a) 2300 (b) 23 (c) 230
  10. 10.√85 to 1 decimal place? (a) 9.1 (b) 9.4 (c) 9.2 (d) 9.3
  11. 11.√34 to 1 decimal place? (a) 5.8 (b) 5.7 (c) 5.6 (d) 5.5
  12. 12.Best estimate of 3473 ÷ 52? (a) 690 (b) 6900 (c) 69
  13. 13.√63 to 1 decimal place? (a) 7.6 (b) 7.9 (c) 7.7 (d) 7.8
  14. 14.Best estimate of 1387 ÷ 23? (a) 69 (b) 6900 (c) 690
  15. 15.Best estimate of 2145 ÷ 56? (a) 36 (b) 360 (c) 3600
  16. 16.Best estimate of 2732 ÷ 61? (a) 460 (b) 46 (c) 4600
  17. 17.√23 to 1 decimal place? (a) 4.8 (b) 5.0 (c) 5.1 (d) 4.9
  18. 18.Best estimate of 4888 ÷ 74? (a) 70 (b) 7000 (c) 700
  19. 19.√53 to 1 decimal place? (a) 7.5 (b) 7.4 (c) 7.6 (d) 7.3
  20. 20.Best estimate of 6273 ÷ 86? (a) 7000 (b) 70 (c) 700
  21. 21.√52 to 1 decimal place? (a) 7.3 (b) 7.4 (c) 7.5 (d) 7.2
  22. 22.Best estimate of 2442 ÷ 36? (a) 610 (b) 6100 (c) 61
  23. 23.Best estimate of 1255 ÷ 42? (a) 310 (b) 3100 (c) 31
  24. 24.Best estimate of 1314 ÷ 39? (a) 330 (b) 3300 (c) 33
  25. 25.√84 to 1 decimal place? (a) 9.4 (b) 9.5 (c) 9.2 (d) 9.3
  26. 26.√55 to 1 decimal place? (a) 7.4 (b) 7.6 (c) 7.3 (d) 7.5
  27. 27.√31 to 1 decimal place? (a) 5.7 (b) 5.8 (c) 5.5 (d) 5.6
  28. 28.√24 to 1 decimal place? (a) 5.2 (b) 5.1 (c) 4.9 (d) 5.0
  29. 29.Best estimate of 4482 ÷ 68? (a) 6400 (b) 64 (c) 640
  30. 30.Best estimate of 2681 ÷ 51? (a) 5400 (b) 540 (c) 54
  31. 31.Best estimate of 6562 ÷ 84? (a) 82 (b) 820 (c) 8200
  32. 32.Best estimate of 4792 ÷ 66? (a) 6800 (b) 680 (c) 68
  33. 33.Best estimate of 912 ÷ 34? (a) 30 (b) 3000 (c) 300
  34. 34.√45 to 1 decimal place? (a) 6.7 (b) 6.8 (c) 6.6 (d) 6.9
  35. 35.Best estimate of 3547 ÷ 47? (a) 71 (b) 7100 (c) 710
  36. 36.Best estimate of 2320 ÷ 84? (a) 290 (b) 2900 (c) 29
  37. 37.Best estimate of 3615 ÷ 51? (a) 72 (b) 7200 (c) 720
  38. 38.Best estimate of 3117 ÷ 88? (a) 350 (b) 3500 (c) 35
  39. 39.√76 to 1 decimal place? (a) 8.5 (b) 8.4 (c) 8.6 (d) 8.7
  40. 40.Best estimate of 1888 ÷ 22? (a) 940 (b) 94 (c) 9400

Answer key

  1. 17
  2. 8.7
  3. 7.1
  4. 62
  5. 17
  6. 5.9
  7. 9.4
  8. 6.3
  9. 23
  10. 9.2
  11. 5.8
  12. 69
  13. 7.9
  14. 69
  15. 36
  16. 46
  17. 4.8
  18. 70
  19. 7.3
  20. 70
  21. 7.2
  22. 61
  23. 31
  24. 33
  25. 9.2
  26. 7.4
  27. 5.6
  28. 4.9
  29. 64
  30. 54
  31. 82
  32. 68
  33. 30
  34. 6.7
  35. 71
  36. 29
  37. 72
  38. 35
  39. 8.7
  40. 94

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