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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 70 · 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.√51 to 1 decimal place? (a) 7.0 (b) 7.3 (c) 7.1 (d) 7.2
  2. 2.√24 to 1 decimal place? (a) 4.8 (b) 5.1 (c) 5.0 (d) 4.9
  3. 3.Best estimate of 1872 ÷ 31? (a) 62 (b) 620 (c) 6200
  4. 4.√94 to 1 decimal place? (a) 9.8 (b) 9.5 (c) 9.6 (d) 9.7
  5. 5.Best estimate of 2319 ÷ 61? (a) 39 (b) 390 (c) 3900
  6. 6.√92 to 1 decimal place? (a) 9.4 (b) 9.5 (c) 9.3 (d) 9.6
  7. 7.√21 to 1 decimal place? (a) 4.6 (b) 4.8 (c) 4.5 (d) 4.7
  8. 8.√70 to 1 decimal place? (a) 8.6 (b) 8.4 (c) 8.3 (d) 8.5
  9. 9.√69 to 1 decimal place? (a) 8.6 (b) 8.3 (c) 8.4 (d) 8.5
  10. 10.√89 to 1 decimal place? (a) 9.3 (b) 9.1 (c) 9.2 (d) 9.4
  11. 11.√65 to 1 decimal place? (a) 8.2 (b) 8.1 (c) 8.3 (d) 8.4
  12. 12.Best estimate of 2244 ÷ 28? (a) 750 (b) 7500 (c) 75
  13. 13.Best estimate of 2182 ÷ 63? (a) 3600 (b) 36 (c) 360
  14. 14.√79 to 1 decimal place? (a) 8.8 (b) 8.7 (c) 9.0 (d) 8.9
  15. 15.Best estimate of 4543 ÷ 76? (a) 570 (b) 57 (c) 5700
  16. 16.√62 to 1 decimal place? (a) 7.9 (b) 8.1 (c) 8.0 (d) 8.2
  17. 17.Best estimate of 5656 ÷ 62? (a) 94 (b) 940 (c) 9400
  18. 18.Best estimate of 1360 ÷ 46? (a) 27 (b) 270 (c) 2700
  19. 19.Best estimate of 2048 ÷ 44? (a) 510 (b) 51 (c) 5100
  20. 20.√63 to 1 decimal place? (a) 7.6 (b) 7.8 (c) 7.7 (d) 7.9
  21. 21.Best estimate of 2809 ÷ 36? (a) 7000 (b) 70 (c) 700
  22. 22.Best estimate of 5212 ÷ 57? (a) 8700 (b) 87 (c) 870
  23. 23.Best estimate of 1744 ÷ 22? (a) 8700 (b) 870 (c) 87
  24. 24.Best estimate of 1252 ÷ 36? (a) 310 (b) 3100 (c) 31
  25. 25.√82 to 1 decimal place? (a) 9.1 (b) 8.8 (c) 8.9 (d) 9.0
  26. 26.Best estimate of 738 ÷ 33? (a) 25 (b) 250 (c) 2500
  27. 27.Best estimate of 4204 ÷ 46? (a) 840 (b) 84 (c) 8400
  28. 28.Best estimate of 915 ÷ 51? (a) 18 (b) 180 (c) 1800
  29. 29.√22 to 1 decimal place? (a) 4.7 (b) 4.8 (c) 4.5 (d) 4.6
  30. 30.√88 to 1 decimal place? (a) 9.4 (b) 9.5 (c) 9.2 (d) 9.3
  31. 31.Best estimate of 3101 ÷ 62? (a) 520 (b) 52 (c) 5200
  32. 32.Best estimate of 688 ÷ 22? (a) 3400 (b) 34 (c) 340
  33. 33.Best estimate of 1070 ÷ 41? (a) 2700 (b) 27 (c) 270
  34. 34.Best estimate of 1604 ÷ 34? (a) 530 (b) 5300 (c) 53
  35. 35.Best estimate of 1935 ÷ 43? (a) 48 (b) 4800 (c) 480
  36. 36.Best estimate of 1107 ÷ 32? (a) 370 (b) 37 (c) 3700
  37. 37.√55 to 1 decimal place? (a) 7.7 (b) 7.5 (c) 7.4 (d) 7.6
  38. 38.√87 to 1 decimal place? (a) 9.3 (b) 9.5 (c) 9.6 (d) 9.4
  39. 39.Best estimate of 2842 ÷ 53? (a) 570 (b) 5700 (c) 57
  40. 40.√80 to 1 decimal place? (a) 9.0 (b) 8.7 (c) 8.9 (d) 8.8

Answer key

  1. 7.1
  2. 4.9
  3. 62
  4. 9.7
  5. 39
  6. 9.6
  7. 4.6
  8. 8.4
  9. 8.3
  10. 9.4
  11. 8.1
  12. 75
  13. 36
  14. 8.9
  15. 57
  16. 7.9
  17. 94
  18. 27
  19. 51
  20. 7.9
  21. 70
  22. 87
  23. 87
  24. 31
  25. 9.1
  26. 25
  27. 84
  28. 18
  29. 4.7
  30. 9.4
  31. 52
  32. 34
  33. 27
  34. 53
  35. 48
  36. 37
  37. 7.4
  38. 9.3
  39. 57
  40. 8.9

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