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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 443 · 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.√69 to 1 decimal place? (a) 8.1 (b) 8.0 (c) 8.2 (d) 8.3
  2. 2.√96 to 1 decimal place? (a) 10.1 (b) 9.9 (c) 10.0 (d) 9.8
  3. 3.√41 to 1 decimal place? (a) 6.5 (b) 6.4 (c) 6.3 (d) 6.6
  4. 4.Best estimate of 2077 ÷ 46? (a) 420 (b) 42 (c) 4200
  5. 5.Best estimate of 3906 ÷ 81? (a) 49 (b) 4900 (c) 490
  6. 6.Best estimate of 2038 ÷ 26? (a) 6800 (b) 68 (c) 680
  7. 7.√72 to 1 decimal place? (a) 8.6 (b) 8.7 (c) 8.5 (d) 8.8
  8. 8.√21 to 1 decimal place? (a) 4.6 (b) 4.3 (c) 4.4 (d) 4.5
  9. 9.√88 to 1 decimal place? (a) 9.4 (b) 9.3 (c) 9.6 (d) 9.5
  10. 10.√92 to 1 decimal place? (a) 9.7 (b) 9.6 (c) 9.8 (d) 9.5
  11. 11.Best estimate of 1236 ÷ 79? (a) 1500 (b) 15 (c) 150
  12. 12.Best estimate of 1207 ÷ 31? (a) 400 (b) 4000 (c) 40
  13. 13.√82 to 1 decimal place? (a) 9.2 (b) 9.1 (c) 9.3 (d) 9.0
  14. 14.√70 to 1 decimal place? (a) 8.6 (b) 8.5 (c) 8.7 (d) 8.4
  15. 15.Best estimate of 667 ÷ 48? (a) 130 (b) 13 (c) 1300
  16. 16.Best estimate of 895 ÷ 21? (a) 450 (b) 4500 (c) 45
  17. 17.Best estimate of 2067 ÷ 82? (a) 2600 (b) 260 (c) 26
  18. 18.√48 to 1 decimal place? (a) 6.8 (b) 6.9 (c) 6.7 (d) 7.0
  19. 19.Best estimate of 6287 ÷ 89? (a) 700 (b) 70 (c) 7000
  20. 20.Best estimate of 2056 ÷ 41? (a) 5100 (b) 510 (c) 51
  21. 21.√65 to 1 decimal place? (a) 8.1 (b) 7.8 (c) 7.9 (d) 8.0
  22. 22.Best estimate of 4950 ÷ 72? (a) 7100 (b) 71 (c) 710
  23. 23.Best estimate of 5101 ÷ 82? (a) 640 (b) 64 (c) 6400
  24. 24.Best estimate of 3956 ÷ 42? (a) 9900 (b) 99 (c) 990
  25. 25.Best estimate of 801 ÷ 34? (a) 270 (b) 27 (c) 2700
  26. 26.Best estimate of 2771 ÷ 51? (a) 55 (b) 5500 (c) 550
  27. 27.√47 to 1 decimal place? (a) 6.9 (b) 7.0 (c) 6.8 (d) 7.1
  28. 28.Best estimate of 905 ÷ 53? (a) 18 (b) 1800 (c) 180
  29. 29.√37 to 1 decimal place? (a) 6.1 (b) 6.0 (c) 5.8 (d) 5.9
  30. 30.Best estimate of 4523 ÷ 53? (a) 9000 (b) 900 (c) 90
  31. 31.Best estimate of 1341 ÷ 77? (a) 170 (b) 1700 (c) 17
  32. 32.√34 to 1 decimal place? (a) 5.6 (b) 5.8 (c) 5.5 (d) 5.7
  33. 33.√86 to 1 decimal place? (a) 9.3 (b) 9.2 (c) 9.1 (d) 9.0
  34. 34.Best estimate of 2240 ÷ 27? (a) 75 (b) 7500 (c) 750
  35. 35.Best estimate of 3322 ÷ 48? (a) 66 (b) 6600 (c) 660
  36. 36.Best estimate of 1995 ÷ 42? (a) 50 (b) 5000 (c) 500
  37. 37.Best estimate of 4749 ÷ 67? (a) 68 (b) 6800 (c) 680
  38. 38.Best estimate of 3275 ÷ 38? (a) 820 (b) 8200 (c) 82
  39. 39.Best estimate of 2157 ÷ 32? (a) 720 (b) 7200 (c) 72
  40. 40.√83 to 1 decimal place? (a) 9.4 (b) 9.2 (c) 9.1 (d) 9.3

Answer key

  1. 8.3
  2. 9.8
  3. 6.4
  4. 42
  5. 49
  6. 68
  7. 8.5
  8. 4.6
  9. 9.4
  10. 9.6
  11. 15
  12. 40
  13. 9.1
  14. 8.4
  15. 13
  16. 45
  17. 26
  18. 6.9
  19. 70
  20. 51
  21. 8.1
  22. 71
  23. 64
  24. 99
  25. 27
  26. 55
  27. 6.9
  28. 18
  29. 6.1
  30. 90
  31. 17
  32. 5.8
  33. 9.3
  34. 75
  35. 66
  36. 50
  37. 68
  38. 82
  39. 72
  40. 9.1

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