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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 597 · 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 966 ÷ 39? (a) 240 (b) 24 (c) 2400
  2. 2.Best estimate of 1933 ÷ 24? (a) 970 (b) 97 (c) 9700
  3. 3.Best estimate of 4086 ÷ 87? (a) 45 (b) 4500 (c) 450
  4. 4.Best estimate of 4151 ÷ 82? (a) 5200 (b) 520 (c) 52
  5. 5.Best estimate of 3125 ÷ 34? (a) 1040 (b) 104 (c) 10400
  6. 6.√40 to 1 decimal place? (a) 6.4 (b) 6.3 (c) 6.1 (d) 6.2
  7. 7.√47 to 1 decimal place? (a) 7.2 (b) 6.9 (c) 7.0 (d) 7.1
  8. 8.Best estimate of 1409 ÷ 47? (a) 280 (b) 2800 (c) 28
  9. 9.√71 to 1 decimal place? (a) 8.4 (b) 8.3 (c) 8.1 (d) 8.2
  10. 10.√30 to 1 decimal place? (a) 5.4 (b) 5.6 (c) 5.3 (d) 5.5
  11. 11.Best estimate of 2067 ÷ 86? (a) 230 (b) 2300 (c) 23
  12. 12.Best estimate of 7027 ÷ 82? (a) 88 (b) 880 (c) 8800
  13. 13.Best estimate of 2398 ÷ 46? (a) 48 (b) 480 (c) 4800
  14. 14.√67 to 1 decimal place? (a) 8.5 (b) 8.4 (c) 8.3 (d) 8.2
  15. 15.Best estimate of 3311 ÷ 83? (a) 4100 (b) 41 (c) 410
  16. 16.√34 to 1 decimal place? (a) 5.8 (b) 5.7 (c) 5.5 (d) 5.6
  17. 17.√65 to 1 decimal place? (a) 8.4 (b) 8.3 (c) 8.2 (d) 8.1
  18. 18.√52 to 1 decimal place? (a) 7.3 (b) 7.4 (c) 7.2 (d) 7.5
  19. 19.Best estimate of 1451 ÷ 31? (a) 480 (b) 4800 (c) 48
  20. 20.√80 to 1 decimal place? (a) 8.7 (b) 8.6 (c) 8.9 (d) 8.8
  21. 21.√61 to 1 decimal place? (a) 7.7 (b) 7.6 (c) 7.9 (d) 7.8
  22. 22.√27 to 1 decimal place? (a) 5.3 (b) 5.5 (c) 5.4 (d) 5.2
  23. 23.√31 to 1 decimal place? (a) 5.7 (b) 5.6 (c) 5.9 (d) 5.8
  24. 24.Best estimate of 3807 ÷ 48? (a) 760 (b) 76 (c) 7600
  25. 25.Best estimate of 1358 ÷ 29? (a) 450 (b) 4500 (c) 45
  26. 26.√32 to 1 decimal place? (a) 5.7 (b) 5.6 (c) 5.8 (d) 5.9
  27. 27.√89 to 1 decimal place? (a) 9.2 (b) 9.5 (c) 9.4 (d) 9.3
  28. 28.Best estimate of 7894 ÷ 88? (a) 88 (b) 8800 (c) 880
  29. 29.Best estimate of 4043 ÷ 87? (a) 450 (b) 45 (c) 4500
  30. 30.√84 to 1 decimal place? (a) 9.1 (b) 9.3 (c) 9.0 (d) 9.2
  31. 31.Best estimate of 3456 ÷ 56? (a) 58 (b) 580 (c) 5800
  32. 32.√53 to 1 decimal place? (a) 7.5 (b) 7.3 (c) 7.4 (d) 7.6
  33. 33.√86 to 1 decimal place? (a) 9.4 (b) 9.3 (c) 9.2 (d) 9.5
  34. 34.Best estimate of 5445 ÷ 71? (a) 780 (b) 78 (c) 7800
  35. 35.Best estimate of 6740 ÷ 86? (a) 75 (b) 750 (c) 7500
  36. 36.√20 to 1 decimal place? (a) 4.5 (b) 4.7 (c) 4.6 (d) 4.4
  37. 37.√35 to 1 decimal place? (a) 6.1 (b) 6.0 (c) 5.9 (d) 5.8
  38. 38.Best estimate of 485 ÷ 37? (a) 120 (b) 12 (c) 1200
  39. 39.√24 to 1 decimal place? (a) 5.1 (b) 5.0 (c) 4.8 (d) 4.9
  40. 40.√76 to 1 decimal place? (a) 8.6 (b) 8.7 (c) 8.8 (d) 8.5

Answer key

  1. 24
  2. 97
  3. 45
  4. 52
  5. 104
  6. 6.3
  7. 6.9
  8. 28
  9. 8.4
  10. 5.5
  11. 23
  12. 88
  13. 48
  14. 8.2
  15. 41
  16. 5.8
  17. 8.1
  18. 7.2
  19. 48
  20. 8.9
  21. 7.8
  22. 5.2
  23. 5.6
  24. 76
  25. 45
  26. 5.7
  27. 9.4
  28. 88
  29. 45
  30. 9.2
  31. 58
  32. 7.3
  33. 9.3
  34. 78
  35. 75
  36. 4.5
  37. 5.9
  38. 12
  39. 4.9
  40. 8.7

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