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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 424 · 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 826 ÷ 29? (a) 280 (b) 2800 (c) 28
  2. 2.Best estimate of 884 ÷ 39? (a) 22 (b) 2200 (c) 220
  3. 3.√42 to 1 decimal place? (a) 6.6 (b) 6.5 (c) 6.7 (d) 6.4
  4. 4.√61 to 1 decimal place? (a) 7.9 (b) 8.1 (c) 8.0 (d) 7.8
  5. 5.Best estimate of 2038 ÷ 31? (a) 68 (b) 680 (c) 6800
  6. 6.Best estimate of 5307 ÷ 56? (a) 880 (b) 88 (c) 8800
  7. 7.√98 to 1 decimal place? (a) 9.9 (b) 9.8 (c) 9.6 (d) 9.7
  8. 8.√37 to 1 decimal place? (a) 6.2 (b) 6.0 (c) 5.9 (d) 6.1
  9. 9.Best estimate of 1637 ÷ 44? (a) 4100 (b) 41 (c) 410
  10. 10.√28 to 1 decimal place? (a) 5.4 (b) 5.2 (c) 5.5 (d) 5.3
  11. 11.√34 to 1 decimal place? (a) 5.7 (b) 5.8 (c) 5.5 (d) 5.6
  12. 12.Best estimate of 2031 ÷ 42? (a) 510 (b) 51 (c) 5100
  13. 13.√26 to 1 decimal place? (a) 5.4 (b) 5.2 (c) 5.1 (d) 5.3
  14. 14.√47 to 1 decimal place? (a) 7.1 (b) 7.0 (c) 7.2 (d) 6.9
  15. 15.√63 to 1 decimal place? (a) 7.9 (b) 8.0 (c) 7.8 (d) 7.7
  16. 16.√90 to 1 decimal place? (a) 9.5 (b) 9.6 (c) 9.7 (d) 9.8
  17. 17.Best estimate of 3105 ÷ 38? (a) 780 (b) 78 (c) 7800
  18. 18.Best estimate of 6409 ÷ 74? (a) 920 (b) 9200 (c) 92
  19. 19.√71 to 1 decimal place? (a) 8.5 (b) 8.7 (c) 8.4 (d) 8.6
  20. 20.Best estimate of 5052 ÷ 82? (a) 63 (b) 6300 (c) 630
  21. 21.Best estimate of 3956 ÷ 68? (a) 570 (b) 5700 (c) 57
  22. 22.√82 to 1 decimal place? (a) 9.1 (b) 9.2 (c) 9.3 (d) 9.0
  23. 23.√69 to 1 decimal place? (a) 8.5 (b) 8.4 (c) 8.3 (d) 8.6
  24. 24.Best estimate of 2876 ÷ 68? (a) 41 (b) 4100 (c) 410
  25. 25.√24 to 1 decimal place? (a) 4.7 (b) 4.6 (c) 4.8 (d) 4.9
  26. 26.√35 to 1 decimal place? (a) 5.8 (b) 6.1 (c) 5.9 (d) 6.0
  27. 27.Best estimate of 2789 ÷ 77? (a) 35 (b) 350 (c) 3500
  28. 28.√29 to 1 decimal place? (a) 5.5 (b) 5.6 (c) 5.7 (d) 5.4
  29. 29.√94 to 1 decimal place? (a) 9.5 (b) 9.7 (c) 9.6 (d) 9.8
  30. 30.√43 to 1 decimal place? (a) 6.5 (b) 6.8 (c) 6.7 (d) 6.6
  31. 31.√53 to 1 decimal place? (a) 7.0 (b) 7.1 (c) 7.3 (d) 7.2
  32. 32.√48 to 1 decimal place? (a) 7.0 (b) 6.9 (c) 7.1 (d) 6.8
  33. 33.Best estimate of 2255 ÷ 56? (a) 3800 (b) 38 (c) 380
  34. 34.√41 to 1 decimal place? (a) 6.7 (b) 6.6 (c) 6.5 (d) 6.4
  35. 35.Best estimate of 2930 ÷ 71? (a) 420 (b) 4200 (c) 42
  36. 36.Best estimate of 1491 ÷ 23? (a) 750 (b) 7500 (c) 75
  37. 37.Best estimate of 1103 ÷ 71? (a) 160 (b) 1600 (c) 16
  38. 38.Best estimate of 1649 ÷ 34? (a) 550 (b) 55 (c) 5500
  39. 39.√40 to 1 decimal place? (a) 6.3 (b) 6.5 (c) 6.2 (d) 6.4
  40. 40.Best estimate of 7826 ÷ 86? (a) 870 (b) 87 (c) 8700

Answer key

  1. 28
  2. 22
  3. 6.5
  4. 7.8
  5. 68
  6. 88
  7. 9.9
  8. 6.1
  9. 41
  10. 5.3
  11. 5.8
  12. 51
  13. 5.1
  14. 6.9
  15. 7.9
  16. 9.5
  17. 78
  18. 92
  19. 8.4
  20. 63
  21. 57
  22. 9.1
  23. 8.3
  24. 41
  25. 4.9
  26. 5.9
  27. 35
  28. 5.4
  29. 9.7
  30. 6.6
  31. 7.3
  32. 6.9
  33. 38
  34. 6.4
  35. 42
  36. 75
  37. 16
  38. 55
  39. 6.3
  40. 87

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