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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 176 · 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.√66 to 1 decimal place? (a) 8.4 (b) 8.3 (c) 8.2 (d) 8.1
  2. 2.√44 to 1 decimal place? (a) 6.5 (b) 6.6 (c) 6.4 (d) 6.7
  3. 3.Best estimate of 3085 ÷ 53? (a) 620 (b) 6200 (c) 62
  4. 4.√84 to 1 decimal place? (a) 8.9 (b) 9.1 (c) 9.0 (d) 9.2
  5. 5.Best estimate of 817 ÷ 26? (a) 27 (b) 2700 (c) 270
  6. 6.√62 to 1 decimal place? (a) 8.0 (b) 7.8 (c) 7.9 (d) 7.7
  7. 7.Best estimate of 5455 ÷ 73? (a) 780 (b) 78 (c) 7800
  8. 8.√82 to 1 decimal place? (a) 9.3 (b) 9.4 (c) 9.2 (d) 9.1
  9. 9.√50 to 1 decimal place? (a) 7.4 (b) 7.2 (c) 7.3 (d) 7.1
  10. 10.Best estimate of 5790 ÷ 63? (a) 9700 (b) 970 (c) 97
  11. 11.√70 to 1 decimal place? (a) 8.4 (b) 8.3 (c) 8.2 (d) 8.5
  12. 12.Best estimate of 790 ÷ 36? (a) 20 (b) 2000 (c) 200
  13. 13.Best estimate of 2928 ÷ 39? (a) 73 (b) 7300 (c) 730
  14. 14.√56 to 1 decimal place? (a) 7.4 (b) 7.5 (c) 7.2 (d) 7.3
  15. 15.Best estimate of 2297 ÷ 81? (a) 2900 (b) 29 (c) 290
  16. 16.Best estimate of 4538 ÷ 74? (a) 6500 (b) 65 (c) 650
  17. 17.Best estimate of 570 ÷ 47? (a) 1100 (b) 110 (c) 11
  18. 18.Best estimate of 2531 ÷ 36? (a) 63 (b) 6300 (c) 630
  19. 19.Best estimate of 3093 ÷ 62? (a) 520 (b) 5200 (c) 52
  20. 20.Best estimate of 5157 ÷ 62? (a) 86 (b) 860 (c) 8600
  21. 21.√98 to 1 decimal place? (a) 9.8 (b) 10.0 (c) 9.9 (d) 9.7
  22. 22.√45 to 1 decimal place? (a) 6.6 (b) 6.7 (c) 6.5 (d) 6.4
  23. 23.√37 to 1 decimal place? (a) 5.8 (b) 5.9 (c) 6.1 (d) 6.0
  24. 24.Best estimate of 6246 ÷ 81? (a) 7800 (b) 78 (c) 780
  25. 25.Best estimate of 3894 ÷ 52? (a) 780 (b) 7800 (c) 78
  26. 26.Best estimate of 1193 ÷ 46? (a) 240 (b) 2400 (c) 24
  27. 27.√38 to 1 decimal place? (a) 6.3 (b) 6.1 (c) 6.2 (d) 6.0
  28. 28.√26 to 1 decimal place? (a) 5.0 (b) 5.1 (c) 4.9 (d) 5.2
  29. 29.√94 to 1 decimal place? (a) 9.7 (b) 10.0 (c) 9.9 (d) 9.8
  30. 30.√31 to 1 decimal place? (a) 5.3 (b) 5.6 (c) 5.4 (d) 5.5
  31. 31.Best estimate of 6950 ÷ 74? (a) 9900 (b) 99 (c) 990
  32. 32.√85 to 1 decimal place? (a) 9.4 (b) 9.5 (c) 9.2 (d) 9.3
  33. 33.Best estimate of 6275 ÷ 74? (a) 90 (b) 900 (c) 9000
  34. 34.√61 to 1 decimal place? (a) 8.0 (b) 7.8 (c) 7.7 (d) 7.9
  35. 35.Best estimate of 1363 ÷ 61? (a) 2300 (b) 230 (c) 23
  36. 36.√92 to 1 decimal place? (a) 9.4 (b) 9.7 (c) 9.6 (d) 9.5
  37. 37.Best estimate of 3629 ÷ 43? (a) 9100 (b) 91 (c) 910
  38. 38.√29 to 1 decimal place? (a) 5.5 (b) 5.2 (c) 5.3 (d) 5.4
  39. 39.Best estimate of 1557 ÷ 58? (a) 26 (b) 2600 (c) 260
  40. 40.Best estimate of 1885 ÷ 86? (a) 210 (b) 2100 (c) 21

Answer key

  1. 8.1
  2. 6.6
  3. 62
  4. 9.2
  5. 27
  6. 7.9
  7. 78
  8. 9.1
  9. 7.1
  10. 97
  11. 8.4
  12. 20
  13. 73
  14. 7.5
  15. 29
  16. 65
  17. 11
  18. 63
  19. 52
  20. 86
  21. 9.9
  22. 6.7
  23. 6.1
  24. 78
  25. 78
  26. 24
  27. 6.2
  28. 5.1
  29. 9.7
  30. 5.6
  31. 99
  32. 9.2
  33. 90
  34. 7.8
  35. 23
  36. 9.6
  37. 91
  38. 5.4
  39. 26
  40. 21

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