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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 372 · 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 4878 ÷ 52? (a) 9800 (b) 980 (c) 98
  2. 2.√61 to 1 decimal place? (a) 7.8 (b) 7.9 (c) 8.0 (d) 8.1
  3. 3.Best estimate of 4509 ÷ 72? (a) 64 (b) 640 (c) 6400
  4. 4.Best estimate of 4347 ÷ 76? (a) 540 (b) 5400 (c) 54
  5. 5.Best estimate of 5114 ÷ 71? (a) 730 (b) 73 (c) 7300
  6. 6.Best estimate of 1794 ÷ 69? (a) 2600 (b) 26 (c) 260
  7. 7.√90 to 1 decimal place? (a) 9.5 (b) 9.7 (c) 9.4 (d) 9.6
  8. 8.√72 to 1 decimal place? (a) 8.3 (b) 8.2 (c) 8.5 (d) 8.4
  9. 9.Best estimate of 3711 ÷ 66? (a) 53 (b) 5300 (c) 530
  10. 10.√40 to 1 decimal place? (a) 6.2 (b) 6.3 (c) 6.1 (d) 6.0
  11. 11.Best estimate of 6499 ÷ 86? (a) 720 (b) 7200 (c) 72
  12. 12.√29 to 1 decimal place? (a) 5.4 (b) 5.3 (c) 5.2 (d) 5.5
  13. 13.Best estimate of 3493 ÷ 61? (a) 580 (b) 5800 (c) 58
  14. 14.√78 to 1 decimal place? (a) 8.9 (b) 8.7 (c) 8.8 (d) 9.0
  15. 15.√79 to 1 decimal place? (a) 8.7 (b) 8.8 (c) 8.6 (d) 8.9
  16. 16.Best estimate of 1907 ÷ 32? (a) 6400 (b) 64 (c) 640
  17. 17.Best estimate of 3241 ÷ 43? (a) 810 (b) 81 (c) 8100
  18. 18.Best estimate of 2166 ÷ 46? (a) 43 (b) 4300 (c) 430
  19. 19.√58 to 1 decimal place? (a) 7.6 (b) 7.4 (c) 7.7 (d) 7.5
  20. 20.√42 to 1 decimal place? (a) 6.6 (b) 6.4 (c) 6.3 (d) 6.5
  21. 21.√96 to 1 decimal place? (a) 9.9 (b) 9.7 (c) 10.0 (d) 9.8
  22. 22.Best estimate of 2734 ÷ 76? (a) 3400 (b) 34 (c) 340
  23. 23.Best estimate of 1724 ÷ 67? (a) 250 (b) 2500 (c) 25
  24. 24.Best estimate of 3794 ÷ 53? (a) 76 (b) 760 (c) 7600
  25. 25.√92 to 1 decimal place? (a) 9.7 (b) 9.9 (c) 9.6 (d) 9.8
  26. 26.Best estimate of 589 ÷ 29? (a) 2000 (b) 200 (c) 20
  27. 27.√74 to 1 decimal place? (a) 8.4 (b) 8.5 (c) 8.7 (d) 8.6
  28. 28.√53 to 1 decimal place? (a) 7.5 (b) 7.6 (c) 7.3 (d) 7.4
  29. 29.Best estimate of 4668 ÷ 86? (a) 520 (b) 5200 (c) 52
  30. 30.√37 to 1 decimal place? (a) 6.0 (b) 6.2 (c) 5.9 (d) 6.1
  31. 31.Best estimate of 1695 ÷ 53? (a) 34 (b) 3400 (c) 340
  32. 32.√27 to 1 decimal place? (a) 5.4 (b) 5.2 (c) 5.3 (d) 5.5
  33. 33.√67 to 1 decimal place? (a) 8.2 (b) 8.3 (c) 8.1 (d) 8.0
  34. 34.Best estimate of 2003 ÷ 26? (a) 6700 (b) 67 (c) 670
  35. 35.√55 to 1 decimal place? (a) 7.3 (b) 7.1 (c) 7.2 (d) 7.4
  36. 36.Best estimate of 4288 ÷ 52? (a) 860 (b) 8600 (c) 86
  37. 37.Best estimate of 1928 ÷ 78? (a) 2400 (b) 240 (c) 24
  38. 38.Best estimate of 2518 ÷ 79? (a) 310 (b) 3100 (c) 31
  39. 39.√21 to 1 decimal place? (a) 4.5 (b) 4.8 (c) 4.7 (d) 4.6
  40. 40.Best estimate of 5036 ÷ 86? (a) 56 (b) 5600 (c) 560

Answer key

  1. 98
  2. 7.8
  3. 64
  4. 54
  5. 73
  6. 26
  7. 9.5
  8. 8.5
  9. 53
  10. 6.3
  11. 72
  12. 5.4
  13. 58
  14. 8.8
  15. 8.9
  16. 64
  17. 81
  18. 43
  19. 7.6
  20. 6.5
  21. 9.8
  22. 34
  23. 25
  24. 76
  25. 9.6
  26. 20
  27. 8.6
  28. 7.3
  29. 52
  30. 6.1
  31. 34
  32. 5.2
  33. 8.2
  34. 67
  35. 7.4
  36. 86
  37. 24
  38. 31
  39. 4.6
  40. 56

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