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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 644 · 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 467 ÷ 22? (a) 2300 (b) 23 (c) 230
  2. 2.√58 to 1 decimal place? (a) 7.7 (b) 7.9 (c) 7.6 (d) 7.8
  3. 3.√45 to 1 decimal place? (a) 7.0 (b) 6.7 (c) 6.9 (d) 6.8
  4. 4.Best estimate of 3321 ÷ 62? (a) 5500 (b) 550 (c) 55
  5. 5.Best estimate of 4190 ÷ 61? (a) 7000 (b) 70 (c) 700
  6. 6.Best estimate of 6140 ÷ 81? (a) 77 (b) 7700 (c) 770
  7. 7.√98 to 1 decimal place? (a) 10.1 (b) 9.9 (c) 10.0 (d) 10.2
  8. 8.√69 to 1 decimal place? (a) 8.4 (b) 8.5 (c) 8.3 (d) 8.6
  9. 9.√62 to 1 decimal place? (a) 7.7 (b) 7.6 (c) 7.8 (d) 7.9
  10. 10.√50 to 1 decimal place? (a) 7.0 (b) 6.8 (c) 6.9 (d) 7.1
  11. 11.√79 to 1 decimal place? (a) 8.8 (b) 8.9 (c) 9.0 (d) 8.7
  12. 12.Best estimate of 2785 ÷ 47? (a) 560 (b) 5600 (c) 56
  13. 13.√96 to 1 decimal place? (a) 9.9 (b) 10.0 (c) 10.1 (d) 9.8
  14. 14.√61 to 1 decimal place? (a) 7.7 (b) 7.8 (c) 7.6 (d) 7.5
  15. 15.√74 to 1 decimal place? (a) 8.7 (b) 8.6 (c) 8.8 (d) 8.9
  16. 16.Best estimate of 4842 ÷ 88? (a) 54 (b) 540 (c) 5400
  17. 17.Best estimate of 5643 ÷ 84? (a) 710 (b) 7100 (c) 71
  18. 18.√26 to 1 decimal place? (a) 5.1 (b) 5.2 (c) 5.0 (d) 5.3
  19. 19.Best estimate of 692 ÷ 29? (a) 230 (b) 23 (c) 2300
  20. 20.Best estimate of 1135 ÷ 33? (a) 380 (b) 3800 (c) 38
  21. 21.Best estimate of 1810 ÷ 42? (a) 45 (b) 450 (c) 4500
  22. 22.√40 to 1 decimal place? (a) 6.5 (b) 6.2 (c) 6.4 (d) 6.3
  23. 23.Best estimate of 7589 ÷ 86? (a) 8400 (b) 84 (c) 840
  24. 24.Best estimate of 3253 ÷ 73? (a) 46 (b) 460 (c) 4600
  25. 25.√59 to 1 decimal place? (a) 7.6 (b) 7.8 (c) 7.7 (d) 7.5
  26. 26.√51 to 1 decimal place? (a) 7.2 (b) 7.4 (c) 7.1 (d) 7.3
  27. 27.Best estimate of 1909 ÷ 42? (a) 480 (b) 48 (c) 4800
  28. 28.√44 to 1 decimal place? (a) 6.7 (b) 6.5 (c) 6.4 (d) 6.6
  29. 29.Best estimate of 1467 ÷ 63? (a) 2400 (b) 240 (c) 24
  30. 30.Best estimate of 1747 ÷ 32? (a) 5800 (b) 58 (c) 580
  31. 31.Best estimate of 3086 ÷ 57? (a) 51 (b) 510 (c) 5100
  32. 32.√71 to 1 decimal place? (a) 8.6 (b) 8.3 (c) 8.5 (d) 8.4
  33. 33.√24 to 1 decimal place? (a) 5.1 (b) 5.0 (c) 5.2 (d) 4.9
  34. 34.√78 to 1 decimal place? (a) 8.8 (b) 8.9 (c) 8.7 (d) 9.0
  35. 35.Best estimate of 2924 ÷ 46? (a) 58 (b) 580 (c) 5800
  36. 36.√41 to 1 decimal place? (a) 6.4 (b) 6.6 (c) 6.5 (d) 6.3
  37. 37.Best estimate of 1137 ÷ 26? (a) 380 (b) 3800 (c) 38
  38. 38.Best estimate of 451 ÷ 32? (a) 150 (b) 15 (c) 1500
  39. 39.√23 to 1 decimal place? (a) 4.5 (b) 4.6 (c) 4.8 (d) 4.7
  40. 40.√42 to 1 decimal place? (a) 6.3 (b) 6.4 (c) 6.5 (d) 6.2

Answer key

  1. 23
  2. 7.6
  3. 6.7
  4. 55
  5. 70
  6. 77
  7. 9.9
  8. 8.3
  9. 7.9
  10. 7.1
  11. 8.9
  12. 56
  13. 9.8
  14. 7.8
  15. 8.6
  16. 54
  17. 71
  18. 5.1
  19. 23
  20. 38
  21. 45
  22. 6.3
  23. 84
  24. 46
  25. 7.7
  26. 7.1
  27. 48
  28. 6.6
  29. 24
  30. 58
  31. 51
  32. 8.4
  33. 4.9
  34. 8.8
  35. 58
  36. 6.4
  37. 38
  38. 15
  39. 4.8
  40. 6.5

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