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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 59 · 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.√89 to 1 decimal place? (a) 9.7 (b) 9.6 (c) 9.5 (d) 9.4
  2. 2.Best estimate of 710 ÷ 23? (a) 360 (b) 3600 (c) 36
  3. 3.Best estimate of 2473 ÷ 86? (a) 27 (b) 270 (c) 2700
  4. 4.√94 to 1 decimal place? (a) 9.8 (b) 9.9 (c) 10.0 (d) 9.7
  5. 5.Best estimate of 2035 ÷ 38? (a) 510 (b) 51 (c) 5100
  6. 6.Best estimate of 2007 ÷ 24? (a) 100 (b) 1000 (c) 10000
  7. 7.√37 to 1 decimal place? (a) 6.0 (b) 5.8 (c) 5.9 (d) 6.1
  8. 8.Best estimate of 1078 ÷ 38? (a) 27 (b) 270 (c) 2700
  9. 9.Best estimate of 6585 ÷ 77? (a) 8200 (b) 82 (c) 820
  10. 10.Best estimate of 1558 ÷ 56? (a) 26 (b) 260 (c) 2600
  11. 11.√77 to 1 decimal place? (a) 9.0 (b) 8.8 (c) 8.9 (d) 8.7
  12. 12.Best estimate of 567 ÷ 28? (a) 190 (b) 1900 (c) 19
  13. 13.Best estimate of 1423 ÷ 72? (a) 200 (b) 2000 (c) 20
  14. 14.Best estimate of 5689 ÷ 89? (a) 63 (b) 6300 (c) 630
  15. 15.Best estimate of 3200 ÷ 88? (a) 360 (b) 3600 (c) 36
  16. 16.√65 to 1 decimal place? (a) 7.8 (b) 7.9 (c) 8.1 (d) 8.0
  17. 17.√27 to 1 decimal place? (a) 5.2 (b) 5.1 (c) 5.3 (d) 5.0
  18. 18.Best estimate of 3771 ÷ 63? (a) 6300 (b) 630 (c) 63
  19. 19.Best estimate of 3157 ÷ 62? (a) 53 (b) 530 (c) 5300
  20. 20.Best estimate of 2991 ÷ 33? (a) 10000 (b) 100 (c) 1000
  21. 21.Best estimate of 2423 ÷ 41? (a) 6100 (b) 61 (c) 610
  22. 22.Best estimate of 2589 ÷ 48? (a) 520 (b) 5200 (c) 52
  23. 23.Best estimate of 1236 ÷ 54? (a) 2500 (b) 250 (c) 25
  24. 24.√98 to 1 decimal place? (a) 9.8 (b) 10.0 (c) 9.9 (d) 9.7
  25. 25.√24 to 1 decimal place? (a) 5.0 (b) 4.9 (c) 4.7 (d) 4.8
  26. 26.√74 to 1 decimal place? (a) 8.4 (b) 8.7 (c) 8.5 (d) 8.6
  27. 27.√92 to 1 decimal place? (a) 9.5 (b) 9.8 (c) 9.6 (d) 9.7
  28. 28.Best estimate of 1546 ÷ 46? (a) 31 (b) 310 (c) 3100
  29. 29.√90 to 1 decimal place? (a) 9.4 (b) 9.5 (c) 9.6 (d) 9.3
  30. 30.√40 to 1 decimal place? (a) 6.4 (b) 6.5 (c) 6.6 (d) 6.3
  31. 31.√82 to 1 decimal place? (a) 8.8 (b) 8.9 (c) 9.0 (d) 9.1
  32. 32.Best estimate of 4837 ÷ 71? (a) 690 (b) 69 (c) 6900
  33. 33.Best estimate of 2305 ÷ 46? (a) 4600 (b) 46 (c) 460
  34. 34.Best estimate of 1060 ÷ 58? (a) 180 (b) 18 (c) 1800
  35. 35.Best estimate of 1288 ÷ 43? (a) 32 (b) 320 (c) 3200
  36. 36.Best estimate of 2960 ÷ 34? (a) 99 (b) 9900 (c) 990
  37. 37.√42 to 1 decimal place? (a) 6.6 (b) 6.5 (c) 6.3 (d) 6.4
  38. 38.Best estimate of 494 ÷ 36? (a) 1200 (b) 120 (c) 12
  39. 39.√41 to 1 decimal place? (a) 6.6 (b) 6.5 (c) 6.4 (d) 6.3
  40. 40.√30 to 1 decimal place? (a) 5.5 (b) 5.7 (c) 5.8 (d) 5.6

Answer key

  1. 9.4
  2. 36
  3. 27
  4. 9.7
  5. 51
  6. 100
  7. 6.1
  8. 27
  9. 82
  10. 26
  11. 8.8
  12. 19
  13. 20
  14. 63
  15. 36
  16. 8.1
  17. 5.2
  18. 63
  19. 53
  20. 100
  21. 61
  22. 52
  23. 25
  24. 9.9
  25. 4.9
  26. 8.6
  27. 9.6
  28. 31
  29. 9.5
  30. 6.3
  31. 9.1
  32. 69
  33. 46
  34. 18
  35. 32
  36. 99
  37. 6.5
  38. 12
  39. 6.4
  40. 5.5

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