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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 366 · 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 1809 ÷ 58? (a) 3000 (b) 30 (c) 300
  2. 2.Best estimate of 5615 ÷ 66? (a) 800 (b) 80 (c) 8000
  3. 3.√41 to 1 decimal place? (a) 6.1 (b) 6.2 (c) 6.4 (d) 6.3
  4. 4.√79 to 1 decimal place? (a) 8.9 (b) 8.7 (c) 9.0 (d) 8.8
  5. 5.Best estimate of 5584 ÷ 89? (a) 62 (b) 620 (c) 6200
  6. 6.√37 to 1 decimal place? (a) 6.0 (b) 6.1 (c) 5.8 (d) 5.9
  7. 7.Best estimate of 2299 ÷ 46? (a) 46 (b) 460 (c) 4600
  8. 8.Best estimate of 1338 ÷ 41? (a) 33 (b) 330 (c) 3300
  9. 9.Best estimate of 3020 ÷ 82? (a) 380 (b) 38 (c) 3800
  10. 10.Best estimate of 1513 ÷ 68? (a) 220 (b) 2200 (c) 22
  11. 11.Best estimate of 2800 ÷ 42? (a) 70 (b) 700 (c) 7000
  12. 12.Best estimate of 600 ÷ 38? (a) 150 (b) 15 (c) 1500
  13. 13.Best estimate of 6314 ÷ 68? (a) 9000 (b) 900 (c) 90
  14. 14.Best estimate of 3137 ÷ 53? (a) 630 (b) 63 (c) 6300
  15. 15.Best estimate of 1667 ÷ 56? (a) 2800 (b) 28 (c) 280
  16. 16.√74 to 1 decimal place? (a) 8.7 (b) 8.4 (c) 8.6 (d) 8.5
  17. 17.√65 to 1 decimal place? (a) 7.9 (b) 8.0 (c) 8.1 (d) 7.8
  18. 18.Best estimate of 382 ÷ 27? (a) 13 (b) 1300 (c) 130
  19. 19.√28 to 1 decimal place? (a) 5.4 (b) 5.3 (c) 5.2 (d) 5.1
  20. 20.√83 to 1 decimal place? (a) 9.2 (b) 9.0 (c) 8.9 (d) 9.1
  21. 21.√61 to 1 decimal place? (a) 8.0 (b) 7.8 (c) 7.9 (d) 7.7
  22. 22.√89 to 1 decimal place? (a) 9.3 (b) 9.2 (c) 9.4 (d) 9.5
  23. 23.Best estimate of 1081 ÷ 33? (a) 36 (b) 360 (c) 3600
  24. 24.√67 to 1 decimal place? (a) 8.3 (b) 8.2 (c) 8.1 (d) 8.4
  25. 25.√70 to 1 decimal place? (a) 8.5 (b) 8.6 (c) 8.4 (d) 8.7
  26. 26.Best estimate of 4462 ÷ 82? (a) 5600 (b) 56 (c) 560
  27. 27.Best estimate of 1590 ÷ 52? (a) 320 (b) 3200 (c) 32
  28. 28.√75 to 1 decimal place? (a) 8.8 (b) 8.6 (c) 8.9 (d) 8.7
  29. 29.√43 to 1 decimal place? (a) 6.9 (b) 6.6 (c) 6.7 (d) 6.8
  30. 30.√58 to 1 decimal place? (a) 7.9 (b) 7.6 (c) 7.8 (d) 7.7
  31. 31.Best estimate of 1396 ÷ 28? (a) 470 (b) 47 (c) 4700
  32. 32.√90 to 1 decimal place? (a) 9.4 (b) 9.3 (c) 9.5 (d) 9.2
  33. 33.√34 to 1 decimal place? (a) 5.7 (b) 5.6 (c) 5.5 (d) 5.8
  34. 34.Best estimate of 4798 ÷ 86? (a) 5300 (b) 530 (c) 53
  35. 35.√84 to 1 decimal place? (a) 9.4 (b) 9.3 (c) 9.1 (d) 9.2
  36. 36.Best estimate of 1749 ÷ 62? (a) 290 (b) 2900 (c) 29
  37. 37.√69 to 1 decimal place? (a) 8.5 (b) 8.6 (c) 8.4 (d) 8.3
  38. 38.Best estimate of 3773 ÷ 44? (a) 940 (b) 9400 (c) 94
  39. 39.Best estimate of 1539 ÷ 88? (a) 17 (b) 170 (c) 1700
  40. 40.√55 to 1 decimal place? (a) 7.2 (b) 7.1 (c) 7.4 (d) 7.3

Answer key

  1. 30
  2. 80
  3. 6.4
  4. 8.9
  5. 62
  6. 6.1
  7. 46
  8. 33
  9. 38
  10. 22
  11. 70
  12. 15
  13. 90
  14. 63
  15. 28
  16. 8.6
  17. 8.1
  18. 13
  19. 5.3
  20. 9.1
  21. 7.8
  22. 9.4
  23. 36
  24. 8.2
  25. 8.4
  26. 56
  27. 32
  28. 8.7
  29. 6.6
  30. 7.6
  31. 47
  32. 9.5
  33. 5.8
  34. 53
  35. 9.2
  36. 29
  37. 8.3
  38. 94
  39. 17
  40. 7.4

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