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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 892 · 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.√58 to 1 decimal place? (a) 7.8 (b) 7.6 (c) 7.7 (d) 7.5
  2. 2.Best estimate of 4587 ÷ 63? (a) 7600 (b) 76 (c) 760
  3. 3.Best estimate of 2289 ÷ 69? (a) 3300 (b) 330 (c) 33
  4. 4.√29 to 1 decimal place? (a) 5.3 (b) 5.4 (c) 5.5 (d) 5.6
  5. 5.√37 to 1 decimal place? (a) 6.0 (b) 5.8 (c) 6.1 (d) 5.9
  6. 6.√74 to 1 decimal place? (a) 8.7 (b) 8.9 (c) 8.8 (d) 8.6
  7. 7.√42 to 1 decimal place? (a) 6.3 (b) 6.5 (c) 6.6 (d) 6.4
  8. 8.Best estimate of 1875 ÷ 22? (a) 94 (b) 9400 (c) 940
  9. 9.Best estimate of 5793 ÷ 81? (a) 72 (b) 720 (c) 7200
  10. 10.√30 to 1 decimal place? (a) 5.5 (b) 5.3 (c) 5.2 (d) 5.4
  11. 11.Best estimate of 1738 ÷ 26? (a) 58 (b) 580 (c) 5800
  12. 12.Best estimate of 4609 ÷ 66? (a) 660 (b) 66 (c) 6600
  13. 13.√23 to 1 decimal place? (a) 4.7 (b) 4.5 (c) 4.6 (d) 4.8
  14. 14.√26 to 1 decimal place? (a) 4.9 (b) 5.0 (c) 4.8 (d) 5.1
  15. 15.Best estimate of 3210 ÷ 72? (a) 4600 (b) 46 (c) 460
  16. 16.√53 to 1 decimal place? (a) 7.6 (b) 7.5 (c) 7.4 (d) 7.3
  17. 17.Best estimate of 5324 ÷ 66? (a) 7600 (b) 760 (c) 76
  18. 18.Best estimate of 630 ÷ 36? (a) 1600 (b) 160 (c) 16
  19. 19.√80 to 1 decimal place? (a) 8.8 (b) 8.9 (c) 8.6 (d) 8.7
  20. 20.Best estimate of 1865 ÷ 64? (a) 31 (b) 3100 (c) 310
  21. 21.Best estimate of 4730 ÷ 86? (a) 5300 (b) 53 (c) 530
  22. 22.Best estimate of 1487 ÷ 83? (a) 190 (b) 1900 (c) 19
  23. 23.Best estimate of 1572 ÷ 58? (a) 260 (b) 26 (c) 2600
  24. 24.Best estimate of 2179 ÷ 71? (a) 3100 (b) 31 (c) 310
  25. 25.Best estimate of 2438 ÷ 78? (a) 300 (b) 30 (c) 3000
  26. 26.√94 to 1 decimal place? (a) 9.9 (b) 9.7 (c) 10.0 (d) 9.8
  27. 27.√31 to 1 decimal place? (a) 5.6 (b) 5.7 (c) 5.8 (d) 5.9
  28. 28.√69 to 1 decimal place? (a) 8.3 (b) 8.4 (c) 8.2 (d) 8.1
  29. 29.√98 to 1 decimal place? (a) 10.1 (b) 10.2 (c) 9.9 (d) 10.0
  30. 30.Best estimate of 4540 ÷ 56? (a) 760 (b) 76 (c) 7600
  31. 31.√72 to 1 decimal place? (a) 8.5 (b) 8.4 (c) 8.6 (d) 8.3
  32. 32.Best estimate of 3967 ÷ 66? (a) 5700 (b) 57 (c) 570
  33. 33.Best estimate of 2474 ÷ 27? (a) 820 (b) 8200 (c) 82
  34. 34.Best estimate of 2267 ÷ 46? (a) 4500 (b) 45 (c) 450
  35. 35.√83 to 1 decimal place? (a) 9.1 (b) 9.0 (c) 9.2 (d) 8.9
  36. 36.Best estimate of 2818 ÷ 66? (a) 4000 (b) 400 (c) 40
  37. 37.√47 to 1 decimal place? (a) 6.7 (b) 6.8 (c) 6.6 (d) 6.9
  38. 38.√22 to 1 decimal place? (a) 5.0 (b) 4.8 (c) 4.9 (d) 4.7
  39. 39.Best estimate of 1802 ÷ 37? (a) 450 (b) 45 (c) 4500
  40. 40.√67 to 1 decimal place? (a) 8.2 (b) 8.1 (c) 8.0 (d) 7.9

Answer key

  1. 7.6
  2. 76
  3. 33
  4. 5.4
  5. 6.1
  6. 8.6
  7. 6.5
  8. 94
  9. 72
  10. 5.5
  11. 58
  12. 66
  13. 4.8
  14. 5.1
  15. 46
  16. 7.3
  17. 76
  18. 16
  19. 8.9
  20. 31
  21. 53
  22. 19
  23. 26
  24. 31
  25. 30
  26. 9.7
  27. 5.6
  28. 8.3
  29. 9.9
  30. 76
  31. 8.5
  32. 57
  33. 82
  34. 45
  35. 9.1
  36. 40
  37. 6.9
  38. 4.7
  39. 45
  40. 8.2

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