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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 703 · 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.√84 to 1 decimal place? (a) 9.1 (b) 9.0 (c) 8.9 (d) 9.2
  2. 2.√50 to 1 decimal place? (a) 7.1 (b) 6.9 (c) 7.0 (d) 7.2
  3. 3.Best estimate of 3601 ÷ 47? (a) 7200 (b) 72 (c) 720
  4. 4.√61 to 1 decimal place? (a) 8.1 (b) 8.0 (c) 7.8 (d) 7.9
  5. 5.√40 to 1 decimal place? (a) 6.1 (b) 6.2 (c) 6.0 (d) 6.3
  6. 6.√65 to 1 decimal place? (a) 8.1 (b) 8.4 (c) 8.3 (d) 8.2
  7. 7.√77 to 1 decimal place? (a) 8.7 (b) 8.8 (c) 8.9 (d) 9.0
  8. 8.Best estimate of 551 ÷ 38? (a) 14 (b) 1400 (c) 140
  9. 9.√31 to 1 decimal place? (a) 5.5 (b) 5.4 (c) 5.3 (d) 5.6
  10. 10.√94 to 1 decimal place? (a) 9.6 (b) 9.9 (c) 9.8 (d) 9.7
  11. 11.Best estimate of 2149 ÷ 43? (a) 5400 (b) 540 (c) 54
  12. 12.√22 to 1 decimal place? (a) 4.8 (b) 4.9 (c) 4.7 (d) 5.0
  13. 13.√75 to 1 decimal place? (a) 8.5 (b) 8.4 (c) 8.6 (d) 8.7
  14. 14.Best estimate of 598 ÷ 32? (a) 20 (b) 2000 (c) 200
  15. 15.Best estimate of 1369 ÷ 37? (a) 34 (b) 340 (c) 3400
  16. 16.Best estimate of 7072 ÷ 76? (a) 880 (b) 88 (c) 8800
  17. 17.Best estimate of 1212 ÷ 46? (a) 240 (b) 24 (c) 2400
  18. 18.√43 to 1 decimal place? (a) 6.7 (b) 6.9 (c) 6.8 (d) 6.6
  19. 19.Best estimate of 1906 ÷ 58? (a) 3200 (b) 320 (c) 32
  20. 20.√67 to 1 decimal place? (a) 8.3 (b) 8.2 (c) 8.4 (d) 8.1
  21. 21.Best estimate of 3258 ÷ 62? (a) 540 (b) 54 (c) 5400
  22. 22.√83 to 1 decimal place? (a) 9.2 (b) 9.3 (c) 9.1 (d) 9.0
  23. 23.Best estimate of 5089 ÷ 54? (a) 102 (b) 1020 (c) 10200
  24. 24.Best estimate of 729 ÷ 24? (a) 360 (b) 3600 (c) 36
  25. 25.Best estimate of 3137 ÷ 39? (a) 780 (b) 78 (c) 7800
  26. 26.√58 to 1 decimal place? (a) 7.7 (b) 7.9 (c) 7.6 (d) 7.8
  27. 27.√82 to 1 decimal place? (a) 9.0 (b) 8.9 (c) 9.1 (d) 9.2
  28. 28.Best estimate of 1865 ÷ 46? (a) 370 (b) 37 (c) 3700
  29. 29.Best estimate of 876 ÷ 38? (a) 2200 (b) 220 (c) 22
  30. 30.√37 to 1 decimal place? (a) 6.3 (b) 6.1 (c) 6.4 (d) 6.2
  31. 31.Best estimate of 7762 ÷ 89? (a) 86 (b) 860 (c) 8600
  32. 32.Best estimate of 1325 ÷ 34? (a) 440 (b) 44 (c) 4400
  33. 33.Best estimate of 464 ÷ 23? (a) 2300 (b) 23 (c) 230
  34. 34.√26 to 1 decimal place? (a) 4.9 (b) 5.2 (c) 5.1 (d) 5.0
  35. 35.√69 to 1 decimal place? (a) 8.4 (b) 8.5 (c) 8.3 (d) 8.6
  36. 36.√79 to 1 decimal place? (a) 8.8 (b) 8.7 (c) 8.9 (d) 9.0
  37. 37.√30 to 1 decimal place? (a) 5.6 (b) 5.5 (c) 5.7 (d) 5.8
  38. 38.√89 to 1 decimal place? (a) 9.5 (b) 9.7 (c) 9.6 (d) 9.4
  39. 39.√55 to 1 decimal place? (a) 7.4 (b) 7.2 (c) 7.5 (d) 7.3
  40. 40.Best estimate of 797 ÷ 46? (a) 16 (b) 1600 (c) 160

Answer key

  1. 9.2
  2. 7.1
  3. 72
  4. 7.8
  5. 6.3
  6. 8.1
  7. 8.8
  8. 14
  9. 5.6
  10. 9.7
  11. 54
  12. 4.7
  13. 8.7
  14. 20
  15. 34
  16. 88
  17. 24
  18. 6.6
  19. 32
  20. 8.2
  21. 54
  22. 9.1
  23. 102
  24. 36
  25. 78
  26. 7.6
  27. 9.1
  28. 37
  29. 22
  30. 6.1
  31. 86
  32. 44
  33. 23
  34. 5.1
  35. 8.3
  36. 8.9
  37. 5.5
  38. 9.4
  39. 7.4
  40. 16

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