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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 685 · 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.√61 to 1 decimal place? (a) 7.9 (b) 8.0 (c) 7.7 (d) 7.8
  2. 2.Best estimate of 387 ÷ 26? (a) 130 (b) 1300 (c) 13
  3. 3.Best estimate of 3375 ÷ 42? (a) 84 (b) 8400 (c) 840
  4. 4.Best estimate of 2161 ÷ 54? (a) 430 (b) 43 (c) 4300
  5. 5.√51 to 1 decimal place? (a) 7.2 (b) 7.3 (c) 7.4 (d) 7.1
  6. 6.√34 to 1 decimal place? (a) 6.0 (b) 5.8 (c) 5.9 (d) 6.1
  7. 7.Best estimate of 828 ÷ 49? (a) 170 (b) 1700 (c) 17
  8. 8.√38 to 1 decimal place? (a) 6.3 (b) 6.4 (c) 6.1 (d) 6.2
  9. 9.√76 to 1 decimal place? (a) 8.7 (b) 8.8 (c) 8.6 (d) 8.9
  10. 10.Best estimate of 307 ÷ 21? (a) 150 (b) 1500 (c) 15
  11. 11.√41 to 1 decimal place? (a) 6.4 (b) 6.1 (c) 6.3 (d) 6.2
  12. 12.√72 to 1 decimal place? (a) 8.8 (b) 8.5 (c) 8.7 (d) 8.6
  13. 13.Best estimate of 3560 ÷ 83? (a) 4500 (b) 45 (c) 450
  14. 14.√63 to 1 decimal place? (a) 8.1 (b) 8.2 (c) 8.0 (d) 7.9
  15. 15.Best estimate of 795 ÷ 22? (a) 40 (b) 4000 (c) 400
  16. 16.Best estimate of 807 ÷ 24? (a) 4000 (b) 400 (c) 40
  17. 17.√78 to 1 decimal place? (a) 8.6 (b) 8.8 (c) 8.7 (d) 8.5
  18. 18.√71 to 1 decimal place? (a) 8.7 (b) 8.6 (c) 8.5 (d) 8.4
  19. 19.√79 to 1 decimal place? (a) 8.7 (b) 8.6 (c) 8.9 (d) 8.8
  20. 20.Best estimate of 4171 ÷ 54? (a) 83 (b) 8300 (c) 830
  21. 21.Best estimate of 2594 ÷ 48? (a) 52 (b) 5200 (c) 520
  22. 22.Best estimate of 5653 ÷ 64? (a) 940 (b) 94 (c) 9400
  23. 23.Best estimate of 1169 ÷ 77? (a) 150 (b) 1500 (c) 15
  24. 24.Best estimate of 1129 ÷ 34? (a) 3800 (b) 38 (c) 380
  25. 25.√58 to 1 decimal place? (a) 7.3 (b) 7.4 (c) 7.5 (d) 7.6
  26. 26.√40 to 1 decimal place? (a) 6.3 (b) 6.2 (c) 6.4 (d) 6.1
  27. 27.Best estimate of 1332 ÷ 71? (a) 190 (b) 1900 (c) 19
  28. 28.√82 to 1 decimal place? (a) 9.2 (b) 9.0 (c) 8.9 (d) 9.1
  29. 29.Best estimate of 6715 ÷ 86? (a) 75 (b) 7500 (c) 750
  30. 30.Best estimate of 4914 ÷ 68? (a) 700 (b) 7000 (c) 70
  31. 31.Best estimate of 1663 ÷ 46? (a) 33 (b) 3300 (c) 330
  32. 32.Best estimate of 486 ÷ 36? (a) 120 (b) 1200 (c) 12
  33. 33.√28 to 1 decimal place? (a) 5.6 (b) 5.4 (c) 5.5 (d) 5.3
  34. 34.Best estimate of 975 ÷ 36? (a) 240 (b) 2400 (c) 24
  35. 35.Best estimate of 942 ÷ 42? (a) 2400 (b) 240 (c) 24
  36. 36.√74 to 1 decimal place? (a) 8.5 (b) 8.8 (c) 8.7 (d) 8.6
  37. 37.√56 to 1 decimal place? (a) 7.4 (b) 7.5 (c) 7.3 (d) 7.2
  38. 38.Best estimate of 5660 ÷ 84? (a) 71 (b) 7100 (c) 710
  39. 39.√45 to 1 decimal place? (a) 6.6 (b) 6.8 (c) 6.5 (d) 6.7
  40. 40.√37 to 1 decimal place? (a) 6.3 (b) 6.1 (c) 6.2 (d) 6.0

Answer key

  1. 7.8
  2. 13
  3. 84
  4. 43
  5. 7.1
  6. 5.8
  7. 17
  8. 6.2
  9. 8.7
  10. 15
  11. 6.4
  12. 8.5
  13. 45
  14. 7.9
  15. 40
  16. 40
  17. 8.8
  18. 8.4
  19. 8.9
  20. 83
  21. 52
  22. 94
  23. 15
  24. 38
  25. 7.6
  26. 6.3
  27. 19
  28. 9.1
  29. 75
  30. 70
  31. 33
  32. 12
  33. 5.3
  34. 24
  35. 24
  36. 8.6
  37. 7.5
  38. 71
  39. 6.7
  40. 6.1

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