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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 986 · 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.√72 to 1 decimal place? (a) 8.5 (b) 8.3 (c) 8.2 (d) 8.4
  2. 2.√65 to 1 decimal place? (a) 8.0 (b) 8.1 (c) 7.9 (d) 7.8
  3. 3.√63 to 1 decimal place? (a) 7.8 (b) 7.7 (c) 8.0 (d) 7.9
  4. 4.√98 to 1 decimal place? (a) 10.0 (b) 10.1 (c) 9.9 (d) 9.8
  5. 5.√92 to 1 decimal place? (a) 9.7 (b) 9.6 (c) 9.5 (d) 9.4
  6. 6.Best estimate of 6941 ÷ 87? (a) 77 (b) 7700 (c) 770
  7. 7.Best estimate of 3208 ÷ 78? (a) 400 (b) 40 (c) 4000
  8. 8.√43 to 1 decimal place? (a) 6.5 (b) 6.6 (c) 6.7 (d) 6.4
  9. 9.Best estimate of 542 ÷ 23? (a) 2700 (b) 27 (c) 270
  10. 10.Best estimate of 4408 ÷ 76? (a) 5500 (b) 55 (c) 550
  11. 11.Best estimate of 3125 ÷ 33? (a) 1040 (b) 10400 (c) 104
  12. 12.Best estimate of 788 ÷ 22? (a) 3900 (b) 390 (c) 39
  13. 13.√87 to 1 decimal place? (a) 9.2 (b) 9.0 (c) 9.3 (d) 9.1
  14. 14.Best estimate of 4451 ÷ 49? (a) 89 (b) 890 (c) 8900
  15. 15.Best estimate of 1195 ÷ 51? (a) 240 (b) 2400 (c) 24
  16. 16.Best estimate of 5070 ÷ 59? (a) 85 (b) 8500 (c) 850
  17. 17.Best estimate of 878 ÷ 37? (a) 2200 (b) 22 (c) 220
  18. 18.√83 to 1 decimal place? (a) 9.3 (b) 9.2 (c) 9.1 (d) 9.0
  19. 19.√48 to 1 decimal place? (a) 6.7 (b) 6.6 (c) 6.8 (d) 6.9
  20. 20.√74 to 1 decimal place? (a) 8.9 (b) 8.7 (c) 8.8 (d) 8.6
  21. 21.√27 to 1 decimal place? (a) 5.1 (b) 5.3 (c) 5.0 (d) 5.2
  22. 22.Best estimate of 2288 ÷ 28? (a) 76 (b) 7600 (c) 760
  23. 23.Best estimate of 2983 ÷ 66? (a) 4300 (b) 430 (c) 43
  24. 24.Best estimate of 4030 ÷ 69? (a) 580 (b) 5800 (c) 58
  25. 25.Best estimate of 6855 ÷ 82? (a) 86 (b) 860 (c) 8600
  26. 26.Best estimate of 2679 ÷ 37? (a) 670 (b) 6700 (c) 67
  27. 27.√37 to 1 decimal place? (a) 5.9 (b) 5.8 (c) 6.1 (d) 6.0
  28. 28.Best estimate of 906 ÷ 42? (a) 23 (b) 2300 (c) 230
  29. 29.√84 to 1 decimal place? (a) 9.3 (b) 9.4 (c) 9.1 (d) 9.2
  30. 30.Best estimate of 3434 ÷ 72? (a) 490 (b) 4900 (c) 49
  31. 31.Best estimate of 6779 ÷ 72? (a) 9700 (b) 97 (c) 970
  32. 32.Best estimate of 2140 ÷ 37? (a) 5400 (b) 54 (c) 540
  33. 33.Best estimate of 2090 ÷ 77? (a) 2600 (b) 260 (c) 26
  34. 34.Best estimate of 722 ÷ 49? (a) 14 (b) 140 (c) 1400
  35. 35.√78 to 1 decimal place? (a) 8.8 (b) 9.0 (c) 8.7 (d) 8.9
  36. 36.√21 to 1 decimal place? (a) 4.4 (b) 4.6 (c) 4.3 (d) 4.5
  37. 37.Best estimate of 4749 ÷ 77? (a) 590 (b) 59 (c) 5900
  38. 38.Best estimate of 3941 ÷ 78? (a) 490 (b) 4900 (c) 49
  39. 39.Best estimate of 1029 ÷ 26? (a) 34 (b) 3400 (c) 340
  40. 40.Best estimate of 2595 ÷ 82? (a) 320 (b) 3200 (c) 32

Answer key

  1. 8.5
  2. 8.1
  3. 7.9
  4. 9.9
  5. 9.6
  6. 77
  7. 40
  8. 6.6
  9. 27
  10. 55
  11. 104
  12. 39
  13. 9.3
  14. 89
  15. 24
  16. 85
  17. 22
  18. 9.1
  19. 6.9
  20. 8.6
  21. 5.2
  22. 76
  23. 43
  24. 58
  25. 86
  26. 67
  27. 6.1
  28. 23
  29. 9.2
  30. 49
  31. 97
  32. 54
  33. 26
  34. 14
  35. 8.8
  36. 4.6
  37. 59
  38. 49
  39. 34
  40. 32

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