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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 513 · 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.√86 to 1 decimal place? (a) 9.5 (b) 9.6 (c) 9.3 (d) 9.4
  2. 2.√71 to 1 decimal place? (a) 8.4 (b) 8.5 (c) 8.3 (d) 8.2
  3. 3.√70 to 1 decimal place? (a) 8.4 (b) 8.2 (c) 8.3 (d) 8.1
  4. 4.Best estimate of 6880 ÷ 86? (a) 76 (b) 760 (c) 7600
  5. 5.√35 to 1 decimal place? (a) 5.7 (b) 5.6 (c) 5.9 (d) 5.8
  6. 6.√40 to 1 decimal place? (a) 6.4 (b) 6.2 (c) 6.5 (d) 6.3
  7. 7.Best estimate of 2861 ÷ 33? (a) 95 (b) 950 (c) 9500
  8. 8.√52 to 1 decimal place? (a) 7.4 (b) 7.3 (c) 7.2 (d) 7.1
  9. 9.√94 to 1 decimal place? (a) 9.8 (b) 9.6 (c) 9.9 (d) 9.7
  10. 10.Best estimate of 1124 ÷ 33? (a) 3700 (b) 370 (c) 37
  11. 11.√41 to 1 decimal place? (a) 6.6 (b) 6.3 (c) 6.5 (d) 6.4
  12. 12.√74 to 1 decimal place? (a) 8.8 (b) 8.7 (c) 8.5 (d) 8.6
  13. 13.Best estimate of 655 ÷ 38? (a) 16 (b) 160 (c) 1600
  14. 14.√38 to 1 decimal place? (a) 6.0 (b) 6.2 (c) 6.1 (d) 5.9
  15. 15.√78 to 1 decimal place? (a) 8.8 (b) 8.9 (c) 8.6 (d) 8.7
  16. 16.Best estimate of 7233 ÷ 86? (a) 8000 (b) 80 (c) 800
  17. 17.Best estimate of 2194 ÷ 26? (a) 7300 (b) 73 (c) 730
  18. 18.Best estimate of 3126 ÷ 37? (a) 78 (b) 780 (c) 7800
  19. 19.Best estimate of 907 ÷ 24? (a) 4500 (b) 450 (c) 45
  20. 20.Best estimate of 2673 ÷ 72? (a) 38 (b) 3800 (c) 380
  21. 21.√46 to 1 decimal place? (a) 6.9 (b) 6.8 (c) 6.6 (d) 6.7
  22. 22.√22 to 1 decimal place? (a) 4.9 (b) 4.6 (c) 4.7 (d) 4.8
  23. 23.Best estimate of 2286 ÷ 44? (a) 57 (b) 570 (c) 5700
  24. 24.Best estimate of 7295 ÷ 77? (a) 9100 (b) 91 (c) 910
  25. 25.Best estimate of 2431 ÷ 31? (a) 8100 (b) 81 (c) 810
  26. 26.Best estimate of 5566 ÷ 64? (a) 930 (b) 93 (c) 9300
  27. 27.Best estimate of 1005 ÷ 49? (a) 20 (b) 2000 (c) 200
  28. 28.Best estimate of 743 ÷ 39? (a) 190 (b) 19 (c) 1900
  29. 29.Best estimate of 6755 ÷ 76? (a) 8400 (b) 840 (c) 84
  30. 30.√43 to 1 decimal place? (a) 6.8 (b) 6.7 (c) 6.5 (d) 6.6
  31. 31.Best estimate of 911 ÷ 43? (a) 23 (b) 2300 (c) 230
  32. 32.Best estimate of 686 ÷ 42? (a) 1700 (b) 170 (c) 17
  33. 33.√20 to 1 decimal place? (a) 4.8 (b) 4.5 (c) 4.7 (d) 4.6
  34. 34.√88 to 1 decimal place? (a) 9.1 (b) 9.4 (c) 9.2 (d) 9.3
  35. 35.√61 to 1 decimal place? (a) 8.0 (b) 7.9 (c) 8.1 (d) 7.8
  36. 36.Best estimate of 1026 ÷ 71? (a) 150 (b) 1500 (c) 15
  37. 37.√58 to 1 decimal place? (a) 7.3 (b) 7.6 (c) 7.5 (d) 7.4
  38. 38.√34 to 1 decimal place? (a) 5.7 (b) 5.6 (c) 5.9 (d) 5.8
  39. 39.√85 to 1 decimal place? (a) 9.2 (b) 9.1 (c) 9.3 (d) 9.0
  40. 40.√26 to 1 decimal place? (a) 5.1 (b) 5.3 (c) 5.2 (d) 5.0

Answer key

  1. 9.3
  2. 8.4
  3. 8.4
  4. 76
  5. 5.9
  6. 6.3
  7. 95
  8. 7.2
  9. 9.7
  10. 37
  11. 6.4
  12. 8.6
  13. 16
  14. 6.2
  15. 8.8
  16. 80
  17. 73
  18. 78
  19. 45
  20. 38
  21. 6.8
  22. 4.7
  23. 57
  24. 91
  25. 81
  26. 93
  27. 20
  28. 19
  29. 84
  30. 6.6
  31. 23
  32. 17
  33. 4.5
  34. 9.4
  35. 7.8
  36. 15
  37. 7.6
  38. 5.8
  39. 9.2
  40. 5.1

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