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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 113 · 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.√74 to 1 decimal place? (a) 8.5 (b) 8.4 (c) 8.3 (d) 8.6
  2. 2.Best estimate of 3525 ÷ 64? (a) 5900 (b) 59 (c) 590
  3. 3.Best estimate of 3596 ÷ 68? (a) 510 (b) 5100 (c) 51
  4. 4.Best estimate of 8184 ÷ 86? (a) 91 (b) 9100 (c) 910
  5. 5.√35 to 1 decimal place? (a) 5.7 (b) 5.8 (c) 5.9 (d) 5.6
  6. 6.√63 to 1 decimal place? (a) 7.6 (b) 7.8 (c) 7.9 (d) 7.7
  7. 7.Best estimate of 2401 ÷ 32? (a) 80 (b) 8000 (c) 800
  8. 8.√71 to 1 decimal place? (a) 8.3 (b) 8.2 (c) 8.4 (d) 8.5
  9. 9.Best estimate of 1089 ÷ 32? (a) 3600 (b) 36 (c) 360
  10. 10.√47 to 1 decimal place? (a) 7.1 (b) 7.0 (c) 7.2 (d) 6.9
  11. 11.Best estimate of 2328 ÷ 32? (a) 780 (b) 7800 (c) 78
  12. 12.Best estimate of 510 ÷ 26? (a) 170 (b) 17 (c) 1700
  13. 13.√26 to 1 decimal place? (a) 4.9 (b) 5.0 (c) 5.1 (d) 5.2
  14. 14.Best estimate of 1864 ÷ 71? (a) 2700 (b) 27 (c) 270
  15. 15.√21 to 1 decimal place? (a) 4.5 (b) 4.6 (c) 4.7 (d) 4.4
  16. 16.√75 to 1 decimal place? (a) 8.6 (b) 8.5 (c) 8.7 (d) 8.4
  17. 17.√65 to 1 decimal place? (a) 8.0 (b) 8.3 (c) 8.2 (d) 8.1
  18. 18.Best estimate of 6420 ÷ 71? (a) 92 (b) 9200 (c) 920
  19. 19.Best estimate of 1090 ÷ 29? (a) 36 (b) 3600 (c) 360
  20. 20.Best estimate of 2228 ÷ 31? (a) 740 (b) 74 (c) 7400
  21. 21.√83 to 1 decimal place? (a) 9.3 (b) 9.2 (c) 9.4 (d) 9.1
  22. 22.√80 to 1 decimal place? (a) 8.9 (b) 8.8 (c) 8.7 (d) 8.6
  23. 23.√28 to 1 decimal place? (a) 5.2 (b) 5.4 (c) 5.5 (d) 5.3
  24. 24.Best estimate of 1486 ÷ 56? (a) 250 (b) 2500 (c) 25
  25. 25.√41 to 1 decimal place? (a) 6.4 (b) 6.3 (c) 6.5 (d) 6.2
  26. 26.Best estimate of 2942 ÷ 76? (a) 37 (b) 3700 (c) 370
  27. 27.√90 to 1 decimal place? (a) 9.6 (b) 9.3 (c) 9.4 (d) 9.5
  28. 28.Best estimate of 1101 ÷ 24? (a) 5500 (b) 55 (c) 550
  29. 29.Best estimate of 3046 ÷ 83? (a) 380 (b) 3800 (c) 38
  30. 30.√51 to 1 decimal place? (a) 7.2 (b) 7.0 (c) 7.1 (d) 7.3
  31. 31.√20 to 1 decimal place? (a) 4.8 (b) 4.7 (c) 4.6 (d) 4.5
  32. 32.√82 to 1 decimal place? (a) 9.1 (b) 9.2 (c) 9.3 (d) 9.0
  33. 33.Best estimate of 2157 ÷ 23? (a) 10800 (b) 1080 (c) 108
  34. 34.Best estimate of 4934 ÷ 87? (a) 550 (b) 5500 (c) 55
  35. 35.Best estimate of 5117 ÷ 63? (a) 85 (b) 850 (c) 8500
  36. 36.Best estimate of 5242 ÷ 72? (a) 75 (b) 7500 (c) 750
  37. 37.Best estimate of 4398 ÷ 72? (a) 63 (b) 630 (c) 6300
  38. 38.√98 to 1 decimal place? (a) 10.0 (b) 9.8 (c) 10.1 (d) 9.9
  39. 39.Best estimate of 1359 ÷ 44? (a) 340 (b) 3400 (c) 34
  40. 40.√77 to 1 decimal place? (a) 8.8 (b) 9.0 (c) 9.1 (d) 8.9

Answer key

  1. 8.6
  2. 59
  3. 51
  4. 91
  5. 5.9
  6. 7.9
  7. 80
  8. 8.4
  9. 36
  10. 6.9
  11. 78
  12. 17
  13. 5.1
  14. 27
  15. 4.6
  16. 8.7
  17. 8.1
  18. 92
  19. 36
  20. 74
  21. 9.1
  22. 8.9
  23. 5.3
  24. 25
  25. 6.4
  26. 37
  27. 9.5
  28. 55
  29. 38
  30. 7.1
  31. 4.5
  32. 9.1
  33. 108
  34. 55
  35. 85
  36. 75
  37. 63
  38. 9.9
  39. 34
  40. 8.8

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