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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 584 · 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.√31 to 1 decimal place? (a) 5.6 (b) 5.8 (c) 5.5 (d) 5.7
  2. 2.Best estimate of 5632 ÷ 86? (a) 63 (b) 630 (c) 6300
  3. 3.Best estimate of 2156 ÷ 37? (a) 540 (b) 5400 (c) 54
  4. 4.Best estimate of 3307 ÷ 68? (a) 4700 (b) 47 (c) 470
  5. 5.Best estimate of 2244 ÷ 77? (a) 280 (b) 2800 (c) 28
  6. 6.√70 to 1 decimal place? (a) 8.5 (b) 8.2 (c) 8.4 (d) 8.3
  7. 7.√61 to 1 decimal place? (a) 8.1 (b) 8.0 (c) 7.8 (d) 7.9
  8. 8.Best estimate of 880 ÷ 72? (a) 130 (b) 1300 (c) 13
  9. 9.√78 to 1 decimal place? (a) 8.8 (b) 8.7 (c) 9.0 (d) 8.9
  10. 10.Best estimate of 1498 ÷ 72? (a) 210 (b) 2100 (c) 21
  11. 11.Best estimate of 531 ÷ 34? (a) 18 (b) 1800 (c) 180
  12. 12.Best estimate of 2612 ÷ 56? (a) 4400 (b) 44 (c) 440
  13. 13.√45 to 1 decimal place? (a) 6.7 (b) 6.4 (c) 6.6 (d) 6.5
  14. 14.√88 to 1 decimal place? (a) 9.5 (b) 9.3 (c) 9.4 (d) 9.2
  15. 15.√37 to 1 decimal place? (a) 6.4 (b) 6.1 (c) 6.2 (d) 6.3
  16. 16.√65 to 1 decimal place? (a) 8.1 (b) 7.9 (c) 8.0 (d) 7.8
  17. 17.Best estimate of 970 ÷ 44? (a) 2400 (b) 24 (c) 240
  18. 18.√80 to 1 decimal place? (a) 8.9 (b) 9.0 (c) 9.2 (d) 9.1
  19. 19.Best estimate of 3059 ÷ 42? (a) 7600 (b) 76 (c) 760
  20. 20.Best estimate of 2167 ÷ 32? (a) 720 (b) 7200 (c) 72
  21. 21.√32 to 1 decimal place? (a) 5.6 (b) 5.4 (c) 5.7 (d) 5.5
  22. 22.Best estimate of 3977 ÷ 42? (a) 990 (b) 9900 (c) 99
  23. 23.√92 to 1 decimal place? (a) 9.3 (b) 9.6 (c) 9.5 (d) 9.4
  24. 24.Best estimate of 823 ÷ 23? (a) 41 (b) 410 (c) 4100
  25. 25.Best estimate of 6713 ÷ 74? (a) 9600 (b) 96 (c) 960
  26. 26.√98 to 1 decimal place? (a) 9.8 (b) 10.0 (c) 9.7 (d) 9.9
  27. 27.Best estimate of 2796 ÷ 34? (a) 9300 (b) 93 (c) 930
  28. 28.√44 to 1 decimal place? (a) 6.6 (b) 6.4 (c) 6.3 (d) 6.5
  29. 29.Best estimate of 1796 ÷ 53? (a) 36 (b) 3600 (c) 360
  30. 30.Best estimate of 3265 ÷ 48? (a) 650 (b) 6500 (c) 65
  31. 31.Best estimate of 1988 ÷ 39? (a) 500 (b) 50 (c) 5000
  32. 32.Best estimate of 3223 ÷ 46? (a) 6400 (b) 64 (c) 640
  33. 33.√83 to 1 decimal place? (a) 9.2 (b) 9.4 (c) 9.1 (d) 9.3
  34. 34.Best estimate of 1908 ÷ 66? (a) 27 (b) 2700 (c) 270
  35. 35.Best estimate of 1576 ÷ 39? (a) 3900 (b) 390 (c) 39
  36. 36.Best estimate of 2798 ÷ 86? (a) 31 (b) 3100 (c) 310
  37. 37.Best estimate of 6416 ÷ 71? (a) 9200 (b) 92 (c) 920
  38. 38.√76 to 1 decimal place? (a) 8.6 (b) 8.7 (c) 8.5 (d) 8.8
  39. 39.Best estimate of 1639 ÷ 77? (a) 2000 (b) 200 (c) 20
  40. 40.Best estimate of 943 ÷ 52? (a) 19 (b) 190 (c) 1900

Answer key

  1. 5.6
  2. 63
  3. 54
  4. 47
  5. 28
  6. 8.4
  7. 7.8
  8. 13
  9. 8.8
  10. 21
  11. 18
  12. 44
  13. 6.7
  14. 9.4
  15. 6.1
  16. 8.1
  17. 24
  18. 8.9
  19. 76
  20. 72
  21. 5.7
  22. 99
  23. 9.6
  24. 41
  25. 96
  26. 9.9
  27. 93
  28. 6.6
  29. 36
  30. 65
  31. 50
  32. 64
  33. 9.1
  34. 27
  35. 39
  36. 31
  37. 92
  38. 8.7
  39. 20
  40. 19

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