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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 74 · 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.√87 to 1 decimal place? (a) 9.5 (b) 9.3 (c) 9.4 (d) 9.2
  2. 2.Best estimate of 1676 ÷ 76? (a) 210 (b) 2100 (c) 21
  3. 3.Best estimate of 4012 ÷ 72? (a) 57 (b) 570 (c) 5700
  4. 4.√67 to 1 decimal place? (a) 8.2 (b) 8.0 (c) 8.1 (d) 7.9
  5. 5.√61 to 1 decimal place? (a) 7.7 (b) 7.9 (c) 7.8 (d) 7.6
  6. 6.√72 to 1 decimal place? (a) 8.6 (b) 8.5 (c) 8.4 (d) 8.3
  7. 7.Best estimate of 6629 ÷ 73? (a) 950 (b) 9500 (c) 95
  8. 8.Best estimate of 484 ÷ 27? (a) 1600 (b) 16 (c) 160
  9. 9.Best estimate of 1226 ÷ 37? (a) 3100 (b) 310 (c) 31
  10. 10.Best estimate of 432 ÷ 33? (a) 14 (b) 140 (c) 1400
  11. 11.√78 to 1 decimal place? (a) 8.5 (b) 8.7 (c) 8.6 (d) 8.8
  12. 12.√92 to 1 decimal place? (a) 9.4 (b) 9.5 (c) 9.6 (d) 9.7
  13. 13.√65 to 1 decimal place? (a) 8.2 (b) 8.1 (c) 8.4 (d) 8.3
  14. 14.Best estimate of 1365 ÷ 69? (a) 200 (b) 2000 (c) 20
  15. 15.Best estimate of 1862 ÷ 26? (a) 6200 (b) 620 (c) 62
  16. 16.√24 to 1 decimal place? (a) 4.8 (b) 5.0 (c) 4.9 (d) 5.1
  17. 17.Best estimate of 5483 ÷ 69? (a) 780 (b) 78 (c) 7800
  18. 18.Best estimate of 913 ÷ 37? (a) 2300 (b) 23 (c) 230
  19. 19.√96 to 1 decimal place? (a) 9.8 (b) 10.0 (c) 10.1 (d) 9.9
  20. 20.Best estimate of 3059 ÷ 42? (a) 76 (b) 7600 (c) 760
  21. 21.√71 to 1 decimal place? (a) 8.6 (b) 8.4 (c) 8.3 (d) 8.5
  22. 22.√76 to 1 decimal place? (a) 8.8 (b) 8.7 (c) 8.9 (d) 8.6
  23. 23.Best estimate of 7410 ÷ 87? (a) 820 (b) 8200 (c) 82
  24. 24.√37 to 1 decimal place? (a) 6.2 (b) 6.4 (c) 6.1 (d) 6.3
  25. 25.Best estimate of 2947 ÷ 63? (a) 490 (b) 49 (c) 4900
  26. 26.Best estimate of 3231 ÷ 63? (a) 5400 (b) 54 (c) 540
  27. 27.Best estimate of 3481 ÷ 81? (a) 440 (b) 44 (c) 4400
  28. 28.Best estimate of 2139 ÷ 59? (a) 36 (b) 3600 (c) 360
  29. 29.√40 to 1 decimal place? (a) 6.2 (b) 6.3 (c) 6.0 (d) 6.1
  30. 30.√41 to 1 decimal place? (a) 6.5 (b) 6.4 (c) 6.3 (d) 6.2
  31. 31.Best estimate of 392 ÷ 23? (a) 20 (b) 200 (c) 2000
  32. 32.Best estimate of 2445 ÷ 39? (a) 61 (b) 6100 (c) 610
  33. 33.√30 to 1 decimal place? (a) 5.4 (b) 5.5 (c) 5.3 (d) 5.2
  34. 34.Best estimate of 3292 ÷ 51? (a) 66 (b) 660 (c) 6600
  35. 35.√27 to 1 decimal place? (a) 5.0 (b) 5.3 (c) 5.2 (d) 5.1
  36. 36.Best estimate of 1305 ÷ 28? (a) 4400 (b) 44 (c) 440
  37. 37.Best estimate of 3602 ÷ 47? (a) 7200 (b) 72 (c) 720
  38. 38.Best estimate of 1944 ÷ 83? (a) 2400 (b) 240 (c) 24
  39. 39.√94 to 1 decimal place? (a) 10.0 (b) 9.9 (c) 9.8 (d) 9.7
  40. 40.√43 to 1 decimal place? (a) 6.5 (b) 6.4 (c) 6.6 (d) 6.7

Answer key

  1. 9.3
  2. 21
  3. 57
  4. 8.2
  5. 7.8
  6. 8.5
  7. 95
  8. 16
  9. 31
  10. 14
  11. 8.8
  12. 9.6
  13. 8.1
  14. 20
  15. 62
  16. 4.9
  17. 78
  18. 23
  19. 9.8
  20. 76
  21. 8.4
  22. 8.7
  23. 82
  24. 6.1
  25. 49
  26. 54
  27. 44
  28. 36
  29. 6.3
  30. 6.4
  31. 20
  32. 61
  33. 5.5
  34. 66
  35. 5.2
  36. 44
  37. 72
  38. 24
  39. 9.7
  40. 6.6

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