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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 122 · 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.√92 to 1 decimal place? (a) 9.7 (b) 9.8 (c) 9.6 (d) 9.5
  2. 2.Best estimate of 1606 ÷ 63? (a) 27 (b) 270 (c) 2700
  3. 3.√78 to 1 decimal place? (a) 8.6 (b) 8.8 (c) 8.7 (d) 8.5
  4. 4.Best estimate of 3739 ÷ 66? (a) 5300 (b) 530 (c) 53
  5. 5.√58 to 1 decimal place? (a) 7.8 (b) 7.9 (c) 7.7 (d) 7.6
  6. 6.Best estimate of 1461 ÷ 28? (a) 4900 (b) 49 (c) 490
  7. 7.Best estimate of 2914 ÷ 33? (a) 970 (b) 97 (c) 9700
  8. 8.Best estimate of 1267 ÷ 37? (a) 3200 (b) 320 (c) 32
  9. 9.Best estimate of 2132 ÷ 41? (a) 530 (b) 5300 (c) 53
  10. 10.√76 to 1 decimal place? (a) 8.7 (b) 8.8 (c) 8.6 (d) 8.5
  11. 11.Best estimate of 2191 ÷ 28? (a) 73 (b) 7300 (c) 730
  12. 12.Best estimate of 642 ÷ 42? (a) 160 (b) 16 (c) 1600
  13. 13.√98 to 1 decimal place? (a) 9.9 (b) 9.7 (c) 9.8 (d) 9.6
  14. 14.√28 to 1 decimal place? (a) 5.5 (b) 5.4 (c) 5.3 (d) 5.2
  15. 15.Best estimate of 1394 ÷ 42? (a) 3500 (b) 35 (c) 350
  16. 16.√40 to 1 decimal place? (a) 6.1 (b) 6.3 (c) 6.2 (d) 6.0
  17. 17.√61 to 1 decimal place? (a) 8.0 (b) 8.1 (c) 7.9 (d) 7.8
  18. 18.√94 to 1 decimal place? (a) 9.8 (b) 9.9 (c) 9.6 (d) 9.7
  19. 19.Best estimate of 2471 ÷ 54? (a) 49 (b) 490 (c) 4900
  20. 20.Best estimate of 5088 ÷ 79? (a) 64 (b) 640 (c) 6400
  21. 21.Best estimate of 3564 ÷ 74? (a) 510 (b) 51 (c) 5100
  22. 22.√50 to 1 decimal place? (a) 7.4 (b) 7.1 (c) 7.3 (d) 7.2
  23. 23.Best estimate of 3812 ÷ 82? (a) 48 (b) 480 (c) 4800
  24. 24.Best estimate of 2949 ÷ 36? (a) 74 (b) 740 (c) 7400
  25. 25.√83 to 1 decimal place? (a) 9.1 (b) 9.0 (c) 8.9 (d) 8.8
  26. 26.Best estimate of 3027 ÷ 84? (a) 3800 (b) 380 (c) 38
  27. 27.Best estimate of 3075 ÷ 46? (a) 620 (b) 6200 (c) 62
  28. 28.√30 to 1 decimal place? (a) 5.3 (b) 5.6 (c) 5.4 (d) 5.5
  29. 29.Best estimate of 1876 ÷ 37? (a) 47 (b) 470 (c) 4700
  30. 30.Best estimate of 8423 ÷ 88? (a) 94 (b) 940 (c) 9400
  31. 31.√35 to 1 decimal place? (a) 5.8 (b) 5.7 (c) 5.9 (d) 6.0
  32. 32.Best estimate of 1104 ÷ 64? (a) 1800 (b) 18 (c) 180
  33. 33.√21 to 1 decimal place? (a) 4.5 (b) 4.7 (c) 4.6 (d) 4.4
  34. 34.Best estimate of 2426 ÷ 56? (a) 400 (b) 4000 (c) 40
  35. 35.Best estimate of 4140 ÷ 49? (a) 830 (b) 83 (c) 8300
  36. 36.√34 to 1 decimal place? (a) 6.1 (b) 6.0 (c) 5.9 (d) 5.8
  37. 37.Best estimate of 1224 ÷ 44? (a) 31 (b) 310 (c) 3100
  38. 38.√20 to 1 decimal place? (a) 4.6 (b) 4.8 (c) 4.7 (d) 4.5
  39. 39.√38 to 1 decimal place? (a) 6.0 (b) 6.1 (c) 6.3 (d) 6.2
  40. 40.Best estimate of 507 ÷ 24? (a) 2500 (b) 250 (c) 25

Answer key

  1. 9.6
  2. 27
  3. 8.8
  4. 53
  5. 7.6
  6. 49
  7. 97
  8. 32
  9. 53
  10. 8.7
  11. 73
  12. 16
  13. 9.9
  14. 5.3
  15. 35
  16. 6.3
  17. 7.8
  18. 9.7
  19. 49
  20. 64
  21. 51
  22. 7.1
  23. 48
  24. 74
  25. 9.1
  26. 38
  27. 62
  28. 5.5
  29. 47
  30. 94
  31. 5.9
  32. 18
  33. 4.6
  34. 40
  35. 83
  36. 5.8
  37. 31
  38. 4.5
  39. 6.2
  40. 25

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