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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 321 · 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.Best estimate of 1958 ÷ 46? (a) 39 (b) 390 (c) 3900
  2. 2.Best estimate of 4960 ÷ 76? (a) 6200 (b) 620 (c) 62
  3. 3.√52 to 1 decimal place? (a) 6.9 (b) 7.0 (c) 7.1 (d) 7.2
  4. 4.√20 to 1 decimal place? (a) 4.5 (b) 4.7 (c) 4.6 (d) 4.4
  5. 5.√96 to 1 decimal place? (a) 9.5 (b) 9.6 (c) 9.7 (d) 9.8
  6. 6.Best estimate of 2158 ÷ 46? (a) 430 (b) 4300 (c) 43
  7. 7.Best estimate of 1256 ÷ 26? (a) 42 (b) 420 (c) 4200
  8. 8.Best estimate of 1428 ÷ 26? (a) 4800 (b) 48 (c) 480
  9. 9.Best estimate of 816 ÷ 53? (a) 160 (b) 1600 (c) 16
  10. 10.√51 to 1 decimal place? (a) 6.9 (b) 6.8 (c) 7.1 (d) 7.0
  11. 11.√69 to 1 decimal place? (a) 8.4 (b) 8.5 (c) 8.6 (d) 8.3
  12. 12.√71 to 1 decimal place? (a) 8.5 (b) 8.4 (c) 8.3 (d) 8.2
  13. 13.√56 to 1 decimal place? (a) 7.5 (b) 7.6 (c) 7.8 (d) 7.7
  14. 14.Best estimate of 3989 ÷ 87? (a) 440 (b) 4400 (c) 44
  15. 15.Best estimate of 5310 ÷ 61? (a) 8900 (b) 89 (c) 890
  16. 16.Best estimate of 4557 ÷ 51? (a) 910 (b) 91 (c) 9100
  17. 17.√62 to 1 decimal place? (a) 7.6 (b) 7.7 (c) 7.8 (d) 7.9
  18. 18.√66 to 1 decimal place? (a) 8.0 (b) 8.1 (c) 7.8 (d) 7.9
  19. 19.√30 to 1 decimal place? (a) 5.5 (b) 5.4 (c) 5.6 (d) 5.7
  20. 20.√58 to 1 decimal place? (a) 7.4 (b) 7.7 (c) 7.6 (d) 7.5
  21. 21.√50 to 1 decimal place? (a) 7.0 (b) 7.3 (c) 7.1 (d) 7.2
  22. 22.√75 to 1 decimal place? (a) 8.9 (b) 8.8 (c) 9.0 (d) 8.7
  23. 23.√55 to 1 decimal place? (a) 7.3 (b) 7.5 (c) 7.4 (d) 7.2
  24. 24.Best estimate of 3710 ÷ 59? (a) 620 (b) 6200 (c) 62
  25. 25.Best estimate of 2174 ÷ 51? (a) 430 (b) 4300 (c) 43
  26. 26.Best estimate of 961 ÷ 42? (a) 2400 (b) 240 (c) 24
  27. 27.Best estimate of 672 ÷ 31? (a) 2200 (b) 22 (c) 220
  28. 28.√41 to 1 decimal place? (a) 6.6 (b) 6.4 (c) 6.5 (d) 6.7
  29. 29.Best estimate of 2592 ÷ 66? (a) 37 (b) 370 (c) 3700
  30. 30.Best estimate of 6040 ÷ 84? (a) 7600 (b) 760 (c) 76
  31. 31.Best estimate of 5757 ÷ 71? (a) 82 (b) 820 (c) 8200
  32. 32.√72 to 1 decimal place? (a) 8.6 (b) 8.3 (c) 8.5 (d) 8.4
  33. 33.Best estimate of 1657 ÷ 61? (a) 28 (b) 2800 (c) 280
  34. 34.Best estimate of 4121 ÷ 49? (a) 8200 (b) 820 (c) 82
  35. 35.Best estimate of 2314 ÷ 88? (a) 2600 (b) 26 (c) 260
  36. 36.Best estimate of 5490 ÷ 72? (a) 780 (b) 7800 (c) 78
  37. 37.Best estimate of 3266 ÷ 51? (a) 65 (b) 650 (c) 6500
  38. 38.√22 to 1 decimal place? (a) 4.5 (b) 4.4 (c) 4.7 (d) 4.6
  39. 39.√40 to 1 decimal place? (a) 6.3 (b) 6.1 (c) 6.2 (d) 6.4
  40. 40.√86 to 1 decimal place? (a) 9.5 (b) 9.3 (c) 9.4 (d) 9.2

Answer key

  1. 39
  2. 62
  3. 7.2
  4. 4.5
  5. 9.8
  6. 43
  7. 42
  8. 48
  9. 16
  10. 7.1
  11. 8.3
  12. 8.4
  13. 7.5
  14. 44
  15. 89
  16. 91
  17. 7.9
  18. 8.1
  19. 5.5
  20. 7.6
  21. 7.1
  22. 8.7
  23. 7.4
  24. 62
  25. 43
  26. 24
  27. 22
  28. 6.4
  29. 37
  30. 76
  31. 82
  32. 8.5
  33. 28
  34. 82
  35. 26
  36. 78
  37. 65
  38. 4.7
  39. 6.3
  40. 9.3

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