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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 17 · 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.√37 to 1 decimal place? (a) 6.2 (b) 6.1 (c) 6.4 (d) 6.3
  2. 2.Best estimate of 5279 ÷ 67? (a) 75 (b) 7500 (c) 750
  3. 3.√30 to 1 decimal place? (a) 5.7 (b) 5.6 (c) 5.8 (d) 5.5
  4. 4.Best estimate of 673 ÷ 21? (a) 34 (b) 340 (c) 3400
  5. 5.Best estimate of 1791 ÷ 83? (a) 2200 (b) 220 (c) 22
  6. 6.Best estimate of 446 ÷ 31? (a) 15 (b) 1500 (c) 150
  7. 7.Best estimate of 3667 ÷ 52? (a) 7300 (b) 73 (c) 730
  8. 8.Best estimate of 849 ÷ 38? (a) 21 (b) 210 (c) 2100
  9. 9.Best estimate of 3239 ÷ 66? (a) 4600 (b) 46 (c) 460
  10. 10.Best estimate of 2380 ÷ 87? (a) 26 (b) 2600 (c) 260
  11. 11.√79 to 1 decimal place? (a) 8.9 (b) 9.0 (c) 9.2 (d) 9.1
  12. 12.√26 to 1 decimal place? (a) 4.8 (b) 4.9 (c) 5.0 (d) 5.1
  13. 13.Best estimate of 1367 ÷ 61? (a) 230 (b) 23 (c) 2300
  14. 14.Best estimate of 2121 ÷ 31? (a) 710 (b) 7100 (c) 71
  15. 15.Best estimate of 2515 ÷ 36? (a) 6300 (b) 63 (c) 630
  16. 16.√58 to 1 decimal place? (a) 7.5 (b) 7.7 (c) 7.4 (d) 7.6
  17. 17.Best estimate of 921 ÷ 46? (a) 180 (b) 1800 (c) 18
  18. 18.√28 to 1 decimal place? (a) 5.5 (b) 5.6 (c) 5.3 (d) 5.4
  19. 19.Best estimate of 867 ÷ 34? (a) 290 (b) 2900 (c) 29
  20. 20.√62 to 1 decimal place? (a) 7.8 (b) 7.9 (c) 8.0 (d) 7.7
  21. 21.√76 to 1 decimal place? (a) 8.6 (b) 8.8 (c) 8.7 (d) 8.9
  22. 22.√40 to 1 decimal place? (a) 6.2 (b) 6.1 (c) 6.4 (d) 6.3
  23. 23.Best estimate of 995 ÷ 52? (a) 20 (b) 200 (c) 2000
  24. 24.√96 to 1 decimal place? (a) 9.6 (b) 9.7 (c) 9.5 (d) 9.8
  25. 25.√71 to 1 decimal place? (a) 8.2 (b) 8.4 (c) 8.5 (d) 8.3
  26. 26.Best estimate of 7629 ÷ 84? (a) 950 (b) 95 (c) 9500
  27. 27.√66 to 1 decimal place? (a) 8.3 (b) 8.1 (c) 8.2 (d) 8.0
  28. 28.Best estimate of 8466 ÷ 89? (a) 940 (b) 94 (c) 9400
  29. 29.√22 to 1 decimal place? (a) 4.6 (b) 4.7 (c) 4.8 (d) 4.5
  30. 30.√72 to 1 decimal place? (a) 8.4 (b) 8.6 (c) 8.5 (d) 8.7
  31. 31.√74 to 1 decimal place? (a) 8.9 (b) 8.8 (c) 8.7 (d) 8.6
  32. 32.Best estimate of 2576 ÷ 36? (a) 6400 (b) 64 (c) 640
  33. 33.Best estimate of 1355 ÷ 54? (a) 270 (b) 27 (c) 2700
  34. 34.√82 to 1 decimal place? (a) 9.2 (b) 9.4 (c) 9.3 (d) 9.1
  35. 35.√90 to 1 decimal place? (a) 9.4 (b) 9.3 (c) 9.2 (d) 9.5
  36. 36.√47 to 1 decimal place? (a) 7.0 (b) 7.1 (c) 6.8 (d) 6.9
  37. 37.Best estimate of 3386 ÷ 87? (a) 3800 (b) 38 (c) 380
  38. 38.Best estimate of 5049 ÷ 76? (a) 630 (b) 6300 (c) 63
  39. 39.Best estimate of 7810 ÷ 88? (a) 870 (b) 87 (c) 8700
  40. 40.√65 to 1 decimal place? (a) 8.1 (b) 8.4 (c) 8.3 (d) 8.2

Answer key

  1. 6.1
  2. 75
  3. 5.5
  4. 34
  5. 22
  6. 15
  7. 73
  8. 21
  9. 46
  10. 26
  11. 8.9
  12. 5.1
  13. 23
  14. 71
  15. 63
  16. 7.6
  17. 18
  18. 5.3
  19. 29
  20. 7.9
  21. 8.7
  22. 6.3
  23. 20
  24. 9.8
  25. 8.4
  26. 95
  27. 8.1
  28. 94
  29. 4.7
  30. 8.5
  31. 8.6
  32. 64
  33. 27
  34. 9.1
  35. 9.5
  36. 6.9
  37. 38
  38. 63
  39. 87
  40. 8.1

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