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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 347 · 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) 6.3 (b) 6.2 (c) 6.0 (d) 6.1
  2. 2.Best estimate of 7160 ÷ 83? (a) 900 (b) 9000 (c) 90
  3. 3.Best estimate of 1686 ÷ 22? (a) 840 (b) 8400 (c) 84
  4. 4.√22 to 1 decimal place? (a) 4.8 (b) 4.7 (c) 4.9 (d) 4.6
  5. 5.√76 to 1 decimal place? (a) 8.7 (b) 8.9 (c) 8.8 (d) 8.6
  6. 6.√63 to 1 decimal place? (a) 7.7 (b) 7.9 (c) 7.6 (d) 7.8
  7. 7.√85 to 1 decimal place? (a) 9.3 (b) 9.5 (c) 9.2 (d) 9.4
  8. 8.Best estimate of 1749 ÷ 62? (a) 2900 (b) 29 (c) 290
  9. 9.√67 to 1 decimal place? (a) 8.1 (b) 8.2 (c) 8.3 (d) 8.4
  10. 10.Best estimate of 6213 ÷ 86? (a) 690 (b) 69 (c) 6900
  11. 11.Best estimate of 1876 ÷ 52? (a) 3800 (b) 380 (c) 38
  12. 12.Best estimate of 2296 ÷ 27? (a) 7700 (b) 77 (c) 770
  13. 13.Best estimate of 866 ÷ 44? (a) 22 (b) 2200 (c) 220
  14. 14.Best estimate of 3165 ÷ 34? (a) 10600 (b) 1060 (c) 106
  15. 15.Best estimate of 2573 ÷ 38? (a) 64 (b) 6400 (c) 640
  16. 16.√82 to 1 decimal place? (a) 9.0 (b) 8.9 (c) 9.1 (d) 8.8
  17. 17.√86 to 1 decimal place? (a) 9.2 (b) 9.4 (c) 9.3 (d) 9.5
  18. 18.√69 to 1 decimal place? (a) 8.4 (b) 8.5 (c) 8.6 (d) 8.3
  19. 19.Best estimate of 1274 ÷ 36? (a) 3200 (b) 32 (c) 320
  20. 20.Best estimate of 5025 ÷ 56? (a) 8400 (b) 840 (c) 84
  21. 21.√92 to 1 decimal place? (a) 9.7 (b) 9.5 (c) 9.8 (d) 9.6
  22. 22.Best estimate of 418 ÷ 27? (a) 14 (b) 1400 (c) 140
  23. 23.√55 to 1 decimal place? (a) 7.7 (b) 7.6 (c) 7.4 (d) 7.5
  24. 24.√58 to 1 decimal place? (a) 7.6 (b) 7.8 (c) 7.5 (d) 7.7
  25. 25.√41 to 1 decimal place? (a) 6.6 (b) 6.7 (c) 6.5 (d) 6.4
  26. 26.Best estimate of 894 ÷ 42? (a) 22 (b) 220 (c) 2200
  27. 27.Best estimate of 2050 ÷ 33? (a) 68 (b) 680 (c) 6800
  28. 28.Best estimate of 2580 ÷ 53? (a) 520 (b) 5200 (c) 52
  29. 29.Best estimate of 1930 ÷ 57? (a) 3200 (b) 32 (c) 320
  30. 30.√43 to 1 decimal place? (a) 6.7 (b) 6.8 (c) 6.6 (d) 6.9
  31. 31.Best estimate of 6309 ÷ 67? (a) 9000 (b) 90 (c) 900
  32. 32.√71 to 1 decimal place? (a) 8.4 (b) 8.6 (c) 8.3 (d) 8.5
  33. 33.√40 to 1 decimal place? (a) 6.3 (b) 6.6 (c) 6.4 (d) 6.5
  34. 34.√47 to 1 decimal place? (a) 7.2 (b) 7.1 (c) 6.9 (d) 7.0
  35. 35.√38 to 1 decimal place? (a) 6.4 (b) 6.1 (c) 6.3 (d) 6.2
  36. 36.Best estimate of 3790 ÷ 56? (a) 6300 (b) 63 (c) 630
  37. 37.Best estimate of 4672 ÷ 69? (a) 6700 (b) 67 (c) 670
  38. 38.Best estimate of 2716 ÷ 52? (a) 5400 (b) 540 (c) 54
  39. 39.Best estimate of 3168 ÷ 37? (a) 79 (b) 7900 (c) 790
  40. 40.Best estimate of 1126 ÷ 39? (a) 280 (b) 2800 (c) 28

Answer key

  1. 6.1
  2. 90
  3. 84
  4. 4.7
  5. 8.7
  6. 7.9
  7. 9.2
  8. 29
  9. 8.2
  10. 69
  11. 38
  12. 77
  13. 22
  14. 106
  15. 64
  16. 9.1
  17. 9.3
  18. 8.3
  19. 32
  20. 84
  21. 9.6
  22. 14
  23. 7.4
  24. 7.6
  25. 6.4
  26. 22
  27. 68
  28. 52
  29. 32
  30. 6.6
  31. 90
  32. 8.4
  33. 6.3
  34. 6.9
  35. 6.2
  36. 63
  37. 67
  38. 54
  39. 79
  40. 28

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