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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 111 · 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.√34 to 1 decimal place? (a) 5.9 (b) 5.7 (c) 6.0 (d) 5.8
  2. 2.Best estimate of 6187 ÷ 68? (a) 8800 (b) 880 (c) 88
  3. 3.√74 to 1 decimal place? (a) 8.6 (b) 8.3 (c) 8.5 (d) 8.4
  4. 4.√98 to 1 decimal place? (a) 9.6 (b) 9.8 (c) 9.7 (d) 9.9
  5. 5.√43 to 1 decimal place? (a) 6.7 (b) 6.5 (c) 6.6 (d) 6.4
  6. 6.√26 to 1 decimal place? (a) 5.4 (b) 5.3 (c) 5.1 (d) 5.2
  7. 7.Best estimate of 2827 ÷ 46? (a) 57 (b) 5700 (c) 570
  8. 8.√32 to 1 decimal place? (a) 5.6 (b) 5.5 (c) 5.8 (d) 5.7
  9. 9.√86 to 1 decimal place? (a) 9.3 (b) 9.4 (c) 9.6 (d) 9.5
  10. 10.Best estimate of 5046 ÷ 56? (a) 8400 (b) 84 (c) 840
  11. 11.Best estimate of 6049 ÷ 64? (a) 10100 (b) 1010 (c) 101
  12. 12.√51 to 1 decimal place? (a) 7.0 (b) 6.9 (c) 7.2 (d) 7.1
  13. 13.Best estimate of 1274 ÷ 21? (a) 640 (b) 64 (c) 6400
  14. 14.Best estimate of 2436 ÷ 68? (a) 3500 (b) 35 (c) 350
  15. 15.√50 to 1 decimal place? (a) 7.0 (b) 6.9 (c) 6.8 (d) 7.1
  16. 16.√65 to 1 decimal place? (a) 8.0 (b) 8.2 (c) 7.9 (d) 8.1
  17. 17.√41 to 1 decimal place? (a) 6.3 (b) 6.5 (c) 6.4 (d) 6.2
  18. 18.Best estimate of 2544 ÷ 39? (a) 64 (b) 640 (c) 6400
  19. 19.√84 to 1 decimal place? (a) 9.2 (b) 9.4 (c) 9.3 (d) 9.1
  20. 20.Best estimate of 1140 ÷ 22? (a) 5700 (b) 570 (c) 57
  21. 21.Best estimate of 1131 ÷ 59? (a) 1900 (b) 19 (c) 190
  22. 22.Best estimate of 5182 ÷ 69? (a) 740 (b) 7400 (c) 74
  23. 23.√29 to 1 decimal place? (a) 5.3 (b) 5.2 (c) 5.1 (d) 5.4
  24. 24.Best estimate of 612 ÷ 37? (a) 150 (b) 1500 (c) 15
  25. 25.Best estimate of 1882 ÷ 21? (a) 940 (b) 94 (c) 9400
  26. 26.Best estimate of 969 ÷ 37? (a) 2400 (b) 24 (c) 240
  27. 27.√47 to 1 decimal place? (a) 6.9 (b) 6.7 (c) 7.0 (d) 6.8
  28. 28.Best estimate of 1045 ÷ 52? (a) 210 (b) 2100 (c) 21
  29. 29.Best estimate of 1426 ÷ 79? (a) 1800 (b) 18 (c) 180
  30. 30.Best estimate of 3468 ÷ 59? (a) 580 (b) 5800 (c) 58
  31. 31.Best estimate of 1545 ÷ 21? (a) 77 (b) 770 (c) 7700
  32. 32.Best estimate of 4578 ÷ 49? (a) 9200 (b) 92 (c) 920
  33. 33.Best estimate of 5265 ÷ 76? (a) 6600 (b) 660 (c) 66
  34. 34.Best estimate of 5884 ÷ 76? (a) 740 (b) 74 (c) 7400
  35. 35.Best estimate of 2031 ÷ 52? (a) 410 (b) 4100 (c) 41
  36. 36.√59 to 1 decimal place? (a) 8.0 (b) 7.8 (c) 7.9 (d) 7.7
  37. 37.√55 to 1 decimal place? (a) 7.5 (b) 7.4 (c) 7.3 (d) 7.6
  38. 38.√61 to 1 decimal place? (a) 8.0 (b) 7.9 (c) 8.1 (d) 7.8
  39. 39.Best estimate of 2118 ÷ 37? (a) 530 (b) 5300 (c) 53
  40. 40.Best estimate of 4573 ÷ 56? (a) 760 (b) 7600 (c) 76

Answer key

  1. 5.8
  2. 88
  3. 8.6
  4. 9.9
  5. 6.6
  6. 5.1
  7. 57
  8. 5.7
  9. 9.3
  10. 84
  11. 101
  12. 7.1
  13. 64
  14. 35
  15. 7.1
  16. 8.1
  17. 6.4
  18. 64
  19. 9.2
  20. 57
  21. 19
  22. 74
  23. 5.4
  24. 15
  25. 94
  26. 24
  27. 6.9
  28. 21
  29. 18
  30. 58
  31. 77
  32. 92
  33. 66
  34. 74
  35. 41
  36. 7.7
  37. 7.4
  38. 7.8
  39. 53
  40. 76

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