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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 630 · 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.√44 to 1 decimal place? (a) 6.8 (b) 6.7 (c) 6.6 (d) 6.5
  2. 2.Best estimate of 3701 ÷ 52? (a) 7400 (b) 740 (c) 74
  3. 3.√69 to 1 decimal place? (a) 8.6 (b) 8.4 (c) 8.5 (d) 8.3
  4. 4.Best estimate of 1637 ÷ 63? (a) 270 (b) 2700 (c) 27
  5. 5.√48 to 1 decimal place? (a) 7.2 (b) 7.0 (c) 7.1 (d) 6.9
  6. 6.Best estimate of 7912 ÷ 88? (a) 8800 (b) 88 (c) 880
  7. 7.Best estimate of 6455 ÷ 89? (a) 7200 (b) 72 (c) 720
  8. 8.√41 to 1 decimal place? (a) 6.3 (b) 6.5 (c) 6.2 (d) 6.4
  9. 9.Best estimate of 5616 ÷ 67? (a) 80 (b) 800 (c) 8000
  10. 10.Best estimate of 981 ÷ 42? (a) 250 (b) 25 (c) 2500
  11. 11.√71 to 1 decimal place? (a) 8.3 (b) 8.4 (c) 8.2 (d) 8.5
  12. 12.Best estimate of 1065 ÷ 59? (a) 18 (b) 1800 (c) 180
  13. 13.√92 to 1 decimal place? (a) 9.6 (b) 9.4 (c) 9.3 (d) 9.5
  14. 14.√63 to 1 decimal place? (a) 8.0 (b) 8.1 (c) 7.9 (d) 8.2
  15. 15.Best estimate of 5304 ÷ 88? (a) 59 (b) 590 (c) 5900
  16. 16.√29 to 1 decimal place? (a) 5.4 (b) 5.3 (c) 5.2 (d) 5.5
  17. 17.Best estimate of 4942 ÷ 77? (a) 620 (b) 6200 (c) 62
  18. 18.√66 to 1 decimal place? (a) 7.9 (b) 8.0 (c) 8.2 (d) 8.1
  19. 19.√61 to 1 decimal place? (a) 7.7 (b) 7.9 (c) 7.8 (d) 7.6
  20. 20.√52 to 1 decimal place? (a) 7.1 (b) 7.2 (c) 7.3 (d) 7.4
  21. 21.Best estimate of 1077 ÷ 39? (a) 27 (b) 270 (c) 2700
  22. 22.√26 to 1 decimal place? (a) 5.2 (b) 4.9 (c) 5.1 (d) 5.0
  23. 23.Best estimate of 2307 ÷ 39? (a) 58 (b) 5800 (c) 580
  24. 24.Best estimate of 1947 ÷ 27? (a) 650 (b) 65 (c) 6500
  25. 25.√70 to 1 decimal place? (a) 8.4 (b) 8.7 (c) 8.5 (d) 8.6
  26. 26.Best estimate of 2487 ÷ 41? (a) 620 (b) 62 (c) 6200
  27. 27.Best estimate of 1916 ÷ 39? (a) 4800 (b) 480 (c) 48
  28. 28.√98 to 1 decimal place? (a) 10.0 (b) 9.8 (c) 9.7 (d) 9.9
  29. 29.√40 to 1 decimal place? (a) 6.2 (b) 6.3 (c) 6.1 (d) 6.4
  30. 30.√77 to 1 decimal place? (a) 8.6 (b) 8.7 (c) 8.5 (d) 8.8
  31. 31.√80 to 1 decimal place? (a) 9.0 (b) 8.9 (c) 8.8 (d) 8.7
  32. 32.Best estimate of 3114 ÷ 64? (a) 520 (b) 5200 (c) 52
  33. 33.√38 to 1 decimal place? (a) 6.2 (b) 6.1 (c) 6.0 (d) 6.3
  34. 34.Best estimate of 4303 ÷ 48? (a) 8600 (b) 860 (c) 86
  35. 35.Best estimate of 5102 ÷ 62? (a) 850 (b) 8500 (c) 85
  36. 36.Best estimate of 1638 ÷ 21? (a) 8200 (b) 820 (c) 82
  37. 37.Best estimate of 1210 ÷ 57? (a) 2000 (b) 200 (c) 20
  38. 38.√28 to 1 decimal place? (a) 5.4 (b) 5.1 (c) 5.3 (d) 5.2
  39. 39.√83 to 1 decimal place? (a) 9.4 (b) 9.2 (c) 9.3 (d) 9.1
  40. 40.Best estimate of 6896 ÷ 78? (a) 8600 (b) 86 (c) 860

Answer key

  1. 6.6
  2. 74
  3. 8.3
  4. 27
  5. 6.9
  6. 88
  7. 72
  8. 6.4
  9. 80
  10. 25
  11. 8.4
  12. 18
  13. 9.6
  14. 7.9
  15. 59
  16. 5.4
  17. 62
  18. 8.1
  19. 7.8
  20. 7.2
  21. 27
  22. 5.1
  23. 58
  24. 65
  25. 8.4
  26. 62
  27. 48
  28. 9.9
  29. 6.3
  30. 8.8
  31. 8.9
  32. 52
  33. 6.2
  34. 86
  35. 85
  36. 82
  37. 20
  38. 5.3
  39. 9.1
  40. 86

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