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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 608 · 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 3864 ÷ 46? (a) 7700 (b) 77 (c) 770
  2. 2.Best estimate of 4350 ÷ 77? (a) 54 (b) 5400 (c) 540
  3. 3.Best estimate of 4809 ÷ 57? (a) 80 (b) 8000 (c) 800
  4. 4.Best estimate of 846 ÷ 21? (a) 420 (b) 42 (c) 4200
  5. 5.Best estimate of 1892 ÷ 21? (a) 950 (b) 95 (c) 9500
  6. 6.√74 to 1 decimal place? (a) 8.7 (b) 8.6 (c) 8.5 (d) 8.8
  7. 7.Best estimate of 3583 ÷ 42? (a) 900 (b) 9000 (c) 90
  8. 8.Best estimate of 1397 ÷ 46? (a) 2800 (b) 280 (c) 28
  9. 9.Best estimate of 1202 ÷ 88? (a) 13 (b) 1300 (c) 130
  10. 10.√35 to 1 decimal place? (a) 5.9 (b) 6.0 (c) 6.2 (d) 6.1
  11. 11.√69 to 1 decimal place? (a) 8.5 (b) 8.4 (c) 8.2 (d) 8.3
  12. 12.Best estimate of 3037 ÷ 89? (a) 3400 (b) 340 (c) 34
  13. 13.Best estimate of 828 ÷ 36? (a) 210 (b) 2100 (c) 21
  14. 14.Best estimate of 1774 ÷ 86? (a) 200 (b) 20 (c) 2000
  15. 15.√48 to 1 decimal place? (a) 6.8 (b) 7.0 (c) 6.9 (d) 7.1
  16. 16.Best estimate of 1723 ÷ 36? (a) 43 (b) 4300 (c) 430
  17. 17.√79 to 1 decimal place? (a) 9.1 (b) 9.0 (c) 8.9 (d) 9.2
  18. 18.Best estimate of 2860 ÷ 51? (a) 5700 (b) 570 (c) 57
  19. 19.Best estimate of 666 ÷ 31? (a) 220 (b) 2200 (c) 22
  20. 20.√94 to 1 decimal place? (a) 9.7 (b) 9.9 (c) 10.0 (d) 9.8
  21. 21.Best estimate of 3708 ÷ 64? (a) 620 (b) 6200 (c) 62
  22. 22.Best estimate of 1265 ÷ 34? (a) 42 (b) 420 (c) 4200
  23. 23.Best estimate of 3616 ÷ 62? (a) 600 (b) 6000 (c) 60
  24. 24.Best estimate of 4912 ÷ 82? (a) 61 (b) 6100 (c) 610
  25. 25.√37 to 1 decimal place? (a) 5.8 (b) 6.0 (c) 6.1 (d) 5.9
  26. 26.√30 to 1 decimal place? (a) 5.2 (b) 5.3 (c) 5.5 (d) 5.4
  27. 27.√26 to 1 decimal place? (a) 5.2 (b) 4.9 (c) 5.0 (d) 5.1
  28. 28.Best estimate of 290 ÷ 24? (a) 15 (b) 150 (c) 1500
  29. 29.√59 to 1 decimal place? (a) 7.4 (b) 7.6 (c) 7.5 (d) 7.7
  30. 30.√32 to 1 decimal place? (a) 5.5 (b) 5.7 (c) 5.6 (d) 5.8
  31. 31.Best estimate of 2886 ÷ 31? (a) 960 (b) 9600 (c) 96
  32. 32.√89 to 1 decimal place? (a) 9.4 (b) 9.3 (c) 9.1 (d) 9.2
  33. 33.Best estimate of 2502 ÷ 61? (a) 42 (b) 420 (c) 4200
  34. 34.√55 to 1 decimal place? (a) 7.3 (b) 7.4 (c) 7.2 (d) 7.1
  35. 35.√56 to 1 decimal place? (a) 7.2 (b) 7.5 (c) 7.4 (d) 7.3
  36. 36.√96 to 1 decimal place? (a) 9.9 (b) 10.0 (c) 9.7 (d) 9.8
  37. 37.√31 to 1 decimal place? (a) 5.9 (b) 5.8 (c) 5.6 (d) 5.7
  38. 38.Best estimate of 6497 ÷ 73? (a) 9300 (b) 930 (c) 93
  39. 39.Best estimate of 1457 ÷ 43? (a) 36 (b) 3600 (c) 360
  40. 40.Best estimate of 2868 ÷ 47? (a) 570 (b) 57 (c) 5700

Answer key

  1. 77
  2. 54
  3. 80
  4. 42
  5. 95
  6. 8.6
  7. 90
  8. 28
  9. 13
  10. 5.9
  11. 8.3
  12. 34
  13. 21
  14. 20
  15. 6.9
  16. 43
  17. 8.9
  18. 57
  19. 22
  20. 9.7
  21. 62
  22. 42
  23. 60
  24. 61
  25. 6.1
  26. 5.5
  27. 5.1
  28. 15
  29. 7.7
  30. 5.7
  31. 96
  32. 9.4
  33. 42
  34. 7.4
  35. 7.5
  36. 9.8
  37. 5.6
  38. 93
  39. 36
  40. 57

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