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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 120 · 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.√92 to 1 decimal place? (a) 9.6 (b) 9.7 (c) 9.4 (d) 9.5
  2. 2.√47 to 1 decimal place? (a) 7.1 (b) 6.8 (c) 6.9 (d) 7.0
  3. 3.√29 to 1 decimal place? (a) 5.3 (b) 5.4 (c) 5.2 (d) 5.5
  4. 4.Best estimate of 4997 ÷ 53? (a) 10000 (b) 100 (c) 1000
  5. 5.Best estimate of 2353 ÷ 73? (a) 3400 (b) 340 (c) 34
  6. 6.√80 to 1 decimal place? (a) 8.9 (b) 8.8 (c) 8.7 (d) 8.6
  7. 7.Best estimate of 5113 ÷ 88? (a) 57 (b) 570 (c) 5700
  8. 8.√69 to 1 decimal place? (a) 8.1 (b) 8.2 (c) 8.4 (d) 8.3
  9. 9.√79 to 1 decimal place? (a) 9.0 (b) 9.1 (c) 8.9 (d) 9.2
  10. 10.Best estimate of 6984 ÷ 79? (a) 870 (b) 8700 (c) 87
  11. 11.Best estimate of 1402 ÷ 33? (a) 4700 (b) 47 (c) 470
  12. 12.Best estimate of 3631 ÷ 86? (a) 400 (b) 40 (c) 4000
  13. 13.Best estimate of 1355 ÷ 56? (a) 2300 (b) 23 (c) 230
  14. 14.√34 to 1 decimal place? (a) 5.7 (b) 5.6 (c) 5.8 (d) 5.5
  15. 15.Best estimate of 2651 ÷ 38? (a) 660 (b) 66 (c) 6600
  16. 16.√50 to 1 decimal place? (a) 7.0 (b) 7.2 (c) 7.3 (d) 7.1
  17. 17.Best estimate of 3997 ÷ 74? (a) 5700 (b) 570 (c) 57
  18. 18.√55 to 1 decimal place? (a) 7.3 (b) 7.5 (c) 7.4 (d) 7.6
  19. 19.Best estimate of 844 ÷ 21? (a) 420 (b) 4200 (c) 42
  20. 20.Best estimate of 3210 ÷ 87? (a) 36 (b) 3600 (c) 360
  21. 21.Best estimate of 2407 ÷ 26? (a) 800 (b) 8000 (c) 80
  22. 22.√28 to 1 decimal place? (a) 5.4 (b) 5.6 (c) 5.3 (d) 5.5
  23. 23.Best estimate of 2716 ÷ 76? (a) 340 (b) 3400 (c) 34
  24. 24.Best estimate of 895 ÷ 26? (a) 300 (b) 30 (c) 3000
  25. 25.Best estimate of 662 ÷ 26? (a) 220 (b) 22 (c) 2200
  26. 26.Best estimate of 2126 ÷ 77? (a) 270 (b) 27 (c) 2700
  27. 27.Best estimate of 2344 ÷ 28? (a) 780 (b) 78 (c) 7800
  28. 28.√53 to 1 decimal place? (a) 7.2 (b) 7.4 (c) 7.5 (d) 7.3
  29. 29.Best estimate of 3566 ÷ 72? (a) 510 (b) 51 (c) 5100
  30. 30.√24 to 1 decimal place? (a) 5.0 (b) 4.9 (c) 5.2 (d) 5.1
  31. 31.Best estimate of 1915 ÷ 83? (a) 24 (b) 2400 (c) 240
  32. 32.Best estimate of 376 ÷ 31? (a) 13 (b) 1300 (c) 130
  33. 33.Best estimate of 6942 ÷ 79? (a) 870 (b) 8700 (c) 87
  34. 34.√89 to 1 decimal place? (a) 9.2 (b) 9.4 (c) 9.3 (d) 9.5
  35. 35.√52 to 1 decimal place? (a) 7.1 (b) 7.2 (c) 7.0 (d) 6.9
  36. 36.√44 to 1 decimal place? (a) 6.7 (b) 6.6 (c) 6.5 (d) 6.8
  37. 37.Best estimate of 3247 ÷ 54? (a) 65 (b) 6500 (c) 650
  38. 38.√26 to 1 decimal place? (a) 5.2 (b) 5.4 (c) 5.3 (d) 5.1
  39. 39.√45 to 1 decimal place? (a) 6.6 (b) 6.5 (c) 6.8 (d) 6.7
  40. 40.Best estimate of 1738 ÷ 69? (a) 2500 (b) 250 (c) 25

Answer key

  1. 9.6
  2. 6.9
  3. 5.4
  4. 100
  5. 34
  6. 8.9
  7. 57
  8. 8.3
  9. 8.9
  10. 87
  11. 47
  12. 40
  13. 23
  14. 5.8
  15. 66
  16. 7.1
  17. 57
  18. 7.4
  19. 42
  20. 36
  21. 80
  22. 5.3
  23. 34
  24. 30
  25. 22
  26. 27
  27. 78
  28. 7.3
  29. 51
  30. 4.9
  31. 24
  32. 13
  33. 87
  34. 9.4
  35. 7.2
  36. 6.6
  37. 65
  38. 5.1
  39. 6.7
  40. 25

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