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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 49 · 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 1981 ÷ 26? (a) 66 (b) 660 (c) 6600
  2. 2.Best estimate of 4156 ÷ 62? (a) 690 (b) 6900 (c) 69
  3. 3.Best estimate of 967 ÷ 57? (a) 1600 (b) 160 (c) 16
  4. 4.√27 to 1 decimal place? (a) 5.1 (b) 5.0 (c) 5.2 (d) 5.3
  5. 5.Best estimate of 1542 ÷ 68? (a) 2200 (b) 22 (c) 220
  6. 6.√32 to 1 decimal place? (a) 6.0 (b) 5.7 (c) 5.9 (d) 5.8
  7. 7.Best estimate of 1639 ÷ 39? (a) 4100 (b) 410 (c) 41
  8. 8.Best estimate of 2582 ÷ 58? (a) 4300 (b) 430 (c) 43
  9. 9.Best estimate of 905 ÷ 24? (a) 450 (b) 4500 (c) 45
  10. 10.√70 to 1 decimal place? (a) 8.1 (b) 8.3 (c) 8.4 (d) 8.2
  11. 11.Best estimate of 1529 ÷ 56? (a) 250 (b) 2500 (c) 25
  12. 12.√74 to 1 decimal place? (a) 8.5 (b) 8.6 (c) 8.4 (d) 8.3
  13. 13.√67 to 1 decimal place? (a) 8.1 (b) 8.2 (c) 8.4 (d) 8.3
  14. 14.√48 to 1 decimal place? (a) 7.1 (b) 6.8 (c) 6.9 (d) 7.0
  15. 15.Best estimate of 1136 ÷ 26? (a) 3800 (b) 38 (c) 380
  16. 16.√34 to 1 decimal place? (a) 6.1 (b) 5.8 (c) 6.0 (d) 5.9
  17. 17.Best estimate of 1137 ÷ 53? (a) 230 (b) 2300 (c) 23
  18. 18.√61 to 1 decimal place? (a) 7.6 (b) 7.7 (c) 7.8 (d) 7.5
  19. 19.√26 to 1 decimal place? (a) 5.3 (b) 5.1 (c) 5.0 (d) 5.2
  20. 20.√56 to 1 decimal place? (a) 7.5 (b) 7.4 (c) 7.6 (d) 7.3
  21. 21.Best estimate of 4487 ÷ 89? (a) 5000 (b) 50 (c) 500
  22. 22.√47 to 1 decimal place? (a) 6.9 (b) 6.6 (c) 6.8 (d) 6.7
  23. 23.√41 to 1 decimal place? (a) 6.2 (b) 6.4 (c) 6.1 (d) 6.3
  24. 24.Best estimate of 2649 ÷ 66? (a) 3800 (b) 38 (c) 380
  25. 25.√83 to 1 decimal place? (a) 9.1 (b) 9.0 (c) 8.9 (d) 8.8
  26. 26.Best estimate of 581 ÷ 32? (a) 190 (b) 1900 (c) 19
  27. 27.Best estimate of 1530 ÷ 52? (a) 31 (b) 3100 (c) 310
  28. 28.Best estimate of 3649 ÷ 66? (a) 52 (b) 5200 (c) 520
  29. 29.Best estimate of 1524 ÷ 42? (a) 380 (b) 3800 (c) 38
  30. 30.Best estimate of 2797 ÷ 57? (a) 4700 (b) 47 (c) 470
  31. 31.√38 to 1 decimal place? (a) 6.4 (b) 6.3 (c) 6.5 (d) 6.2
  32. 32.Best estimate of 4593 ÷ 61? (a) 770 (b) 7700 (c) 77
  33. 33.Best estimate of 2739 ÷ 56? (a) 46 (b) 460 (c) 4600
  34. 34.Best estimate of 1679 ÷ 31? (a) 560 (b) 5600 (c) 56
  35. 35.√76 to 1 decimal place? (a) 8.8 (b) 8.7 (c) 9.0 (d) 8.9
  36. 36.√88 to 1 decimal place? (a) 9.4 (b) 9.1 (c) 9.3 (d) 9.2
  37. 37.√30 to 1 decimal place? (a) 5.5 (b) 5.4 (c) 5.7 (d) 5.6
  38. 38.Best estimate of 6644 ÷ 71? (a) 9500 (b) 95 (c) 950
  39. 39.Best estimate of 5836 ÷ 81? (a) 730 (b) 7300 (c) 73
  40. 40.Best estimate of 3282 ÷ 52? (a) 66 (b) 6600 (c) 660

Answer key

  1. 66
  2. 69
  3. 16
  4. 5.2
  5. 22
  6. 5.7
  7. 41
  8. 43
  9. 45
  10. 8.4
  11. 25
  12. 8.6
  13. 8.2
  14. 6.9
  15. 38
  16. 5.8
  17. 23
  18. 7.8
  19. 5.1
  20. 7.5
  21. 50
  22. 6.9
  23. 6.4
  24. 38
  25. 9.1
  26. 19
  27. 31
  28. 52
  29. 38
  30. 47
  31. 6.2
  32. 77
  33. 46
  34. 56
  35. 8.7
  36. 9.4
  37. 5.5
  38. 95
  39. 73
  40. 66

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