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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 543 · 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.√56 to 1 decimal place? (a) 7.6 (b) 7.8 (c) 7.7 (d) 7.5
  2. 2.Best estimate of 2331 ÷ 64? (a) 3900 (b) 39 (c) 390
  3. 3.Best estimate of 3674 ÷ 86? (a) 410 (b) 41 (c) 4100
  4. 4.Best estimate of 2878 ÷ 61? (a) 4800 (b) 48 (c) 480
  5. 5.√50 to 1 decimal place? (a) 7.1 (b) 6.9 (c) 7.0 (d) 6.8
  6. 6.√20 to 1 decimal place? (a) 4.7 (b) 4.4 (c) 4.6 (d) 4.5
  7. 7.√34 to 1 decimal place? (a) 5.9 (b) 5.8 (c) 5.7 (d) 6.0
  8. 8.√31 to 1 decimal place? (a) 5.9 (b) 5.8 (c) 5.7 (d) 5.6
  9. 9.Best estimate of 1632 ÷ 41? (a) 4100 (b) 410 (c) 41
  10. 10.Best estimate of 4784 ÷ 76? (a) 600 (b) 60 (c) 6000
  11. 11.√77 to 1 decimal place? (a) 8.9 (b) 8.8 (c) 8.7 (d) 8.6
  12. 12.√92 to 1 decimal place? (a) 9.5 (b) 9.8 (c) 9.6 (d) 9.7
  13. 13.Best estimate of 2688 ÷ 61? (a) 4500 (b) 45 (c) 450
  14. 14.Best estimate of 837 ÷ 28? (a) 280 (b) 28 (c) 2800
  15. 15.√69 to 1 decimal place? (a) 8.2 (b) 8.5 (c) 8.3 (d) 8.4
  16. 16.Best estimate of 1484 ÷ 41? (a) 370 (b) 3700 (c) 37
  17. 17.Best estimate of 3450 ÷ 72? (a) 490 (b) 4900 (c) 49
  18. 18.Best estimate of 2109 ÷ 34? (a) 7000 (b) 700 (c) 70
  19. 19.Best estimate of 538 ÷ 32? (a) 1800 (b) 18 (c) 180
  20. 20.√42 to 1 decimal place? (a) 6.2 (b) 6.4 (c) 6.3 (d) 6.5
  21. 21.√26 to 1 decimal place? (a) 4.9 (b) 5.2 (c) 5.0 (d) 5.1
  22. 22.√86 to 1 decimal place? (a) 9.4 (b) 9.2 (c) 9.3 (d) 9.5
  23. 23.√87 to 1 decimal place? (a) 9.0 (b) 9.3 (c) 9.1 (d) 9.2
  24. 24.√35 to 1 decimal place? (a) 5.9 (b) 5.8 (c) 6.1 (d) 6.0
  25. 25.√37 to 1 decimal place? (a) 6.4 (b) 6.3 (c) 6.2 (d) 6.1
  26. 26.√79 to 1 decimal place? (a) 8.9 (b) 8.8 (c) 8.7 (d) 8.6
  27. 27.√41 to 1 decimal place? (a) 6.4 (b) 6.6 (c) 6.7 (d) 6.5
  28. 28.√65 to 1 decimal place? (a) 8.2 (b) 8.3 (c) 8.1 (d) 8.0
  29. 29.Best estimate of 686 ÷ 22? (a) 3400 (b) 340 (c) 34
  30. 30.Best estimate of 5348 ÷ 78? (a) 67 (b) 670 (c) 6700
  31. 31.√88 to 1 decimal place? (a) 9.7 (b) 9.4 (c) 9.5 (d) 9.6
  32. 32.Best estimate of 3349 ÷ 72? (a) 48 (b) 480 (c) 4800
  33. 33.Best estimate of 2993 ÷ 39? (a) 75 (b) 750 (c) 7500
  34. 34.Best estimate of 1019 ÷ 83? (a) 13 (b) 1300 (c) 130
  35. 35.√32 to 1 decimal place? (a) 5.6 (b) 5.8 (c) 5.7 (d) 5.5
  36. 36.Best estimate of 3221 ÷ 57? (a) 54 (b) 540 (c) 5400
  37. 37.Best estimate of 1126 ÷ 42? (a) 28 (b) 2800 (c) 280
  38. 38.√40 to 1 decimal place? (a) 6.4 (b) 6.3 (c) 6.1 (d) 6.2
  39. 39.√38 to 1 decimal place? (a) 6.2 (b) 6.5 (c) 6.3 (d) 6.4
  40. 40.Best estimate of 2814 ÷ 56? (a) 470 (b) 47 (c) 4700

Answer key

  1. 7.5
  2. 39
  3. 41
  4. 48
  5. 7.1
  6. 4.5
  7. 5.8
  8. 5.6
  9. 41
  10. 60
  11. 8.8
  12. 9.6
  13. 45
  14. 28
  15. 8.3
  16. 37
  17. 49
  18. 70
  19. 18
  20. 6.5
  21. 5.1
  22. 9.3
  23. 9.3
  24. 5.9
  25. 6.1
  26. 8.9
  27. 6.4
  28. 8.1
  29. 34
  30. 67
  31. 9.4
  32. 48
  33. 75
  34. 13
  35. 5.7
  36. 54
  37. 28
  38. 6.3
  39. 6.2
  40. 47

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