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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 63 · 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 4877 ÷ 56? (a) 810 (b) 8100 (c) 81
  2. 2.√21 to 1 decimal place? (a) 4.9 (b) 4.6 (c) 4.7 (d) 4.8
  3. 3.√90 to 1 decimal place? (a) 9.6 (b) 9.4 (c) 9.5 (d) 9.3
  4. 4.Best estimate of 1269 ÷ 63? (a) 21 (b) 210 (c) 2100
  5. 5.Best estimate of 1689 ÷ 64? (a) 280 (b) 28 (c) 2800
  6. 6.√56 to 1 decimal place? (a) 7.4 (b) 7.5 (c) 7.3 (d) 7.6
  7. 7.√20 to 1 decimal place? (a) 4.8 (b) 4.7 (c) 4.6 (d) 4.5
  8. 8.√85 to 1 decimal place? (a) 9.5 (b) 9.3 (c) 9.4 (d) 9.2
  9. 9.√40 to 1 decimal place? (a) 6.3 (b) 6.6 (c) 6.5 (d) 6.4
  10. 10.√98 to 1 decimal place? (a) 9.9 (b) 9.8 (c) 10.0 (d) 9.7
  11. 11.√53 to 1 decimal place? (a) 7.3 (b) 7.5 (c) 7.4 (d) 7.2
  12. 12.√61 to 1 decimal place? (a) 8.0 (b) 7.9 (c) 8.1 (d) 7.8
  13. 13.Best estimate of 2020 ÷ 38? (a) 510 (b) 5100 (c) 51
  14. 14.Best estimate of 1537 ÷ 23? (a) 770 (b) 77 (c) 7700
  15. 15.Best estimate of 2415 ÷ 71? (a) 350 (b) 35 (c) 3500
  16. 16.√65 to 1 decimal place? (a) 7.9 (b) 8.2 (c) 8.0 (d) 8.1
  17. 17.Best estimate of 2951 ÷ 51? (a) 590 (b) 5900 (c) 59
  18. 18.√70 to 1 decimal place? (a) 8.5 (b) 8.4 (c) 8.3 (d) 8.2
  19. 19.Best estimate of 2620 ÷ 38? (a) 6600 (b) 66 (c) 660
  20. 20.Best estimate of 618 ÷ 36? (a) 1500 (b) 150 (c) 15
  21. 21.Best estimate of 3182 ÷ 52? (a) 6400 (b) 640 (c) 64
  22. 22.√50 to 1 decimal place? (a) 7.3 (b) 7.4 (c) 7.1 (d) 7.2
  23. 23.√69 to 1 decimal place? (a) 8.3 (b) 8.4 (c) 8.2 (d) 8.5
  24. 24.√94 to 1 decimal place? (a) 9.8 (b) 9.9 (c) 9.7 (d) 10.0
  25. 25.Best estimate of 3093 ÷ 54? (a) 620 (b) 62 (c) 6200
  26. 26.Best estimate of 3961 ÷ 87? (a) 44 (b) 440 (c) 4400
  27. 27.Best estimate of 4522 ÷ 52? (a) 9000 (b) 900 (c) 90
  28. 28.Best estimate of 1335 ÷ 24? (a) 6700 (b) 67 (c) 670
  29. 29.√83 to 1 decimal place? (a) 8.9 (b) 9.1 (c) 9.2 (d) 9.0
  30. 30.√82 to 1 decimal place? (a) 9.2 (b) 9.4 (c) 9.3 (d) 9.1
  31. 31.√77 to 1 decimal place? (a) 8.8 (b) 9.0 (c) 8.9 (d) 9.1
  32. 32.Best estimate of 3850 ÷ 67? (a) 550 (b) 55 (c) 5500
  33. 33.Best estimate of 1744 ÷ 32? (a) 580 (b) 5800 (c) 58
  34. 34.Best estimate of 4705 ÷ 61? (a) 780 (b) 7800 (c) 78
  35. 35.Best estimate of 615 ÷ 43? (a) 15 (b) 1500 (c) 150
  36. 36.√47 to 1 decimal place? (a) 6.7 (b) 6.9 (c) 6.8 (d) 6.6
  37. 37.√37 to 1 decimal place? (a) 6.1 (b) 5.9 (c) 6.0 (d) 6.2
  38. 38.√27 to 1 decimal place? (a) 5.3 (b) 5.2 (c) 5.4 (d) 5.5
  39. 39.Best estimate of 797 ÷ 33? (a) 2700 (b) 270 (c) 27
  40. 40.Best estimate of 716 ÷ 22? (a) 360 (b) 3600 (c) 36

Answer key

  1. 81
  2. 4.6
  3. 9.5
  4. 21
  5. 28
  6. 7.5
  7. 4.5
  8. 9.2
  9. 6.3
  10. 9.9
  11. 7.3
  12. 7.8
  13. 51
  14. 77
  15. 35
  16. 8.1
  17. 59
  18. 8.4
  19. 66
  20. 15
  21. 64
  22. 7.1
  23. 8.3
  24. 9.7
  25. 62
  26. 44
  27. 90
  28. 67
  29. 9.1
  30. 9.1
  31. 8.8
  32. 55
  33. 58
  34. 78
  35. 15
  36. 6.9
  37. 6.1
  38. 5.2
  39. 27
  40. 36

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