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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 782 · 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.√40 to 1 decimal place? (a) 6.2 (b) 6.1 (c) 6.3 (d) 6.4
  2. 2.Best estimate of 820 ÷ 41? (a) 21 (b) 2100 (c) 210
  3. 3.Best estimate of 4395 ÷ 47? (a) 8800 (b) 880 (c) 88
  4. 4.√41 to 1 decimal place? (a) 6.2 (b) 6.5 (c) 6.3 (d) 6.4
  5. 5.Best estimate of 3287 ÷ 47? (a) 66 (b) 6600 (c) 660
  6. 6.√26 to 1 decimal place? (a) 5.1 (b) 5.0 (c) 4.8 (d) 4.9
  7. 7.Best estimate of 1630 ÷ 21? (a) 82 (b) 8200 (c) 820
  8. 8.√28 to 1 decimal place? (a) 5.1 (b) 5.4 (c) 5.2 (d) 5.3
  9. 9.Best estimate of 2815 ÷ 37? (a) 70 (b) 700 (c) 7000
  10. 10.√38 to 1 decimal place? (a) 6.1 (b) 6.0 (c) 5.9 (d) 6.2
  11. 11.√69 to 1 decimal place? (a) 8.3 (b) 8.0 (c) 8.2 (d) 8.1
  12. 12.√67 to 1 decimal place? (a) 8.5 (b) 8.3 (c) 8.2 (d) 8.4
  13. 13.√30 to 1 decimal place? (a) 5.5 (b) 5.7 (c) 5.4 (d) 5.6
  14. 14.Best estimate of 3427 ÷ 36? (a) 8600 (b) 86 (c) 860
  15. 15.√20 to 1 decimal place? (a) 4.6 (b) 4.7 (c) 4.8 (d) 4.5
  16. 16.Best estimate of 6269 ÷ 74? (a) 9000 (b) 900 (c) 90
  17. 17.√50 to 1 decimal place? (a) 7.2 (b) 7.3 (c) 7.1 (d) 7.0
  18. 18.√31 to 1 decimal place? (a) 5.6 (b) 5.7 (c) 5.8 (d) 5.5
  19. 19.Best estimate of 1800 ÷ 24? (a) 900 (b) 90 (c) 9000
  20. 20.Best estimate of 997 ÷ 32? (a) 3300 (b) 330 (c) 33
  21. 21.Best estimate of 5768 ÷ 83? (a) 720 (b) 72 (c) 7200
  22. 22.Best estimate of 4825 ÷ 86? (a) 540 (b) 54 (c) 5400
  23. 23.Best estimate of 4435 ÷ 56? (a) 7400 (b) 74 (c) 740
  24. 24.Best estimate of 1240 ÷ 39? (a) 310 (b) 3100 (c) 31
  25. 25.Best estimate of 3163 ÷ 64? (a) 5300 (b) 53 (c) 530
  26. 26.Best estimate of 2191 ÷ 68? (a) 3100 (b) 310 (c) 31
  27. 27.√88 to 1 decimal place? (a) 9.6 (b) 9.5 (c) 9.4 (d) 9.3
  28. 28.Best estimate of 2837 ÷ 54? (a) 57 (b) 570 (c) 5700
  29. 29.Best estimate of 1456 ÷ 46? (a) 2900 (b) 290 (c) 29
  30. 30.√34 to 1 decimal place? (a) 5.8 (b) 5.9 (c) 5.6 (d) 5.7
  31. 31.√76 to 1 decimal place? (a) 9.0 (b) 8.8 (c) 8.7 (d) 8.9
  32. 32.√22 to 1 decimal place? (a) 4.4 (b) 4.6 (c) 4.5 (d) 4.7
  33. 33.Best estimate of 1466 ÷ 24? (a) 7300 (b) 730 (c) 73
  34. 34.Best estimate of 1767 ÷ 47? (a) 350 (b) 35 (c) 3500
  35. 35.√82 to 1 decimal place? (a) 9.1 (b) 9.4 (c) 9.3 (d) 9.2
  36. 36.√29 to 1 decimal place? (a) 5.6 (b) 5.4 (c) 5.3 (d) 5.5
  37. 37.Best estimate of 2713 ÷ 36? (a) 6800 (b) 68 (c) 680
  38. 38.Best estimate of 780 ÷ 21? (a) 3900 (b) 39 (c) 390
  39. 39.Best estimate of 2129 ÷ 44? (a) 53 (b) 5300 (c) 530
  40. 40.√58 to 1 decimal place? (a) 7.6 (b) 7.3 (c) 7.5 (d) 7.4

Answer key

  1. 6.3
  2. 21
  3. 88
  4. 6.4
  5. 66
  6. 5.1
  7. 82
  8. 5.3
  9. 70
  10. 6.2
  11. 8.3
  12. 8.2
  13. 5.5
  14. 86
  15. 4.5
  16. 90
  17. 7.1
  18. 5.6
  19. 90
  20. 33
  21. 72
  22. 54
  23. 74
  24. 31
  25. 53
  26. 31
  27. 9.4
  28. 57
  29. 29
  30. 5.8
  31. 8.7
  32. 4.7
  33. 73
  34. 35
  35. 9.1
  36. 5.4
  37. 68
  38. 39
  39. 53
  40. 7.6

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