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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 918 · 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 4258 ÷ 56? (a) 7100 (b) 71 (c) 710
  2. 2.√30 to 1 decimal place? (a) 5.3 (b) 5.6 (c) 5.4 (d) 5.5
  3. 3.Best estimate of 4086 ÷ 56? (a) 680 (b) 6800 (c) 68
  4. 4.√83 to 1 decimal place? (a) 9.2 (b) 9.0 (c) 9.1 (d) 8.9
  5. 5.√40 to 1 decimal place? (a) 6.4 (b) 6.5 (c) 6.6 (d) 6.3
  6. 6.√61 to 1 decimal place? (a) 7.9 (b) 7.7 (c) 7.8 (d) 7.6
  7. 7.√38 to 1 decimal place? (a) 6.0 (b) 6.2 (c) 6.3 (d) 6.1
  8. 8.√32 to 1 decimal place? (a) 5.6 (b) 5.5 (c) 5.7 (d) 5.4
  9. 9.Best estimate of 3015 ÷ 33? (a) 10100 (b) 1010 (c) 101
  10. 10.Best estimate of 2575 ÷ 43? (a) 6400 (b) 64 (c) 640
  11. 11.Best estimate of 2257 ÷ 51? (a) 450 (b) 45 (c) 4500
  12. 12.√56 to 1 decimal place? (a) 7.2 (b) 7.3 (c) 7.5 (d) 7.4
  13. 13.Best estimate of 2508 ÷ 36? (a) 630 (b) 6300 (c) 63
  14. 14.Best estimate of 1134 ÷ 76? (a) 1400 (b) 140 (c) 14
  15. 15.Best estimate of 3510 ÷ 67? (a) 50 (b) 5000 (c) 500
  16. 16.Best estimate of 914 ÷ 24? (a) 4600 (b) 46 (c) 460
  17. 17.√92 to 1 decimal place? (a) 9.5 (b) 9.6 (c) 9.3 (d) 9.4
  18. 18.Best estimate of 510 ÷ 23? (a) 260 (b) 26 (c) 2600
  19. 19.Best estimate of 2585 ÷ 87? (a) 290 (b) 2900 (c) 29
  20. 20.√98 to 1 decimal place? (a) 9.9 (b) 9.6 (c) 9.8 (d) 9.7
  21. 21.√37 to 1 decimal place? (a) 6.0 (b) 6.1 (c) 5.9 (d) 5.8
  22. 22.√43 to 1 decimal place? (a) 6.7 (b) 6.8 (c) 6.6 (d) 6.5
  23. 23.Best estimate of 2016 ÷ 28? (a) 670 (b) 6700 (c) 67
  24. 24.Best estimate of 5598 ÷ 68? (a) 800 (b) 8000 (c) 80
  25. 25.Best estimate of 998 ÷ 22? (a) 50 (b) 5000 (c) 500
  26. 26.Best estimate of 3120 ÷ 41? (a) 7800 (b) 780 (c) 78
  27. 27.√84 to 1 decimal place? (a) 9.2 (b) 9.4 (c) 9.3 (d) 9.5
  28. 28.Best estimate of 625 ÷ 32? (a) 21 (b) 210 (c) 2100
  29. 29.Best estimate of 5189 ÷ 78? (a) 650 (b) 65 (c) 6500
  30. 30.√48 to 1 decimal place? (a) 6.8 (b) 6.6 (c) 6.7 (d) 6.9
  31. 31.Best estimate of 1635 ÷ 23? (a) 8200 (b) 820 (c) 82
  32. 32.Best estimate of 3976 ÷ 76? (a) 5000 (b) 50 (c) 500
  33. 33.√58 to 1 decimal place? (a) 7.7 (b) 7.9 (c) 7.8 (d) 7.6
  34. 34.Best estimate of 1863 ÷ 82? (a) 23 (b) 230 (c) 2300
  35. 35.√34 to 1 decimal place? (a) 5.8 (b) 6.0 (c) 5.9 (d) 6.1
  36. 36.Best estimate of 2296 ÷ 69? (a) 330 (b) 3300 (c) 33
  37. 37.Best estimate of 2662 ÷ 72? (a) 3800 (b) 38 (c) 380
  38. 38.√45 to 1 decimal place? (a) 6.8 (b) 6.7 (c) 6.5 (d) 6.6
  39. 39.Best estimate of 5661 ÷ 69? (a) 8100 (b) 810 (c) 81
  40. 40.Best estimate of 2428 ÷ 29? (a) 810 (b) 8100 (c) 81

Answer key

  1. 71
  2. 5.5
  3. 68
  4. 9.1
  5. 6.3
  6. 7.8
  7. 6.2
  8. 5.7
  9. 101
  10. 64
  11. 45
  12. 7.5
  13. 63
  14. 14
  15. 50
  16. 46
  17. 9.6
  18. 26
  19. 29
  20. 9.9
  21. 6.1
  22. 6.6
  23. 67
  24. 80
  25. 50
  26. 78
  27. 9.2
  28. 21
  29. 65
  30. 6.9
  31. 82
  32. 50
  33. 7.6
  34. 23
  35. 5.8
  36. 33
  37. 38
  38. 6.7
  39. 81
  40. 81

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