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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 107 · 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 2710 ÷ 51? (a) 54 (b) 5400 (c) 540
  2. 2.Best estimate of 2016 ÷ 56? (a) 34 (b) 340 (c) 3400
  3. 3.√79 to 1 decimal place? (a) 9.0 (b) 8.9 (c) 9.1 (d) 8.8
  4. 4.√40 to 1 decimal place? (a) 6.3 (b) 6.1 (c) 6.4 (d) 6.2
  5. 5.√75 to 1 decimal place? (a) 8.5 (b) 8.7 (c) 8.8 (d) 8.6
  6. 6.√21 to 1 decimal place? (a) 4.5 (b) 4.7 (c) 4.6 (d) 4.8
  7. 7.√26 to 1 decimal place? (a) 5.3 (b) 5.1 (c) 5.0 (d) 5.2
  8. 8.Best estimate of 484 ÷ 36? (a) 12 (b) 1200 (c) 120
  9. 9.√82 to 1 decimal place? (a) 9.1 (b) 9.0 (c) 8.9 (d) 8.8
  10. 10.Best estimate of 3166 ÷ 38? (a) 790 (b) 7900 (c) 79
  11. 11.Best estimate of 2740 ÷ 48? (a) 5500 (b) 550 (c) 55
  12. 12.√35 to 1 decimal place? (a) 5.8 (b) 5.7 (c) 6.0 (d) 5.9
  13. 13.√55 to 1 decimal place? (a) 7.6 (b) 7.5 (c) 7.4 (d) 7.7
  14. 14.√28 to 1 decimal place? (a) 5.4 (b) 5.3 (c) 5.2 (d) 5.1
  15. 15.√58 to 1 decimal place? (a) 7.6 (b) 7.7 (c) 7.5 (d) 7.8
  16. 16.Best estimate of 1089 ÷ 51? (a) 2200 (b) 220 (c) 22
  17. 17.Best estimate of 5707 ÷ 76? (a) 7100 (b) 710 (c) 71
  18. 18.√32 to 1 decimal place? (a) 5.7 (b) 5.9 (c) 5.8 (d) 5.6
  19. 19.Best estimate of 4761 ÷ 74? (a) 68 (b) 6800 (c) 680
  20. 20.Best estimate of 3925 ÷ 53? (a) 790 (b) 79 (c) 7900
  21. 21.√48 to 1 decimal place? (a) 6.7 (b) 6.8 (c) 7.0 (d) 6.9
  22. 22.Best estimate of 2112 ÷ 28? (a) 700 (b) 70 (c) 7000
  23. 23.Best estimate of 2132 ÷ 28? (a) 7100 (b) 710 (c) 71
  24. 24.Best estimate of 1902 ÷ 48? (a) 380 (b) 38 (c) 3800
  25. 25.Best estimate of 2276 ÷ 37? (a) 57 (b) 570 (c) 5700
  26. 26.√23 to 1 decimal place? (a) 4.9 (b) 4.8 (c) 5.0 (d) 4.7
  27. 27.Best estimate of 3207 ÷ 49? (a) 640 (b) 6400 (c) 64
  28. 28.√34 to 1 decimal place? (a) 5.9 (b) 6.1 (c) 6.0 (d) 5.8
  29. 29.Best estimate of 3867 ÷ 46? (a) 770 (b) 77 (c) 7700
  30. 30.√42 to 1 decimal place? (a) 6.6 (b) 6.5 (c) 6.7 (d) 6.8
  31. 31.Best estimate of 1085 ÷ 21? (a) 5400 (b) 54 (c) 540
  32. 32.Best estimate of 4789 ÷ 76? (a) 600 (b) 60 (c) 6000
  33. 33.Best estimate of 2628 ÷ 81? (a) 330 (b) 3300 (c) 33
  34. 34.Best estimate of 944 ÷ 51? (a) 19 (b) 1900 (c) 190
  35. 35.√59 to 1 decimal place? (a) 7.7 (b) 7.6 (c) 7.9 (d) 7.8
  36. 36.√61 to 1 decimal place? (a) 7.9 (b) 7.8 (c) 7.7 (d) 7.6
  37. 37.√89 to 1 decimal place? (a) 9.5 (b) 9.4 (c) 9.2 (d) 9.3
  38. 38.√20 to 1 decimal place? (a) 4.4 (b) 4.6 (c) 4.3 (d) 4.5
  39. 39.Best estimate of 1218 ÷ 42? (a) 300 (b) 30 (c) 3000
  40. 40.Best estimate of 1620 ÷ 62? (a) 2700 (b) 270 (c) 27

Answer key

  1. 54
  2. 34
  3. 8.9
  4. 6.3
  5. 8.7
  6. 4.6
  7. 5.1
  8. 12
  9. 9.1
  10. 79
  11. 55
  12. 5.9
  13. 7.4
  14. 5.3
  15. 7.6
  16. 22
  17. 71
  18. 5.7
  19. 68
  20. 79
  21. 6.9
  22. 70
  23. 71
  24. 38
  25. 57
  26. 4.8
  27. 64
  28. 5.8
  29. 77
  30. 6.5
  31. 54
  32. 60
  33. 33
  34. 19
  35. 7.7
  36. 7.8
  37. 9.4
  38. 4.5
  39. 30
  40. 27

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