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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 431 · 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 1236 ÷ 49? (a) 2500 (b) 250 (c) 25
  2. 2.Best estimate of 6314 ÷ 78? (a) 79 (b) 790 (c) 7900
  3. 3.√26 to 1 decimal place? (a) 5.2 (b) 4.9 (c) 5.0 (d) 5.1
  4. 4.√46 to 1 decimal place? (a) 6.6 (b) 6.7 (c) 6.9 (d) 6.8
  5. 5.Best estimate of 3372 ÷ 84? (a) 4200 (b) 42 (c) 420
  6. 6.Best estimate of 1865 ÷ 32? (a) 620 (b) 62 (c) 6200
  7. 7.Best estimate of 835 ÷ 38? (a) 2100 (b) 21 (c) 210
  8. 8.Best estimate of 1549 ÷ 26? (a) 52 (b) 520 (c) 5200
  9. 9.√66 to 1 decimal place? (a) 8.1 (b) 8.2 (c) 8.3 (d) 8.4
  10. 10.Best estimate of 2129 ÷ 69? (a) 3000 (b) 300 (c) 30
  11. 11.√75 to 1 decimal place? (a) 8.5 (b) 8.7 (c) 8.4 (d) 8.6
  12. 12.√84 to 1 decimal place? (a) 9.0 (b) 9.2 (c) 9.1 (d) 9.3
  13. 13.Best estimate of 3478 ÷ 43? (a) 870 (b) 8700 (c) 87
  14. 14.Best estimate of 2019 ÷ 57? (a) 3400 (b) 34 (c) 340
  15. 15.Best estimate of 2970 ÷ 73? (a) 420 (b) 4200 (c) 42
  16. 16.√86 to 1 decimal place? (a) 9.0 (b) 9.2 (c) 9.1 (d) 9.3
  17. 17.√32 to 1 decimal place? (a) 5.6 (b) 5.8 (c) 5.5 (d) 5.7
  18. 18.√61 to 1 decimal place? (a) 7.8 (b) 7.9 (c) 8.1 (d) 8.0
  19. 19.√34 to 1 decimal place? (a) 5.7 (b) 5.8 (c) 5.9 (d) 5.6
  20. 20.√74 to 1 decimal place? (a) 8.9 (b) 8.8 (c) 8.7 (d) 8.6
  21. 21.Best estimate of 560 ÷ 37? (a) 14 (b) 140 (c) 1400
  22. 22.Best estimate of 947 ÷ 34? (a) 32 (b) 320 (c) 3200
  23. 23.√89 to 1 decimal place? (a) 9.4 (b) 9.3 (c) 9.5 (d) 9.2
  24. 24.Best estimate of 865 ÷ 21? (a) 4300 (b) 43 (c) 430
  25. 25.Best estimate of 1807 ÷ 44? (a) 450 (b) 4500 (c) 45
  26. 26.Best estimate of 5393 ÷ 89? (a) 600 (b) 60 (c) 6000
  27. 27.√69 to 1 decimal place? (a) 8.4 (b) 8.3 (c) 8.5 (d) 8.6
  28. 28.Best estimate of 3931 ÷ 71? (a) 56 (b) 5600 (c) 560
  29. 29.Best estimate of 3857 ÷ 43? (a) 960 (b) 96 (c) 9600
  30. 30.Best estimate of 927 ÷ 32? (a) 3100 (b) 31 (c) 310
  31. 31.√96 to 1 decimal place? (a) 9.7 (b) 9.8 (c) 9.9 (d) 10.0
  32. 32.Best estimate of 981 ÷ 68? (a) 140 (b) 1400 (c) 14
  33. 33.√23 to 1 decimal place? (a) 5.0 (b) 5.1 (c) 4.9 (d) 4.8
  34. 34.√94 to 1 decimal place? (a) 9.5 (b) 9.7 (c) 9.8 (d) 9.6
  35. 35.√44 to 1 decimal place? (a) 6.5 (b) 6.7 (c) 6.4 (d) 6.6
  36. 36.Best estimate of 1086 ÷ 42? (a) 2700 (b) 270 (c) 27
  37. 37.Best estimate of 2127 ÷ 57? (a) 3500 (b) 35 (c) 350
  38. 38.Best estimate of 2508 ÷ 51? (a) 500 (b) 5000 (c) 50
  39. 39.Best estimate of 2953 ÷ 44? (a) 740 (b) 74 (c) 7400
  40. 40.√67 to 1 decimal place? (a) 8.1 (b) 8.0 (c) 8.2 (d) 8.3

Answer key

  1. 25
  2. 79
  3. 5.1
  4. 6.8
  5. 42
  6. 62
  7. 21
  8. 52
  9. 8.1
  10. 30
  11. 8.7
  12. 9.2
  13. 87
  14. 34
  15. 42
  16. 9.3
  17. 5.7
  18. 7.8
  19. 5.8
  20. 8.6
  21. 14
  22. 32
  23. 9.4
  24. 43
  25. 45
  26. 60
  27. 8.3
  28. 56
  29. 96
  30. 31
  31. 9.8
  32. 14
  33. 4.8
  34. 9.7
  35. 6.6
  36. 27
  37. 35
  38. 50
  39. 74
  40. 8.2

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