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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 78 · 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.√34 to 1 decimal place? (a) 6.0 (b) 5.7 (c) 5.9 (d) 5.8
  2. 2.√74 to 1 decimal place? (a) 8.6 (b) 8.4 (c) 8.5 (d) 8.7
  3. 3.√58 to 1 decimal place? (a) 7.9 (b) 7.7 (c) 7.8 (d) 7.6
  4. 4.Best estimate of 6309 ÷ 71? (a) 900 (b) 9000 (c) 90
  5. 5.Best estimate of 1105 ÷ 39? (a) 280 (b) 28 (c) 2800
  6. 6.Best estimate of 1924 ÷ 26? (a) 6400 (b) 640 (c) 64
  7. 7.√72 to 1 decimal place? (a) 8.6 (b) 8.7 (c) 8.5 (d) 8.4
  8. 8.√28 to 1 decimal place? (a) 5.5 (b) 5.3 (c) 5.6 (d) 5.4
  9. 9.Best estimate of 2610 ÷ 68? (a) 37 (b) 370 (c) 3700
  10. 10.Best estimate of 2594 ÷ 52? (a) 52 (b) 520 (c) 5200
  11. 11.√50 to 1 decimal place? (a) 7.0 (b) 7.1 (c) 6.9 (d) 6.8
  12. 12.Best estimate of 879 ÷ 39? (a) 22 (b) 2200 (c) 220
  13. 13.√94 to 1 decimal place? (a) 9.7 (b) 9.6 (c) 9.8 (d) 9.5
  14. 14.Best estimate of 2394 ÷ 39? (a) 600 (b) 60 (c) 6000
  15. 15.√83 to 1 decimal place? (a) 8.9 (b) 9.1 (c) 8.8 (d) 9.0
  16. 16.Best estimate of 4098 ÷ 79? (a) 510 (b) 51 (c) 5100
  17. 17.√27 to 1 decimal place? (a) 5.2 (b) 5.3 (c) 5.4 (d) 5.1
  18. 18.√40 to 1 decimal place? (a) 6.2 (b) 6.0 (c) 6.1 (d) 6.3
  19. 19.Best estimate of 3778 ÷ 56? (a) 630 (b) 6300 (c) 63
  20. 20.√31 to 1 decimal place? (a) 5.8 (b) 5.7 (c) 5.9 (d) 5.6
  21. 21.Best estimate of 1807 ÷ 41? (a) 450 (b) 4500 (c) 45
  22. 22.Best estimate of 3774 ÷ 69? (a) 54 (b) 5400 (c) 540
  23. 23.Best estimate of 815 ÷ 34? (a) 270 (b) 27 (c) 2700
  24. 24.√65 to 1 decimal place? (a) 8.2 (b) 8.4 (c) 8.1 (d) 8.3
  25. 25.Best estimate of 465 ÷ 36? (a) 1200 (b) 120 (c) 12
  26. 26.Best estimate of 892 ÷ 37? (a) 220 (b) 2200 (c) 22
  27. 27.Best estimate of 7453 ÷ 79? (a) 93 (b) 9300 (c) 930
  28. 28.Best estimate of 2905 ÷ 86? (a) 32 (b) 320 (c) 3200
  29. 29.Best estimate of 689 ÷ 31? (a) 230 (b) 2300 (c) 23
  30. 30.√82 to 1 decimal place? (a) 9.2 (b) 9.1 (c) 9.3 (d) 9.0
  31. 31.√67 to 1 decimal place? (a) 8.3 (b) 8.2 (c) 8.5 (d) 8.4
  32. 32.Best estimate of 2355 ÷ 42? (a) 59 (b) 5900 (c) 590
  33. 33.Best estimate of 1300 ÷ 27? (a) 43 (b) 430 (c) 4300
  34. 34.√41 to 1 decimal place? (a) 6.4 (b) 6.3 (c) 6.1 (d) 6.2
  35. 35.Best estimate of 1893 ÷ 62? (a) 3200 (b) 32 (c) 320
  36. 36.Best estimate of 7147 ÷ 79? (a) 8900 (b) 890 (c) 89
  37. 37.Best estimate of 3601 ÷ 84? (a) 4500 (b) 45 (c) 450
  38. 38.Best estimate of 1773 ÷ 36? (a) 440 (b) 44 (c) 4400
  39. 39.Best estimate of 3326 ÷ 69? (a) 480 (b) 4800 (c) 48
  40. 40.Best estimate of 2620 ÷ 32? (a) 87 (b) 8700 (c) 870

Answer key

  1. 5.8
  2. 8.6
  3. 7.6
  4. 90
  5. 28
  6. 64
  7. 8.5
  8. 5.3
  9. 37
  10. 52
  11. 7.1
  12. 22
  13. 9.7
  14. 60
  15. 9.1
  16. 51
  17. 5.2
  18. 6.3
  19. 63
  20. 5.6
  21. 45
  22. 54
  23. 27
  24. 8.1
  25. 12
  26. 22
  27. 93
  28. 32
  29. 23
  30. 9.1
  31. 8.2
  32. 59
  33. 43
  34. 6.4
  35. 32
  36. 89
  37. 45
  38. 44
  39. 48
  40. 87

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