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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 709 · 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.√23 to 1 decimal place? (a) 5.0 (b) 4.9 (c) 4.8 (d) 4.7
  2. 2.Best estimate of 795 ÷ 22? (a) 4000 (b) 40 (c) 400
  3. 3.Best estimate of 2685 ÷ 89? (a) 30 (b) 3000 (c) 300
  4. 4.Best estimate of 1947 ÷ 56? (a) 320 (b) 32 (c) 3200
  5. 5.Best estimate of 4349 ÷ 71? (a) 620 (b) 6200 (c) 62
  6. 6.Best estimate of 2370 ÷ 76? (a) 30 (b) 300 (c) 3000
  7. 7.Best estimate of 4466 ÷ 67? (a) 64 (b) 640 (c) 6400
  8. 8.Best estimate of 7078 ÷ 81? (a) 8800 (b) 88 (c) 880
  9. 9.√61 to 1 decimal place? (a) 7.6 (b) 7.5 (c) 7.8 (d) 7.7
  10. 10.√20 to 1 decimal place? (a) 4.6 (b) 4.3 (c) 4.5 (d) 4.4
  11. 11.√30 to 1 decimal place? (a) 5.7 (b) 5.5 (c) 5.6 (d) 5.8
  12. 12.√53 to 1 decimal place? (a) 7.1 (b) 7.2 (c) 7.3 (d) 7.0
  13. 13.Best estimate of 4184 ÷ 52? (a) 840 (b) 84 (c) 8400
  14. 14.Best estimate of 3455 ÷ 62? (a) 580 (b) 5800 (c) 58
  15. 15.√79 to 1 decimal place? (a) 9.1 (b) 8.9 (c) 8.8 (d) 9.0
  16. 16.√86 to 1 decimal place? (a) 9.4 (b) 9.3 (c) 9.2 (d) 9.5
  17. 17.√58 to 1 decimal place? (a) 7.3 (b) 7.6 (c) 7.5 (d) 7.4
  18. 18.Best estimate of 3419 ÷ 74? (a) 4900 (b) 49 (c) 490
  19. 19.Best estimate of 2832 ÷ 38? (a) 710 (b) 71 (c) 7100
  20. 20.√40 to 1 decimal place? (a) 6.2 (b) 6.1 (c) 6.3 (d) 6.0
  21. 21.Best estimate of 2088 ÷ 66? (a) 3000 (b) 30 (c) 300
  22. 22.Best estimate of 5009 ÷ 68? (a) 7200 (b) 720 (c) 72
  23. 23.Best estimate of 6807 ÷ 86? (a) 7600 (b) 760 (c) 76
  24. 24.Best estimate of 6546 ÷ 83? (a) 82 (b) 820 (c) 8200
  25. 25.Best estimate of 4947 ÷ 52? (a) 99 (b) 990 (c) 9900
  26. 26.√32 to 1 decimal place? (a) 5.5 (b) 5.6 (c) 5.8 (d) 5.7
  27. 27.√26 to 1 decimal place? (a) 5.0 (b) 5.1 (c) 5.2 (d) 4.9
  28. 28.Best estimate of 750 ÷ 26? (a) 2500 (b) 25 (c) 250
  29. 29.Best estimate of 1484 ÷ 46? (a) 30 (b) 300 (c) 3000
  30. 30.√46 to 1 decimal place? (a) 6.8 (b) 6.7 (c) 6.9 (d) 6.6
  31. 31.√94 to 1 decimal place? (a) 9.4 (b) 9.5 (c) 9.6 (d) 9.7
  32. 32.√34 to 1 decimal place? (a) 5.7 (b) 5.8 (c) 5.9 (d) 5.6
  33. 33.Best estimate of 1051 ÷ 73? (a) 150 (b) 1500 (c) 15
  34. 34.√63 to 1 decimal place? (a) 7.9 (b) 7.6 (c) 7.7 (d) 7.8
  35. 35.Best estimate of 4974 ÷ 71? (a) 71 (b) 7100 (c) 710
  36. 36.Best estimate of 1605 ÷ 26? (a) 5400 (b) 54 (c) 540
  37. 37.Best estimate of 1859 ÷ 22? (a) 9300 (b) 930 (c) 93
  38. 38.Best estimate of 2906 ÷ 38? (a) 73 (b) 730 (c) 7300
  39. 39.√28 to 1 decimal place? (a) 5.4 (b) 5.1 (c) 5.3 (d) 5.2
  40. 40.Best estimate of 4911 ÷ 56? (a) 820 (b) 8200 (c) 82

Answer key

  1. 4.8
  2. 40
  3. 30
  4. 32
  5. 62
  6. 30
  7. 64
  8. 88
  9. 7.8
  10. 4.5
  11. 5.5
  12. 7.3
  13. 84
  14. 58
  15. 8.9
  16. 9.3
  17. 7.6
  18. 49
  19. 71
  20. 6.3
  21. 30
  22. 72
  23. 76
  24. 82
  25. 99
  26. 5.7
  27. 5.1
  28. 25
  29. 30
  30. 6.8
  31. 9.7
  32. 5.8
  33. 15
  34. 7.9
  35. 71
  36. 54
  37. 93
  38. 73
  39. 5.3
  40. 82

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