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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 401 · 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.√44 to 1 decimal place? (a) 6.7 (b) 6.5 (c) 6.8 (d) 6.6
  2. 2.√40 to 1 decimal place? (a) 6.3 (b) 6.2 (c) 6.1 (d) 6.4
  3. 3.√31 to 1 decimal place? (a) 5.5 (b) 5.6 (c) 5.8 (d) 5.7
  4. 4.√55 to 1 decimal place? (a) 7.4 (b) 7.3 (c) 7.1 (d) 7.2
  5. 5.Best estimate of 1939 ÷ 87? (a) 2200 (b) 22 (c) 220
  6. 6.Best estimate of 891 ÷ 52? (a) 18 (b) 1800 (c) 180
  7. 7.√80 to 1 decimal place? (a) 8.9 (b) 9.2 (c) 9.0 (d) 9.1
  8. 8.Best estimate of 1732 ÷ 61? (a) 29 (b) 290 (c) 2900
  9. 9.Best estimate of 1488 ÷ 36? (a) 370 (b) 3700 (c) 37
  10. 10.√26 to 1 decimal place? (a) 5.2 (b) 4.9 (c) 5.1 (d) 5.0
  11. 11.Best estimate of 4036 ÷ 52? (a) 81 (b) 810 (c) 8100
  12. 12.√20 to 1 decimal place? (a) 4.5 (b) 4.3 (c) 4.4 (d) 4.2
  13. 13.√30 to 1 decimal place? (a) 5.6 (b) 5.5 (c) 5.7 (d) 5.8
  14. 14.√69 to 1 decimal place? (a) 8.6 (b) 8.4 (c) 8.5 (d) 8.3
  15. 15.Best estimate of 3962 ÷ 49? (a) 790 (b) 7900 (c) 79
  16. 16.√34 to 1 decimal place? (a) 5.6 (b) 5.5 (c) 5.8 (d) 5.7
  17. 17.Best estimate of 4587 ÷ 52? (a) 9200 (b) 920 (c) 92
  18. 18.Best estimate of 3829 ÷ 72? (a) 550 (b) 55 (c) 5500
  19. 19.Best estimate of 1460 ÷ 76? (a) 1800 (b) 18 (c) 180
  20. 20.Best estimate of 2230 ÷ 32? (a) 74 (b) 740 (c) 7400
  21. 21.√76 to 1 decimal place? (a) 8.6 (b) 8.8 (c) 8.9 (d) 8.7
  22. 22.Best estimate of 4745 ÷ 79? (a) 5900 (b) 590 (c) 59
  23. 23.√38 to 1 decimal place? (a) 6.1 (b) 6.0 (c) 5.9 (d) 6.2
  24. 24.Best estimate of 3138 ÷ 51? (a) 6300 (b) 630 (c) 63
  25. 25.Best estimate of 1736 ÷ 41? (a) 430 (b) 4300 (c) 43
  26. 26.Best estimate of 3631 ÷ 86? (a) 4000 (b) 400 (c) 40
  27. 27.Best estimate of 6857 ÷ 78? (a) 8600 (b) 86 (c) 860
  28. 28.√89 to 1 decimal place? (a) 9.2 (b) 9.4 (c) 9.1 (d) 9.3
  29. 29.Best estimate of 4710 ÷ 78? (a) 59 (b) 590 (c) 5900
  30. 30.Best estimate of 4106 ÷ 58? (a) 680 (b) 6800 (c) 68
  31. 31.√37 to 1 decimal place? (a) 5.9 (b) 6.0 (c) 5.8 (d) 6.1
  32. 32.√92 to 1 decimal place? (a) 9.5 (b) 9.4 (c) 9.7 (d) 9.6
  33. 33.√58 to 1 decimal place? (a) 7.7 (b) 7.4 (c) 7.6 (d) 7.5
  34. 34.Best estimate of 3381 ÷ 42? (a) 8500 (b) 85 (c) 850
  35. 35.Best estimate of 5921 ÷ 82? (a) 7400 (b) 74 (c) 740
  36. 36.Best estimate of 614 ÷ 26? (a) 200 (b) 2000 (c) 20
  37. 37.√23 to 1 decimal place? (a) 4.7 (b) 4.6 (c) 4.8 (d) 4.5
  38. 38.√28 to 1 decimal place? (a) 5.4 (b) 5.6 (c) 5.3 (d) 5.5
  39. 39.√66 to 1 decimal place? (a) 8.1 (b) 8.3 (c) 8.0 (d) 8.2
  40. 40.Best estimate of 3037 ÷ 42? (a) 76 (b) 7600 (c) 760

Answer key

  1. 6.6
  2. 6.3
  3. 5.6
  4. 7.4
  5. 22
  6. 18
  7. 8.9
  8. 29
  9. 37
  10. 5.1
  11. 81
  12. 4.5
  13. 5.5
  14. 8.3
  15. 79
  16. 5.8
  17. 92
  18. 55
  19. 18
  20. 74
  21. 8.7
  22. 59
  23. 6.2
  24. 63
  25. 43
  26. 40
  27. 86
  28. 9.4
  29. 59
  30. 68
  31. 6.1
  32. 9.6
  33. 7.6
  34. 85
  35. 74
  36. 20
  37. 4.8
  38. 5.3
  39. 8.1
  40. 76

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