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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 545 · 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.√75 to 1 decimal place? (a) 8.7 (b) 8.6 (c) 8.8 (d) 8.9
  2. 2.Best estimate of 5958 ÷ 72? (a) 85 (b) 850 (c) 8500
  3. 3.√90 to 1 decimal place? (a) 9.7 (b) 9.5 (c) 9.8 (d) 9.6
  4. 4.√40 to 1 decimal place? (a) 6.3 (b) 6.2 (c) 6.4 (d) 6.1
  5. 5.Best estimate of 1384 ÷ 22? (a) 69 (b) 6900 (c) 690
  6. 6.Best estimate of 3797 ÷ 54? (a) 7600 (b) 76 (c) 760
  7. 7.√44 to 1 decimal place? (a) 6.6 (b) 6.5 (c) 6.7 (d) 6.8
  8. 8.√65 to 1 decimal place? (a) 8.1 (b) 8.3 (c) 8.2 (d) 8.0
  9. 9.√63 to 1 decimal place? (a) 8.0 (b) 7.7 (c) 7.8 (d) 7.9
  10. 10.Best estimate of 1814 ÷ 42? (a) 4500 (b) 45 (c) 450
  11. 11.Best estimate of 1401 ÷ 22? (a) 700 (b) 7000 (c) 70
  12. 12.Best estimate of 3708 ÷ 41? (a) 9300 (b) 930 (c) 93
  13. 13.√55 to 1 decimal place? (a) 7.3 (b) 7.6 (c) 7.4 (d) 7.5
  14. 14.√48 to 1 decimal place? (a) 6.7 (b) 6.9 (c) 6.8 (d) 6.6
  15. 15.√46 to 1 decimal place? (a) 6.7 (b) 7.0 (c) 6.8 (d) 6.9
  16. 16.Best estimate of 3463 ÷ 53? (a) 69 (b) 6900 (c) 690
  17. 17.Best estimate of 6450 ÷ 68? (a) 920 (b) 9200 (c) 92
  18. 18.Best estimate of 1765 ÷ 89? (a) 20 (b) 200 (c) 2000
  19. 19.√38 to 1 decimal place? (a) 6.5 (b) 6.2 (c) 6.4 (d) 6.3
  20. 20.Best estimate of 959 ÷ 29? (a) 3200 (b) 32 (c) 320
  21. 21.Best estimate of 630 ÷ 26? (a) 210 (b) 2100 (c) 21
  22. 22.√24 to 1 decimal place? (a) 4.7 (b) 4.8 (c) 4.9 (d) 5.0
  23. 23.Best estimate of 3372 ÷ 42? (a) 84 (b) 8400 (c) 840
  24. 24.√26 to 1 decimal place? (a) 5.2 (b) 5.1 (c) 5.3 (d) 5.4
  25. 25.√77 to 1 decimal place? (a) 8.9 (b) 8.8 (c) 8.7 (d) 8.6
  26. 26.Best estimate of 4467 ÷ 56? (a) 74 (b) 7400 (c) 740
  27. 27.Best estimate of 2704 ÷ 83? (a) 34 (b) 340 (c) 3400
  28. 28.Best estimate of 1666 ÷ 32? (a) 56 (b) 5600 (c) 560
  29. 29.√66 to 1 decimal place? (a) 8.0 (b) 8.3 (c) 8.2 (d) 8.1
  30. 30.Best estimate of 1101 ÷ 34? (a) 37 (b) 3700 (c) 370
  31. 31.Best estimate of 1133 ÷ 32? (a) 380 (b) 38 (c) 3800
  32. 32.Best estimate of 2699 ÷ 42? (a) 67 (b) 6700 (c) 670
  33. 33.Best estimate of 6355 ÷ 77? (a) 79 (b) 790 (c) 7900
  34. 34.Best estimate of 438 ÷ 32? (a) 1500 (b) 150 (c) 15
  35. 35.√34 to 1 decimal place? (a) 5.8 (b) 5.6 (c) 5.7 (d) 5.5
  36. 36.Best estimate of 1871 ÷ 31? (a) 62 (b) 6200 (c) 620
  37. 37.√72 to 1 decimal place? (a) 8.4 (b) 8.6 (c) 8.5 (d) 8.3
  38. 38.√82 to 1 decimal place? (a) 8.8 (b) 9.1 (c) 9.0 (d) 8.9
  39. 39.Best estimate of 5932 ÷ 68? (a) 85 (b) 850 (c) 8500
  40. 40.Best estimate of 2903 ÷ 42? (a) 730 (b) 73 (c) 7300

Answer key

  1. 8.7
  2. 85
  3. 9.5
  4. 6.3
  5. 69
  6. 76
  7. 6.6
  8. 8.1
  9. 7.9
  10. 45
  11. 70
  12. 93
  13. 7.4
  14. 6.9
  15. 6.8
  16. 69
  17. 92
  18. 20
  19. 6.2
  20. 32
  21. 21
  22. 4.9
  23. 84
  24. 5.1
  25. 8.8
  26. 74
  27. 34
  28. 56
  29. 8.1
  30. 37
  31. 38
  32. 67
  33. 79
  34. 15
  35. 5.8
  36. 62
  37. 8.5
  38. 9.1
  39. 85
  40. 73

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