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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 931 · 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.√29 to 1 decimal place? (a) 5.5 (b) 5.4 (c) 5.3 (d) 5.6
  2. 2.√41 to 1 decimal place? (a) 6.4 (b) 6.5 (c) 6.6 (d) 6.3
  3. 3.√67 to 1 decimal place? (a) 8.1 (b) 7.9 (c) 8.0 (d) 8.2
  4. 4.√22 to 1 decimal place? (a) 4.8 (b) 4.6 (c) 4.7 (d) 4.9
  5. 5.√23 to 1 decimal place? (a) 4.9 (b) 4.8 (c) 4.7 (d) 5.0
  6. 6.√72 to 1 decimal place? (a) 8.5 (b) 8.4 (c) 8.3 (d) 8.6
  7. 7.Best estimate of 5134 ÷ 79? (a) 640 (b) 6400 (c) 64
  8. 8.Best estimate of 2861 ÷ 33? (a) 950 (b) 9500 (c) 95
  9. 9.Best estimate of 1849 ÷ 34? (a) 62 (b) 6200 (c) 620
  10. 10.√50 to 1 decimal place? (a) 6.9 (b) 6.8 (c) 7.0 (d) 7.1
  11. 11.Best estimate of 2942 ÷ 38? (a) 7400 (b) 74 (c) 740
  12. 12.Best estimate of 2074 ÷ 24? (a) 10400 (b) 1040 (c) 104
  13. 13.Best estimate of 4041 ÷ 62? (a) 67 (b) 670 (c) 6700
  14. 14.√65 to 1 decimal place? (a) 8.1 (b) 8.3 (c) 8.4 (d) 8.2
  15. 15.√37 to 1 decimal place? (a) 6.2 (b) 6.4 (c) 6.1 (d) 6.3
  16. 16.Best estimate of 1707 ÷ 22? (a) 85 (b) 8500 (c) 850
  17. 17.Best estimate of 2252 ÷ 38? (a) 560 (b) 56 (c) 5600
  18. 18.Best estimate of 1034 ÷ 36? (a) 2600 (b) 260 (c) 26
  19. 19.√77 to 1 decimal place? (a) 8.7 (b) 8.9 (c) 8.8 (d) 9.0
  20. 20.√31 to 1 decimal place? (a) 5.8 (b) 5.9 (c) 5.7 (d) 5.6
  21. 21.Best estimate of 3152 ÷ 71? (a) 450 (b) 4500 (c) 45
  22. 22.√53 to 1 decimal place? (a) 7.6 (b) 7.3 (c) 7.4 (d) 7.5
  23. 23.Best estimate of 591 ÷ 43? (a) 1500 (b) 150 (c) 15
  24. 24.√70 to 1 decimal place? (a) 8.5 (b) 8.3 (c) 8.6 (d) 8.4
  25. 25.√94 to 1 decimal place? (a) 9.7 (b) 9.8 (c) 9.9 (d) 9.6
  26. 26.Best estimate of 2608 ÷ 48? (a) 5200 (b) 52 (c) 520
  27. 27.√32 to 1 decimal place? (a) 5.4 (b) 5.7 (c) 5.5 (d) 5.6
  28. 28.Best estimate of 2119 ÷ 82? (a) 26 (b) 260 (c) 2600
  29. 29.Best estimate of 2554 ÷ 86? (a) 280 (b) 2800 (c) 28
  30. 30.Best estimate of 743 ÷ 23? (a) 37 (b) 370 (c) 3700
  31. 31.√20 to 1 decimal place? (a) 4.3 (b) 4.5 (c) 4.4 (d) 4.2
  32. 32.Best estimate of 3016 ÷ 64? (a) 500 (b) 5000 (c) 50
  33. 33.√44 to 1 decimal place? (a) 6.4 (b) 6.5 (c) 6.7 (d) 6.6
  34. 34.√75 to 1 decimal place? (a) 8.5 (b) 8.8 (c) 8.6 (d) 8.7
  35. 35.Best estimate of 850 ÷ 53? (a) 17 (b) 170 (c) 1700
  36. 36.Best estimate of 3857 ÷ 72? (a) 550 (b) 55 (c) 5500
  37. 37.Best estimate of 1327 ÷ 43? (a) 3300 (b) 330 (c) 33
  38. 38.Best estimate of 1860 ÷ 52? (a) 370 (b) 37 (c) 3700
  39. 39.Best estimate of 5537 ÷ 79? (a) 690 (b) 6900 (c) 69
  40. 40.Best estimate of 1848 ÷ 42? (a) 46 (b) 460 (c) 4600

Answer key

  1. 5.4
  2. 6.4
  3. 8.2
  4. 4.7
  5. 4.8
  6. 8.5
  7. 64
  8. 95
  9. 62
  10. 7.1
  11. 74
  12. 104
  13. 67
  14. 8.1
  15. 6.1
  16. 85
  17. 56
  18. 26
  19. 8.8
  20. 5.6
  21. 45
  22. 7.3
  23. 15
  24. 8.4
  25. 9.7
  26. 52
  27. 5.7
  28. 26
  29. 28
  30. 37
  31. 4.5
  32. 50
  33. 6.6
  34. 8.7
  35. 17
  36. 55
  37. 33
  38. 37
  39. 69
  40. 46

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