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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 71 · 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.Best estimate of 3719 ÷ 56? (a) 6200 (b) 62 (c) 620
  2. 2.Best estimate of 1528 ÷ 62? (a) 250 (b) 2500 (c) 25
  3. 3.√42 to 1 decimal place? (a) 6.4 (b) 6.3 (c) 6.5 (d) 6.2
  4. 4.Best estimate of 2444 ÷ 42? (a) 610 (b) 6100 (c) 61
  5. 5.Best estimate of 2991 ÷ 36? (a) 7500 (b) 75 (c) 750
  6. 6.Best estimate of 2097 ÷ 72? (a) 30 (b) 300 (c) 3000
  7. 7.Best estimate of 899 ÷ 62? (a) 150 (b) 15 (c) 1500
  8. 8.Best estimate of 2921 ÷ 49? (a) 580 (b) 5800 (c) 58
  9. 9.√63 to 1 decimal place? (a) 7.9 (b) 8.0 (c) 7.8 (d) 8.1
  10. 10.Best estimate of 860 ÷ 36? (a) 220 (b) 22 (c) 2200
  11. 11.√75 to 1 decimal place? (a) 8.5 (b) 8.7 (c) 8.6 (d) 8.8
  12. 12.Best estimate of 4696 ÷ 73? (a) 67 (b) 670 (c) 6700
  13. 13.√58 to 1 decimal place? (a) 7.6 (b) 7.5 (c) 7.3 (d) 7.4
  14. 14.√83 to 1 decimal place? (a) 9.2 (b) 9.0 (c) 9.1 (d) 9.3
  15. 15.√31 to 1 decimal place? (a) 5.9 (b) 5.8 (c) 5.6 (d) 5.7
  16. 16.Best estimate of 7583 ÷ 87? (a) 840 (b) 8400 (c) 84
  17. 17.Best estimate of 982 ÷ 27? (a) 33 (b) 330 (c) 3300
  18. 18.Best estimate of 7322 ÷ 84? (a) 9200 (b) 92 (c) 920
  19. 19.√34 to 1 decimal place? (a) 6.0 (b) 5.7 (c) 5.9 (d) 5.8
  20. 20.Best estimate of 1650 ÷ 63? (a) 2800 (b) 280 (c) 28
  21. 21.√65 to 1 decimal place? (a) 8.0 (b) 8.1 (c) 7.9 (d) 8.2
  22. 22.Best estimate of 4077 ÷ 44? (a) 1020 (b) 10200 (c) 102
  23. 23.Best estimate of 2072 ÷ 23? (a) 1040 (b) 104 (c) 10400
  24. 24.Best estimate of 741 ÷ 33? (a) 250 (b) 25 (c) 2500
  25. 25.Best estimate of 1023 ÷ 22? (a) 510 (b) 51 (c) 5100
  26. 26.√37 to 1 decimal place? (a) 6.1 (b) 5.9 (c) 5.8 (d) 6.0
  27. 27.√41 to 1 decimal place? (a) 6.4 (b) 6.3 (c) 6.2 (d) 6.1
  28. 28.Best estimate of 4158 ÷ 73? (a) 590 (b) 5900 (c) 59
  29. 29.√22 to 1 decimal place? (a) 4.6 (b) 4.5 (c) 4.7 (d) 4.4
  30. 30.Best estimate of 2121 ÷ 54? (a) 420 (b) 4200 (c) 42
  31. 31.Best estimate of 1811 ÷ 59? (a) 300 (b) 30 (c) 3000
  32. 32.Best estimate of 1811 ÷ 21? (a) 9100 (b) 910 (c) 91
  33. 33.√69 to 1 decimal place? (a) 8.5 (b) 8.4 (c) 8.3 (d) 8.2
  34. 34.Best estimate of 486 ÷ 33? (a) 160 (b) 1600 (c) 16
  35. 35.√85 to 1 decimal place? (a) 9.3 (b) 9.0 (c) 9.2 (d) 9.1
  36. 36.Best estimate of 4213 ÷ 46? (a) 84 (b) 840 (c) 8400
  37. 37.√40 to 1 decimal place? (a) 6.3 (b) 6.4 (c) 6.2 (d) 6.1
  38. 38.Best estimate of 1838 ÷ 32? (a) 6100 (b) 61 (c) 610
  39. 39.Best estimate of 1719 ÷ 23? (a) 860 (b) 86 (c) 8600
  40. 40.Best estimate of 6420 ÷ 79? (a) 80 (b) 800 (c) 8000

Answer key

  1. 62
  2. 25
  3. 6.5
  4. 61
  5. 75
  6. 30
  7. 15
  8. 58
  9. 7.9
  10. 22
  11. 8.7
  12. 67
  13. 7.6
  14. 9.1
  15. 5.6
  16. 84
  17. 33
  18. 92
  19. 5.8
  20. 28
  21. 8.1
  22. 102
  23. 104
  24. 25
  25. 51
  26. 6.1
  27. 6.4
  28. 59
  29. 4.7
  30. 42
  31. 30
  32. 91
  33. 8.3
  34. 16
  35. 9.2
  36. 84
  37. 6.3
  38. 61
  39. 86
  40. 80

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