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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 85 · 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 2658 ÷ 39? (a) 6600 (b) 660 (c) 66
  2. 2.Best estimate of 2017 ÷ 33? (a) 6700 (b) 67 (c) 670
  3. 3.√48 to 1 decimal place? (a) 7.1 (b) 7.0 (c) 6.9 (d) 6.8
  4. 4.Best estimate of 6034 ÷ 82? (a) 750 (b) 7500 (c) 75
  5. 5.√70 to 1 decimal place? (a) 8.3 (b) 8.5 (c) 8.6 (d) 8.4
  6. 6.√72 to 1 decimal place? (a) 8.6 (b) 8.5 (c) 8.3 (d) 8.4
  7. 7.Best estimate of 2385 ÷ 69? (a) 34 (b) 3400 (c) 340
  8. 8.√98 to 1 decimal place? (a) 9.6 (b) 9.7 (c) 9.8 (d) 9.9
  9. 9.√96 to 1 decimal place? (a) 10.0 (b) 9.9 (c) 9.8 (d) 10.1
  10. 10.Best estimate of 4472 ÷ 87? (a) 5000 (b) 500 (c) 50
  11. 11.Best estimate of 4846 ÷ 72? (a) 6900 (b) 69 (c) 690
  12. 12.√63 to 1 decimal place? (a) 8.1 (b) 8.0 (c) 7.9 (d) 7.8
  13. 13.Best estimate of 1498 ÷ 26? (a) 500 (b) 50 (c) 5000
  14. 14.√34 to 1 decimal place? (a) 5.8 (b) 5.6 (c) 5.9 (d) 5.7
  15. 15.Best estimate of 5677 ÷ 68? (a) 810 (b) 8100 (c) 81
  16. 16.√58 to 1 decimal place? (a) 7.8 (b) 7.7 (c) 7.6 (d) 7.9
  17. 17.Best estimate of 1869 ÷ 54? (a) 370 (b) 3700 (c) 37
  18. 18.√79 to 1 decimal place? (a) 9.1 (b) 9.0 (c) 9.2 (d) 8.9
  19. 19.Best estimate of 6905 ÷ 73? (a) 9900 (b) 990 (c) 99
  20. 20.Best estimate of 2187 ÷ 59? (a) 360 (b) 36 (c) 3600
  21. 21.√69 to 1 decimal place? (a) 8.3 (b) 8.6 (c) 8.5 (d) 8.4
  22. 22.Best estimate of 3380 ÷ 72? (a) 480 (b) 4800 (c) 48
  23. 23.√77 to 1 decimal place? (a) 9.1 (b) 9.0 (c) 8.9 (d) 8.8
  24. 24.Best estimate of 1774 ÷ 24? (a) 890 (b) 89 (c) 8900
  25. 25.Best estimate of 1240 ÷ 56? (a) 210 (b) 21 (c) 2100
  26. 26.√24 to 1 decimal place? (a) 4.7 (b) 5.0 (c) 4.8 (d) 4.9
  27. 27.Best estimate of 621 ÷ 36? (a) 160 (b) 1600 (c) 16
  28. 28.Best estimate of 2485 ÷ 36? (a) 620 (b) 6200 (c) 62
  29. 29.√43 to 1 decimal place? (a) 6.7 (b) 6.5 (c) 6.8 (d) 6.6
  30. 30.Best estimate of 6609 ÷ 69? (a) 94 (b) 940 (c) 9400
  31. 31.Best estimate of 909 ÷ 61? (a) 1500 (b) 15 (c) 150
  32. 32.Best estimate of 2581 ÷ 39? (a) 650 (b) 6500 (c) 65
  33. 33.Best estimate of 1879 ÷ 39? (a) 47 (b) 4700 (c) 470
  34. 34.√56 to 1 decimal place? (a) 7.5 (b) 7.8 (c) 7.6 (d) 7.7
  35. 35.√94 to 1 decimal place? (a) 9.5 (b) 9.4 (c) 9.7 (d) 9.6
  36. 36.Best estimate of 745 ÷ 62? (a) 1200 (b) 12 (c) 120
  37. 37.√50 to 1 decimal place? (a) 7.2 (b) 7.1 (c) 7.3 (d) 7.4
  38. 38.√51 to 1 decimal place? (a) 7.0 (b) 6.8 (c) 7.1 (d) 6.9
  39. 39.Best estimate of 930 ÷ 43? (a) 23 (b) 2300 (c) 230
  40. 40.Best estimate of 3479 ÷ 46? (a) 700 (b) 7000 (c) 70

Answer key

  1. 66
  2. 67
  3. 6.9
  4. 75
  5. 8.4
  6. 8.5
  7. 34
  8. 9.9
  9. 9.8
  10. 50
  11. 69
  12. 7.9
  13. 50
  14. 5.8
  15. 81
  16. 7.6
  17. 37
  18. 8.9
  19. 99
  20. 36
  21. 8.3
  22. 48
  23. 8.8
  24. 89
  25. 21
  26. 4.9
  27. 16
  28. 62
  29. 6.6
  30. 94
  31. 15
  32. 65
  33. 47
  34. 7.5
  35. 9.7
  36. 12
  37. 7.1
  38. 7.1
  39. 23
  40. 70

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