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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 247 · 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 1795 ÷ 22? (a) 9000 (b) 900 (c) 90
  2. 2.√94 to 1 decimal place? (a) 9.5 (b) 9.6 (c) 9.7 (d) 9.4
  3. 3.Best estimate of 1665 ÷ 58? (a) 280 (b) 2800 (c) 28
  4. 4.√92 to 1 decimal place? (a) 9.8 (b) 9.9 (c) 9.7 (d) 9.6
  5. 5.Best estimate of 6677 ÷ 84? (a) 8300 (b) 83 (c) 830
  6. 6.Best estimate of 977 ÷ 33? (a) 3300 (b) 330 (c) 33
  7. 7.Best estimate of 3357 ÷ 56? (a) 56 (b) 5600 (c) 560
  8. 8.√82 to 1 decimal place? (a) 9.4 (b) 9.2 (c) 9.3 (d) 9.1
  9. 9.Best estimate of 1932 ÷ 54? (a) 390 (b) 3900 (c) 39
  10. 10.√26 to 1 decimal place? (a) 5.1 (b) 5.3 (c) 5.2 (d) 5.0
  11. 11.√20 to 1 decimal place? (a) 4.4 (b) 4.5 (c) 4.6 (d) 4.7
  12. 12.Best estimate of 386 ÷ 22? (a) 190 (b) 19 (c) 1900
  13. 13.Best estimate of 3746 ÷ 48? (a) 750 (b) 7500 (c) 75
  14. 14.Best estimate of 4618 ÷ 78? (a) 58 (b) 5800 (c) 580
  15. 15.Best estimate of 1983 ÷ 22? (a) 990 (b) 99 (c) 9900
  16. 16.Best estimate of 4026 ÷ 66? (a) 580 (b) 5800 (c) 58
  17. 17.√34 to 1 decimal place? (a) 6.0 (b) 5.8 (c) 5.7 (d) 5.9
  18. 18.Best estimate of 3625 ÷ 53? (a) 730 (b) 73 (c) 7300
  19. 19.√41 to 1 decimal place? (a) 6.5 (b) 6.4 (c) 6.2 (d) 6.3
  20. 20.Best estimate of 2768 ÷ 52? (a) 55 (b) 5500 (c) 550
  21. 21.Best estimate of 6484 ÷ 81? (a) 81 (b) 810 (c) 8100
  22. 22.√75 to 1 decimal place? (a) 8.9 (b) 8.6 (c) 8.7 (d) 8.8
  23. 23.√87 to 1 decimal place? (a) 9.4 (b) 9.6 (c) 9.5 (d) 9.3
  24. 24.√43 to 1 decimal place? (a) 6.5 (b) 6.8 (c) 6.6 (d) 6.7
  25. 25.Best estimate of 2171 ÷ 31? (a) 7200 (b) 72 (c) 720
  26. 26.Best estimate of 784 ÷ 42? (a) 200 (b) 2000 (c) 20
  27. 27.Best estimate of 2221 ÷ 34? (a) 740 (b) 7400 (c) 74
  28. 28.Best estimate of 6345 ÷ 84? (a) 7900 (b) 79 (c) 790
  29. 29.√46 to 1 decimal place? (a) 6.8 (b) 7.0 (c) 7.1 (d) 6.9
  30. 30.√27 to 1 decimal place? (a) 5.2 (b) 5.3 (c) 5.4 (d) 5.1
  31. 31.Best estimate of 2495 ÷ 76? (a) 31 (b) 3100 (c) 310
  32. 32.√71 to 1 decimal place? (a) 8.5 (b) 8.3 (c) 8.4 (d) 8.6
  33. 33.√28 to 1 decimal place? (a) 5.4 (b) 5.5 (c) 5.6 (d) 5.3
  34. 34.Best estimate of 4733 ÷ 57? (a) 79 (b) 790 (c) 7900
  35. 35.√61 to 1 decimal place? (a) 7.7 (b) 7.6 (c) 7.8 (d) 7.9
  36. 36.Best estimate of 4204 ÷ 62? (a) 70 (b) 700 (c) 7000
  37. 37.√98 to 1 decimal place? (a) 10.0 (b) 10.2 (c) 10.1 (d) 9.9
  38. 38.√58 to 1 decimal place? (a) 7.6 (b) 7.5 (c) 7.8 (d) 7.7
  39. 39.√69 to 1 decimal place? (a) 8.5 (b) 8.2 (c) 8.4 (d) 8.3
  40. 40.Best estimate of 2685 ÷ 36? (a) 670 (b) 6700 (c) 67

Answer key

  1. 90
  2. 9.7
  3. 28
  4. 9.6
  5. 83
  6. 33
  7. 56
  8. 9.1
  9. 39
  10. 5.1
  11. 4.5
  12. 19
  13. 75
  14. 58
  15. 99
  16. 58
  17. 5.8
  18. 73
  19. 6.4
  20. 55
  21. 81
  22. 8.7
  23. 9.3
  24. 6.6
  25. 72
  26. 20
  27. 74
  28. 79
  29. 6.8
  30. 5.2
  31. 31
  32. 8.4
  33. 5.3
  34. 79
  35. 7.8
  36. 70
  37. 9.9
  38. 7.6
  39. 8.3
  40. 67

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