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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 438 · 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 4589 ÷ 54? (a) 920 (b) 92 (c) 9200
  2. 2.√46 to 1 decimal place? (a) 7.0 (b) 6.9 (c) 6.8 (d) 6.7
  3. 3.Best estimate of 2112 ÷ 39? (a) 53 (b) 5300 (c) 530
  4. 4.Best estimate of 2579 ÷ 31? (a) 8600 (b) 860 (c) 86
  5. 5.√65 to 1 decimal place? (a) 7.9 (b) 8.1 (c) 8.2 (d) 8.0
  6. 6.√61 to 1 decimal place? (a) 7.9 (b) 8.0 (c) 7.7 (d) 7.8
  7. 7.Best estimate of 6275 ÷ 77? (a) 7800 (b) 78 (c) 780
  8. 8.Best estimate of 780 ÷ 31? (a) 26 (b) 2600 (c) 260
  9. 9.√34 to 1 decimal place? (a) 5.7 (b) 5.8 (c) 6.0 (d) 5.9
  10. 10.√26 to 1 decimal place? (a) 5.2 (b) 5.4 (c) 5.1 (d) 5.3
  11. 11.Best estimate of 2336 ÷ 37? (a) 58 (b) 580 (c) 5800
  12. 12.Best estimate of 2291 ÷ 51? (a) 460 (b) 46 (c) 4600
  13. 13.√35 to 1 decimal place? (a) 5.9 (b) 6.1 (c) 6.0 (d) 5.8
  14. 14.√92 to 1 decimal place? (a) 9.3 (b) 9.4 (c) 9.5 (d) 9.6
  15. 15.√62 to 1 decimal place? (a) 7.8 (b) 8.0 (c) 7.9 (d) 7.7
  16. 16.Best estimate of 1639 ÷ 32? (a) 5500 (b) 550 (c) 55
  17. 17.Best estimate of 1582 ÷ 63? (a) 260 (b) 26 (c) 2600
  18. 18.Best estimate of 1673 ÷ 29? (a) 5600 (b) 56 (c) 560
  19. 19.Best estimate of 2808 ÷ 54? (a) 5600 (b) 560 (c) 56
  20. 20.√23 to 1 decimal place? (a) 4.8 (b) 4.9 (c) 4.7 (d) 5.0
  21. 21.√55 to 1 decimal place? (a) 7.3 (b) 7.2 (c) 7.4 (d) 7.5
  22. 22.Best estimate of 2109 ÷ 69? (a) 300 (b) 3000 (c) 30
  23. 23.√22 to 1 decimal place? (a) 4.9 (b) 5.0 (c) 4.8 (d) 4.7
  24. 24.√50 to 1 decimal place? (a) 7.3 (b) 7.2 (c) 7.1 (d) 7.4
  25. 25.Best estimate of 1230 ÷ 87? (a) 140 (b) 1400 (c) 14
  26. 26.Best estimate of 5983 ÷ 72? (a) 8500 (b) 85 (c) 850
  27. 27.Best estimate of 1832 ÷ 36? (a) 4600 (b) 460 (c) 46
  28. 28.Best estimate of 7913 ÷ 84? (a) 99 (b) 9900 (c) 990
  29. 29.Best estimate of 1787 ÷ 71? (a) 260 (b) 26 (c) 2600
  30. 30.Best estimate of 3858 ÷ 63? (a) 640 (b) 6400 (c) 64
  31. 31.√53 to 1 decimal place? (a) 7.4 (b) 7.3 (c) 7.5 (d) 7.2
  32. 32.Best estimate of 3027 ÷ 74? (a) 4300 (b) 430 (c) 43
  33. 33.√44 to 1 decimal place? (a) 6.6 (b) 6.9 (c) 6.7 (d) 6.8
  34. 34.Best estimate of 2663 ÷ 56? (a) 440 (b) 44 (c) 4400
  35. 35.√37 to 1 decimal place? (a) 6.1 (b) 5.9 (c) 5.8 (d) 6.0
  36. 36.Best estimate of 2017 ÷ 83? (a) 25 (b) 250 (c) 2500
  37. 37.Best estimate of 2274 ÷ 27? (a) 7600 (b) 760 (c) 76
  38. 38.√45 to 1 decimal place? (a) 6.8 (b) 6.6 (c) 6.9 (d) 6.7
  39. 39.√58 to 1 decimal place? (a) 7.9 (b) 7.8 (c) 7.6 (d) 7.7
  40. 40.√69 to 1 decimal place? (a) 8.4 (b) 8.3 (c) 8.6 (d) 8.5

Answer key

  1. 92
  2. 6.8
  3. 53
  4. 86
  5. 8.1
  6. 7.8
  7. 78
  8. 26
  9. 5.8
  10. 5.1
  11. 58
  12. 46
  13. 5.9
  14. 9.6
  15. 7.9
  16. 55
  17. 26
  18. 56
  19. 56
  20. 4.8
  21. 7.4
  22. 30
  23. 4.7
  24. 7.1
  25. 14
  26. 85
  27. 46
  28. 99
  29. 26
  30. 64
  31. 7.3
  32. 43
  33. 6.6
  34. 44
  35. 6.1
  36. 25
  37. 76
  38. 6.7
  39. 7.6
  40. 8.3

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