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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 950 · 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 1395 ÷ 44? (a) 350 (b) 3500 (c) 35
  2. 2.√69 to 1 decimal place? (a) 8.4 (b) 8.3 (c) 8.2 (d) 8.1
  3. 3.Best estimate of 1892 ÷ 37? (a) 470 (b) 47 (c) 4700
  4. 4.Best estimate of 3206 ÷ 69? (a) 46 (b) 460 (c) 4600
  5. 5.Best estimate of 892 ÷ 34? (a) 30 (b) 300 (c) 3000
  6. 6.Best estimate of 2375 ÷ 31? (a) 790 (b) 79 (c) 7900
  7. 7.Best estimate of 2184 ÷ 71? (a) 31 (b) 310 (c) 3100
  8. 8.Best estimate of 877 ÷ 38? (a) 22 (b) 2200 (c) 220
  9. 9.√29 to 1 decimal place? (a) 5.4 (b) 5.7 (c) 5.5 (d) 5.6
  10. 10.√65 to 1 decimal place? (a) 8.2 (b) 8.0 (c) 8.1 (d) 8.3
  11. 11.Best estimate of 718 ÷ 52? (a) 140 (b) 14 (c) 1400
  12. 12.Best estimate of 1463 ÷ 44? (a) 370 (b) 3700 (c) 37
  13. 13.Best estimate of 1396 ÷ 39? (a) 3500 (b) 35 (c) 350
  14. 14.Best estimate of 2025 ÷ 82? (a) 2500 (b) 25 (c) 250
  15. 15.Best estimate of 2698 ÷ 32? (a) 900 (b) 9000 (c) 90
  16. 16.Best estimate of 1307 ÷ 26? (a) 4400 (b) 440 (c) 44
  17. 17.√55 to 1 decimal place? (a) 7.4 (b) 7.6 (c) 7.5 (d) 7.7
  18. 18.Best estimate of 1842 ÷ 77? (a) 230 (b) 23 (c) 2300
  19. 19.√70 to 1 decimal place? (a) 8.5 (b) 8.3 (c) 8.4 (d) 8.2
  20. 20.Best estimate of 3111 ÷ 34? (a) 1040 (b) 104 (c) 10400
  21. 21.√62 to 1 decimal place? (a) 7.8 (b) 7.7 (c) 7.9 (d) 7.6
  22. 22.√59 to 1 decimal place? (a) 7.7 (b) 7.8 (c) 7.9 (d) 7.6
  23. 23.√61 to 1 decimal place? (a) 7.8 (b) 8.0 (c) 7.9 (d) 8.1
  24. 24.√82 to 1 decimal place? (a) 8.9 (b) 9.0 (c) 9.2 (d) 9.1
  25. 25.Best estimate of 7914 ÷ 86? (a) 880 (b) 88 (c) 8800
  26. 26.√34 to 1 decimal place? (a) 6.0 (b) 6.1 (c) 5.8 (d) 5.9
  27. 27.√83 to 1 decimal place? (a) 9.3 (b) 9.1 (c) 9.2 (d) 9.4
  28. 28.Best estimate of 1261 ÷ 21? (a) 630 (b) 6300 (c) 63
  29. 29.Best estimate of 3728 ÷ 78? (a) 470 (b) 4700 (c) 47
  30. 30.Best estimate of 1604 ÷ 82? (a) 2000 (b) 200 (c) 20
  31. 31.√31 to 1 decimal place? (a) 5.3 (b) 5.4 (c) 5.5 (d) 5.6
  32. 32.√28 to 1 decimal place? (a) 5.4 (b) 5.2 (c) 5.3 (d) 5.5
  33. 33.√42 to 1 decimal place? (a) 6.5 (b) 6.8 (c) 6.7 (d) 6.6
  34. 34.√37 to 1 decimal place? (a) 6.2 (b) 6.3 (c) 6.1 (d) 6.4
  35. 35.Best estimate of 2181 ÷ 32? (a) 7300 (b) 730 (c) 73
  36. 36.Best estimate of 904 ÷ 33? (a) 3000 (b) 30 (c) 300
  37. 37.√72 to 1 decimal place? (a) 8.5 (b) 8.8 (c) 8.7 (d) 8.6
  38. 38.√23 to 1 decimal place? (a) 5.1 (b) 4.9 (c) 5.0 (d) 4.8
  39. 39.Best estimate of 1039 ÷ 62? (a) 1700 (b) 170 (c) 17
  40. 40.√22 to 1 decimal place? (a) 4.7 (b) 4.6 (c) 4.5 (d) 4.4

Answer key

  1. 35
  2. 8.3
  3. 47
  4. 46
  5. 30
  6. 79
  7. 31
  8. 22
  9. 5.4
  10. 8.1
  11. 14
  12. 37
  13. 35
  14. 25
  15. 90
  16. 44
  17. 7.4
  18. 23
  19. 8.4
  20. 104
  21. 7.9
  22. 7.7
  23. 7.8
  24. 9.1
  25. 88
  26. 5.8
  27. 9.1
  28. 63
  29. 47
  30. 20
  31. 5.6
  32. 5.3
  33. 6.5
  34. 6.1
  35. 73
  36. 30
  37. 8.5
  38. 4.8
  39. 17
  40. 4.7

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