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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 602 · 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.√55 to 1 decimal place? (a) 7.7 (b) 7.4 (c) 7.6 (d) 7.5
  2. 2.√96 to 1 decimal place? (a) 9.6 (b) 9.7 (c) 9.9 (d) 9.8
  3. 3.Best estimate of 2804 ÷ 34? (a) 93 (b) 930 (c) 9300
  4. 4.√29 to 1 decimal place? (a) 5.6 (b) 5.5 (c) 5.7 (d) 5.4
  5. 5.Best estimate of 4935 ÷ 76? (a) 62 (b) 620 (c) 6200
  6. 6.Best estimate of 1703 ÷ 34? (a) 570 (b) 5700 (c) 57
  7. 7.√38 to 1 decimal place? (a) 6.4 (b) 6.2 (c) 6.3 (d) 6.5
  8. 8.Best estimate of 3067 ÷ 42? (a) 770 (b) 77 (c) 7700
  9. 9.Best estimate of 2334 ÷ 86? (a) 26 (b) 2600 (c) 260
  10. 10.√34 to 1 decimal place? (a) 6.1 (b) 5.9 (c) 5.8 (d) 6.0
  11. 11.Best estimate of 1929 ÷ 32? (a) 64 (b) 6400 (c) 640
  12. 12.√61 to 1 decimal place? (a) 7.9 (b) 8.0 (c) 7.8 (d) 8.1
  13. 13.√43 to 1 decimal place? (a) 6.4 (b) 6.5 (c) 6.3 (d) 6.6
  14. 14.Best estimate of 3354 ÷ 39? (a) 84 (b) 8400 (c) 840
  15. 15.Best estimate of 1331 ÷ 62? (a) 2200 (b) 220 (c) 22
  16. 16.√79 to 1 decimal place? (a) 8.9 (b) 9.2 (c) 9.0 (d) 9.1
  17. 17.Best estimate of 5967 ÷ 63? (a) 99 (b) 990 (c) 9900
  18. 18.√35 to 1 decimal place? (a) 5.7 (b) 6.0 (c) 5.9 (d) 5.8
  19. 19.√22 to 1 decimal place? (a) 4.7 (b) 4.9 (c) 4.6 (d) 4.8
  20. 20.√40 to 1 decimal place? (a) 6.6 (b) 6.5 (c) 6.4 (d) 6.3
  21. 21.√31 to 1 decimal place? (a) 5.5 (b) 5.7 (c) 5.8 (d) 5.6
  22. 22.√58 to 1 decimal place? (a) 7.3 (b) 7.6 (c) 7.5 (d) 7.4
  23. 23.√50 to 1 decimal place? (a) 7.0 (b) 6.9 (c) 7.1 (d) 6.8
  24. 24.Best estimate of 6209 ÷ 83? (a) 78 (b) 780 (c) 7800
  25. 25.Best estimate of 2142 ÷ 32? (a) 710 (b) 71 (c) 7100
  26. 26.Best estimate of 2959 ÷ 62? (a) 490 (b) 49 (c) 4900
  27. 27.Best estimate of 881 ÷ 21? (a) 4400 (b) 440 (c) 44
  28. 28.Best estimate of 1538 ÷ 21? (a) 770 (b) 7700 (c) 77
  29. 29.Best estimate of 811 ÷ 32? (a) 27 (b) 270 (c) 2700
  30. 30.Best estimate of 823 ÷ 31? (a) 270 (b) 27 (c) 2700
  31. 31.Best estimate of 3034 ÷ 87? (a) 34 (b) 340 (c) 3400
  32. 32.Best estimate of 2684 ÷ 44? (a) 67 (b) 670 (c) 6700
  33. 33.Best estimate of 1997 ÷ 63? (a) 3300 (b) 330 (c) 33
  34. 34.Best estimate of 1776 ÷ 49? (a) 360 (b) 36 (c) 3600
  35. 35.Best estimate of 5307 ÷ 62? (a) 88 (b) 880 (c) 8800
  36. 36.√77 to 1 decimal place? (a) 8.8 (b) 8.7 (c) 8.9 (d) 8.6
  37. 37.Best estimate of 1422 ÷ 84? (a) 18 (b) 1800 (c) 180
  38. 38.√37 to 1 decimal place? (a) 6.1 (b) 6.2 (c) 6.0 (d) 5.9
  39. 39.Best estimate of 1209 ÷ 49? (a) 24 (b) 240 (c) 2400
  40. 40.√63 to 1 decimal place? (a) 7.7 (b) 7.8 (c) 8.0 (d) 7.9

Answer key

  1. 7.4
  2. 9.8
  3. 93
  4. 5.4
  5. 62
  6. 57
  7. 6.2
  8. 77
  9. 26
  10. 5.8
  11. 64
  12. 7.8
  13. 6.6
  14. 84
  15. 22
  16. 8.9
  17. 99
  18. 5.9
  19. 4.7
  20. 6.3
  21. 5.6
  22. 7.6
  23. 7.1
  24. 78
  25. 71
  26. 49
  27. 44
  28. 77
  29. 27
  30. 27
  31. 34
  32. 67
  33. 33
  34. 36
  35. 88
  36. 8.8
  37. 18
  38. 6.1
  39. 24
  40. 7.9

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