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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 895 · 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 1672 ÷ 66? (a) 2400 (b) 240 (c) 24
  2. 2.Best estimate of 981 ÷ 26? (a) 330 (b) 33 (c) 3300
  3. 3.√46 to 1 decimal place? (a) 6.9 (b) 7.0 (c) 6.8 (d) 7.1
  4. 4.√58 to 1 decimal place? (a) 7.6 (b) 7.9 (c) 7.8 (d) 7.7
  5. 5.√79 to 1 decimal place? (a) 8.9 (b) 9.2 (c) 9.1 (d) 9.0
  6. 6.√31 to 1 decimal place? (a) 5.6 (b) 5.4 (c) 5.5 (d) 5.7
  7. 7.Best estimate of 5314 ÷ 82? (a) 6600 (b) 66 (c) 660
  8. 8.√84 to 1 decimal place? (a) 9.0 (b) 8.9 (c) 9.1 (d) 9.2
  9. 9.Best estimate of 2070 ÷ 23? (a) 1040 (b) 10400 (c) 104
  10. 10.Best estimate of 2703 ÷ 52? (a) 54 (b) 5400 (c) 540
  11. 11.Best estimate of 615 ÷ 41? (a) 15 (b) 150 (c) 1500
  12. 12.√88 to 1 decimal place? (a) 9.4 (b) 9.5 (c) 9.7 (d) 9.6
  13. 13.√35 to 1 decimal place? (a) 5.8 (b) 6.0 (c) 6.1 (d) 5.9
  14. 14.√42 to 1 decimal place? (a) 6.5 (b) 6.8 (c) 6.7 (d) 6.6
  15. 15.√98 to 1 decimal place? (a) 10.1 (b) 10.0 (c) 10.2 (d) 9.9
  16. 16.Best estimate of 2469 ÷ 69? (a) 350 (b) 35 (c) 3500
  17. 17.Best estimate of 6958 ÷ 89? (a) 7700 (b) 770 (c) 77
  18. 18.Best estimate of 1860 ÷ 62? (a) 3100 (b) 310 (c) 31
  19. 19.Best estimate of 3771 ÷ 77? (a) 4700 (b) 470 (c) 47
  20. 20.Best estimate of 3365 ÷ 48? (a) 6700 (b) 670 (c) 67
  21. 21.√28 to 1 decimal place? (a) 5.3 (b) 5.0 (c) 5.2 (d) 5.1
  22. 22.√63 to 1 decimal place? (a) 7.7 (b) 7.8 (c) 7.9 (d) 8.0
  23. 23.√34 to 1 decimal place? (a) 5.9 (b) 6.0 (c) 6.1 (d) 5.8
  24. 24.√86 to 1 decimal place? (a) 9.5 (b) 9.3 (c) 9.6 (d) 9.4
  25. 25.Best estimate of 1692 ÷ 28? (a) 5600 (b) 560 (c) 56
  26. 26.Best estimate of 4722 ÷ 67? (a) 670 (b) 67 (c) 6700
  27. 27.Best estimate of 1422 ÷ 68? (a) 20 (b) 2000 (c) 200
  28. 28.√96 to 1 decimal place? (a) 9.7 (b) 9.5 (c) 9.8 (d) 9.6
  29. 29.Best estimate of 6332 ÷ 76? (a) 790 (b) 7900 (c) 79
  30. 30.Best estimate of 1222 ÷ 22? (a) 61 (b) 610 (c) 6100
  31. 31.Best estimate of 1800 ÷ 37? (a) 45 (b) 450 (c) 4500
  32. 32.√83 to 1 decimal place? (a) 9.1 (b) 9.3 (c) 9.4 (d) 9.2
  33. 33.Best estimate of 1367 ÷ 26? (a) 460 (b) 4600 (c) 46
  34. 34.Best estimate of 3055 ÷ 76? (a) 380 (b) 3800 (c) 38
  35. 35.Best estimate of 2934 ÷ 48? (a) 590 (b) 59 (c) 5900
  36. 36.√37 to 1 decimal place? (a) 5.9 (b) 6.0 (c) 6.1 (d) 6.2
  37. 37.√30 to 1 decimal place? (a) 5.4 (b) 5.6 (c) 5.3 (d) 5.5
  38. 38.Best estimate of 257 ÷ 21? (a) 130 (b) 13 (c) 1300
  39. 39.Best estimate of 2653 ÷ 73? (a) 3800 (b) 380 (c) 38
  40. 40.Best estimate of 3278 ÷ 36? (a) 82 (b) 820 (c) 8200

Answer key

  1. 24
  2. 33
  3. 6.8
  4. 7.6
  5. 8.9
  6. 5.6
  7. 66
  8. 9.2
  9. 104
  10. 54
  11. 15
  12. 9.4
  13. 5.9
  14. 6.5
  15. 9.9
  16. 35
  17. 77
  18. 31
  19. 47
  20. 67
  21. 5.3
  22. 7.9
  23. 5.8
  24. 9.3
  25. 56
  26. 67
  27. 20
  28. 9.8
  29. 79
  30. 61
  31. 45
  32. 9.1
  33. 46
  34. 38
  35. 59
  36. 6.1
  37. 5.5
  38. 13
  39. 38
  40. 82

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