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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 110 · 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 2622 ÷ 58? (a) 4400 (b) 440 (c) 44
  2. 2.√59 to 1 decimal place? (a) 7.7 (b) 7.9 (c) 7.8 (d) 7.6
  3. 3.√63 to 1 decimal place? (a) 7.8 (b) 7.9 (c) 8.0 (d) 7.7
  4. 4.Best estimate of 3988 ÷ 72? (a) 5700 (b) 570 (c) 57
  5. 5.Best estimate of 4196 ÷ 62? (a) 70 (b) 7000 (c) 700
  6. 6.Best estimate of 5163 ÷ 62? (a) 860 (b) 8600 (c) 86
  7. 7.Best estimate of 5632 ÷ 71? (a) 800 (b) 8000 (c) 80
  8. 8.√69 to 1 decimal place? (a) 8.2 (b) 8.1 (c) 8.0 (d) 8.3
  9. 9.√58 to 1 decimal place? (a) 7.7 (b) 7.8 (c) 7.6 (d) 7.9
  10. 10.√65 to 1 decimal place? (a) 8.4 (b) 8.3 (c) 8.2 (d) 8.1
  11. 11.Best estimate of 887 ÷ 28? (a) 3000 (b) 300 (c) 30
  12. 12.√72 to 1 decimal place? (a) 8.5 (b) 8.3 (c) 8.4 (d) 8.6
  13. 13.Best estimate of 1119 ÷ 36? (a) 28 (b) 2800 (c) 280
  14. 14.√56 to 1 decimal place? (a) 7.2 (b) 7.3 (c) 7.5 (d) 7.4
  15. 15.√80 to 1 decimal place? (a) 8.6 (b) 8.8 (c) 8.7 (d) 8.9
  16. 16.√92 to 1 decimal place? (a) 9.6 (b) 9.4 (c) 9.7 (d) 9.5
  17. 17.Best estimate of 1847 ÷ 36? (a) 4600 (b) 460 (c) 46
  18. 18.Best estimate of 2918 ÷ 32? (a) 970 (b) 97 (c) 9700
  19. 19.√43 to 1 decimal place? (a) 6.6 (b) 6.9 (c) 6.7 (d) 6.8
  20. 20.√71 to 1 decimal place? (a) 8.4 (b) 8.5 (c) 8.2 (d) 8.3
  21. 21.√55 to 1 decimal place? (a) 7.2 (b) 7.1 (c) 7.4 (d) 7.3
  22. 22.Best estimate of 839 ÷ 44? (a) 21 (b) 2100 (c) 210
  23. 23.√79 to 1 decimal place? (a) 9.1 (b) 9.2 (c) 9.0 (d) 8.9
  24. 24.Best estimate of 1822 ÷ 22? (a) 9100 (b) 91 (c) 910
  25. 25.√45 to 1 decimal place? (a) 6.5 (b) 6.8 (c) 6.6 (d) 6.7
  26. 26.Best estimate of 819 ÷ 57? (a) 140 (b) 1400 (c) 14
  27. 27.Best estimate of 5575 ÷ 86? (a) 620 (b) 62 (c) 6200
  28. 28.Best estimate of 822 ÷ 63? (a) 1400 (b) 140 (c) 14
  29. 29.Best estimate of 5813 ÷ 71? (a) 8300 (b) 830 (c) 83
  30. 30.√34 to 1 decimal place? (a) 5.7 (b) 5.8 (c) 5.9 (d) 6.0
  31. 31.Best estimate of 1523 ÷ 52? (a) 300 (b) 30 (c) 3000
  32. 32.√83 to 1 decimal place? (a) 8.9 (b) 9.0 (c) 9.2 (d) 9.1
  33. 33.Best estimate of 2443 ÷ 29? (a) 810 (b) 81 (c) 8100
  34. 34.√21 to 1 decimal place? (a) 4.5 (b) 4.3 (c) 4.6 (d) 4.4
  35. 35.Best estimate of 1912 ÷ 56? (a) 3200 (b) 320 (c) 32
  36. 36.Best estimate of 2107 ÷ 48? (a) 42 (b) 420 (c) 4200
  37. 37.√85 to 1 decimal place? (a) 9.4 (b) 9.1 (c) 9.3 (d) 9.2
  38. 38.Best estimate of 5372 ÷ 83? (a) 6700 (b) 670 (c) 67
  39. 39.√22 to 1 decimal place? (a) 4.7 (b) 4.8 (c) 4.6 (d) 4.9
  40. 40.√41 to 1 decimal place? (a) 6.6 (b) 6.7 (c) 6.5 (d) 6.4

Answer key

  1. 44
  2. 7.7
  3. 7.9
  4. 57
  5. 70
  6. 86
  7. 80
  8. 8.3
  9. 7.6
  10. 8.1
  11. 30
  12. 8.5
  13. 28
  14. 7.5
  15. 8.9
  16. 9.6
  17. 46
  18. 97
  19. 6.6
  20. 8.4
  21. 7.4
  22. 21
  23. 8.9
  24. 91
  25. 6.7
  26. 14
  27. 62
  28. 14
  29. 83
  30. 5.8
  31. 30
  32. 9.1
  33. 81
  34. 4.6
  35. 32
  36. 42
  37. 9.2
  38. 67
  39. 4.7
  40. 6.4

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