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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 581 · 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 4097 ÷ 44? (a) 1020 (b) 102 (c) 10200
  2. 2.Best estimate of 464 ÷ 26? (a) 1500 (b) 15 (c) 150
  3. 3.√61 to 1 decimal place? (a) 7.8 (b) 7.7 (c) 8.0 (d) 7.9
  4. 4.Best estimate of 1194 ÷ 72? (a) 170 (b) 17 (c) 1700
  5. 5.√74 to 1 decimal place? (a) 8.3 (b) 8.4 (c) 8.5 (d) 8.6
  6. 6.√62 to 1 decimal place? (a) 8.0 (b) 7.8 (c) 7.7 (d) 7.9
  7. 7.Best estimate of 3507 ÷ 76? (a) 44 (b) 440 (c) 4400
  8. 8.√98 to 1 decimal place? (a) 9.8 (b) 9.6 (c) 9.7 (d) 9.9
  9. 9.√69 to 1 decimal place? (a) 8.3 (b) 8.1 (c) 8.2 (d) 8.4
  10. 10.Best estimate of 2262 ÷ 29? (a) 75 (b) 7500 (c) 750
  11. 11.√37 to 1 decimal place? (a) 6.3 (b) 6.4 (c) 6.2 (d) 6.1
  12. 12.Best estimate of 1455 ÷ 33? (a) 4900 (b) 490 (c) 49
  13. 13.√46 to 1 decimal place? (a) 6.9 (b) 6.7 (c) 6.6 (d) 6.8
  14. 14.Best estimate of 1079 ÷ 53? (a) 220 (b) 2200 (c) 22
  15. 15.√75 to 1 decimal place? (a) 8.7 (b) 8.6 (c) 8.5 (d) 8.4
  16. 16.√92 to 1 decimal place? (a) 9.7 (b) 9.8 (c) 9.6 (d) 9.9
  17. 17.Best estimate of 1403 ÷ 86? (a) 160 (b) 1600 (c) 16
  18. 18.Best estimate of 2822 ÷ 44? (a) 710 (b) 71 (c) 7100
  19. 19.Best estimate of 1373 ÷ 59? (a) 230 (b) 2300 (c) 23
  20. 20.√55 to 1 decimal place? (a) 7.7 (b) 7.6 (c) 7.4 (d) 7.5
  21. 21.Best estimate of 3835 ÷ 88? (a) 43 (b) 4300 (c) 430
  22. 22.Best estimate of 5685 ÷ 86? (a) 63 (b) 6300 (c) 630
  23. 23.√43 to 1 decimal place? (a) 6.6 (b) 6.7 (c) 6.5 (d) 6.4
  24. 24.√45 to 1 decimal place? (a) 6.9 (b) 6.8 (c) 6.7 (d) 6.6
  25. 25.√63 to 1 decimal place? (a) 8.1 (b) 7.9 (c) 8.2 (d) 8.0
  26. 26.√70 to 1 decimal place? (a) 8.1 (b) 8.2 (c) 8.4 (d) 8.3
  27. 27.Best estimate of 5609 ÷ 86? (a) 62 (b) 620 (c) 6200
  28. 28.√44 to 1 decimal place? (a) 6.7 (b) 6.9 (c) 6.8 (d) 6.6
  29. 29.√22 to 1 decimal place? (a) 4.7 (b) 4.6 (c) 4.9 (d) 4.8
  30. 30.Best estimate of 364 ÷ 26? (a) 12 (b) 1200 (c) 120
  31. 31.√40 to 1 decimal place? (a) 6.5 (b) 6.4 (c) 6.3 (d) 6.2
  32. 32.Best estimate of 1538 ÷ 23? (a) 770 (b) 77 (c) 7700
  33. 33.√83 to 1 decimal place? (a) 9.1 (b) 9.3 (c) 9.0 (d) 9.2
  34. 34.Best estimate of 2408 ÷ 26? (a) 800 (b) 8000 (c) 80
  35. 35.Best estimate of 4535 ÷ 54? (a) 9100 (b) 91 (c) 910
  36. 36.Best estimate of 1850 ÷ 46? (a) 3700 (b) 370 (c) 37
  37. 37.√20 to 1 decimal place? (a) 4.5 (b) 4.7 (c) 4.6 (d) 4.4
  38. 38.Best estimate of 1482 ÷ 23? (a) 7400 (b) 74 (c) 740
  39. 39.√76 to 1 decimal place? (a) 8.8 (b) 8.6 (c) 8.5 (d) 8.7
  40. 40.√87 to 1 decimal place? (a) 9.2 (b) 9.1 (c) 9.0 (d) 9.3

Answer key

  1. 102
  2. 15
  3. 7.8
  4. 17
  5. 8.6
  6. 7.9
  7. 44
  8. 9.9
  9. 8.3
  10. 75
  11. 6.1
  12. 49
  13. 6.8
  14. 22
  15. 8.7
  16. 9.6
  17. 16
  18. 71
  19. 23
  20. 7.4
  21. 43
  22. 63
  23. 6.6
  24. 6.7
  25. 7.9
  26. 8.4
  27. 62
  28. 6.6
  29. 4.7
  30. 12
  31. 6.3
  32. 77
  33. 9.1
  34. 80
  35. 91
  36. 37
  37. 4.5
  38. 74
  39. 8.7
  40. 9.3

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