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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 680 · 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.√34 to 1 decimal place? (a) 5.8 (b) 6.0 (c) 6.1 (d) 5.9
  2. 2.√31 to 1 decimal place? (a) 5.5 (b) 5.7 (c) 5.4 (d) 5.6
  3. 3.√53 to 1 decimal place? (a) 7.3 (b) 7.2 (c) 7.4 (d) 7.1
  4. 4.Best estimate of 4925 ÷ 84? (a) 62 (b) 620 (c) 6200
  5. 5.Best estimate of 5283 ÷ 63? (a) 88 (b) 8800 (c) 880
  6. 6.√92 to 1 decimal place? (a) 9.7 (b) 9.5 (c) 9.6 (d) 9.8
  7. 7.Best estimate of 4216 ÷ 54? (a) 84 (b) 8400 (c) 840
  8. 8.Best estimate of 1793 ÷ 28? (a) 600 (b) 6000 (c) 60
  9. 9.Best estimate of 1443 ÷ 77? (a) 18 (b) 180 (c) 1800
  10. 10.Best estimate of 3816 ÷ 89? (a) 420 (b) 4200 (c) 42
  11. 11.√78 to 1 decimal place? (a) 8.6 (b) 8.5 (c) 8.7 (d) 8.8
  12. 12.√20 to 1 decimal place? (a) 4.4 (b) 4.5 (c) 4.6 (d) 4.7
  13. 13.Best estimate of 1491 ÷ 46? (a) 30 (b) 3000 (c) 300
  14. 14.Best estimate of 4399 ÷ 63? (a) 7300 (b) 73 (c) 730
  15. 15.√61 to 1 decimal place? (a) 7.7 (b) 7.8 (c) 7.5 (d) 7.6
  16. 16.Best estimate of 536 ÷ 41? (a) 1300 (b) 13 (c) 130
  17. 17.√74 to 1 decimal place? (a) 8.7 (b) 8.8 (c) 8.5 (d) 8.6
  18. 18.Best estimate of 5729 ÷ 84? (a) 720 (b) 7200 (c) 72
  19. 19.Best estimate of 5618 ÷ 81? (a) 700 (b) 70 (c) 7000
  20. 20.Best estimate of 2179 ÷ 77? (a) 270 (b) 27 (c) 2700
  21. 21.Best estimate of 1488 ÷ 89? (a) 17 (b) 1700 (c) 170
  22. 22.Best estimate of 2209 ÷ 43? (a) 550 (b) 55 (c) 5500
  23. 23.√88 to 1 decimal place? (a) 9.4 (b) 9.5 (c) 9.3 (d) 9.6
  24. 24.√46 to 1 decimal place? (a) 6.6 (b) 6.7 (c) 6.9 (d) 6.8
  25. 25.Best estimate of 3505 ÷ 39? (a) 880 (b) 88 (c) 8800
  26. 26.Best estimate of 3728 ÷ 49? (a) 75 (b) 7500 (c) 750
  27. 27.Best estimate of 860 ÷ 62? (a) 140 (b) 1400 (c) 14
  28. 28.√47 to 1 decimal place? (a) 7.0 (b) 7.2 (c) 6.9 (d) 7.1
  29. 29.Best estimate of 670 ÷ 38? (a) 170 (b) 17 (c) 1700
  30. 30.√52 to 1 decimal place? (a) 7.1 (b) 7.3 (c) 7.4 (d) 7.2
  31. 31.Best estimate of 3021 ÷ 87? (a) 340 (b) 3400 (c) 34
  32. 32.√65 to 1 decimal place? (a) 8.2 (b) 8.0 (c) 8.1 (d) 8.3
  33. 33.√29 to 1 decimal place? (a) 5.1 (b) 5.4 (c) 5.3 (d) 5.2
  34. 34.Best estimate of 4046 ÷ 82? (a) 51 (b) 5100 (c) 510
  35. 35.Best estimate of 2762 ÷ 42? (a) 6900 (b) 69 (c) 690
  36. 36.Best estimate of 3003 ÷ 37? (a) 75 (b) 7500 (c) 750
  37. 37.Best estimate of 713 ÷ 21? (a) 360 (b) 3600 (c) 36
  38. 38.√40 to 1 decimal place? (a) 6.3 (b) 6.4 (c) 6.2 (d) 6.1
  39. 39.Best estimate of 1851 ÷ 32? (a) 620 (b) 62 (c) 6200
  40. 40.Best estimate of 2411 ÷ 44? (a) 6000 (b) 600 (c) 60

Answer key

  1. 5.8
  2. 5.6
  3. 7.3
  4. 62
  5. 88
  6. 9.6
  7. 84
  8. 60
  9. 18
  10. 42
  11. 8.8
  12. 4.5
  13. 30
  14. 73
  15. 7.8
  16. 13
  17. 8.6
  18. 72
  19. 70
  20. 27
  21. 17
  22. 55
  23. 9.4
  24. 6.8
  25. 88
  26. 75
  27. 14
  28. 6.9
  29. 17
  30. 7.2
  31. 34
  32. 8.1
  33. 5.4
  34. 51
  35. 69
  36. 75
  37. 36
  38. 6.3
  39. 62
  40. 60

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