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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 413 · 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 3167 ÷ 76? (a) 400 (b) 4000 (c) 40
  2. 2.√58 to 1 decimal place? (a) 7.9 (b) 7.6 (c) 7.7 (d) 7.8
  3. 3.√50 to 1 decimal place? (a) 7.4 (b) 7.1 (c) 7.3 (d) 7.2
  4. 4.√72 to 1 decimal place? (a) 8.2 (b) 8.3 (c) 8.5 (d) 8.4
  5. 5.√92 to 1 decimal place? (a) 9.6 (b) 9.7 (c) 9.9 (d) 9.8
  6. 6.Best estimate of 4411 ÷ 54? (a) 8800 (b) 880 (c) 88
  7. 7.√59 to 1 decimal place? (a) 7.8 (b) 8.0 (c) 7.9 (d) 7.7
  8. 8.√82 to 1 decimal place? (a) 9.1 (b) 8.9 (c) 9.0 (d) 8.8
  9. 9.Best estimate of 4259 ÷ 72? (a) 61 (b) 6100 (c) 610
  10. 10.Best estimate of 3053 ÷ 58? (a) 51 (b) 510 (c) 5100
  11. 11.Best estimate of 2497 ÷ 77? (a) 31 (b) 310 (c) 3100
  12. 12.Best estimate of 981 ÷ 36? (a) 250 (b) 2500 (c) 25
  13. 13.√88 to 1 decimal place? (a) 9.3 (b) 9.2 (c) 9.1 (d) 9.4
  14. 14.Best estimate of 3185 ÷ 62? (a) 53 (b) 5300 (c) 530
  15. 15.Best estimate of 2133 ÷ 26? (a) 71 (b) 7100 (c) 710
  16. 16.√85 to 1 decimal place? (a) 9.1 (b) 9.3 (c) 9.0 (d) 9.2
  17. 17.Best estimate of 1714 ÷ 32? (a) 57 (b) 5700 (c) 570
  18. 18.Best estimate of 1571 ÷ 36? (a) 3900 (b) 390 (c) 39
  19. 19.Best estimate of 1327 ÷ 68? (a) 190 (b) 19 (c) 1900
  20. 20.√24 to 1 decimal place? (a) 5.1 (b) 5.0 (c) 5.2 (d) 4.9
  21. 21.√65 to 1 decimal place? (a) 8.0 (b) 8.1 (c) 8.2 (d) 7.9
  22. 22.√67 to 1 decimal place? (a) 8.2 (b) 8.1 (c) 8.4 (d) 8.3
  23. 23.Best estimate of 1923 ÷ 38? (a) 480 (b) 48 (c) 4800
  24. 24.√96 to 1 decimal place? (a) 9.9 (b) 9.7 (c) 9.8 (d) 9.6
  25. 25.Best estimate of 4457 ÷ 83? (a) 560 (b) 5600 (c) 56
  26. 26.Best estimate of 2046 ÷ 22? (a) 10200 (b) 1020 (c) 102
  27. 27.Best estimate of 1463 ÷ 33? (a) 49 (b) 4900 (c) 490
  28. 28.Best estimate of 1572 ÷ 26? (a) 5200 (b) 52 (c) 520
  29. 29.Best estimate of 3028 ÷ 37? (a) 7600 (b) 76 (c) 760
  30. 30.√42 to 1 decimal place? (a) 6.4 (b) 6.5 (c) 6.6 (d) 6.3
  31. 31.Best estimate of 4706 ÷ 69? (a) 670 (b) 6700 (c) 67
  32. 32.Best estimate of 4515 ÷ 58? (a) 7500 (b) 75 (c) 750
  33. 33.Best estimate of 1259 ÷ 62? (a) 21 (b) 210 (c) 2100
  34. 34.√86 to 1 decimal place? (a) 9.2 (b) 9.0 (c) 9.3 (d) 9.1
  35. 35.√31 to 1 decimal place? (a) 5.4 (b) 5.5 (c) 5.7 (d) 5.6
  36. 36.√37 to 1 decimal place? (a) 5.9 (b) 6.1 (c) 6.0 (d) 5.8
  37. 37.Best estimate of 2708 ÷ 59? (a) 450 (b) 4500 (c) 45
  38. 38.√98 to 1 decimal place? (a) 10.2 (b) 10.1 (c) 10.0 (d) 9.9
  39. 39.Best estimate of 3139 ÷ 36? (a) 780 (b) 78 (c) 7800
  40. 40.Best estimate of 2091 ÷ 46? (a) 42 (b) 4200 (c) 420

Answer key

  1. 40
  2. 7.6
  3. 7.1
  4. 8.5
  5. 9.6
  6. 88
  7. 7.7
  8. 9.1
  9. 61
  10. 51
  11. 31
  12. 25
  13. 9.4
  14. 53
  15. 71
  16. 9.2
  17. 57
  18. 39
  19. 19
  20. 4.9
  21. 8.1
  22. 8.2
  23. 48
  24. 9.8
  25. 56
  26. 102
  27. 49
  28. 52
  29. 76
  30. 6.5
  31. 67
  32. 75
  33. 21
  34. 9.3
  35. 5.6
  36. 6.1
  37. 45
  38. 9.9
  39. 78
  40. 42

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