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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 697 · 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.√31 to 1 decimal place? (a) 5.4 (b) 5.6 (c) 5.3 (d) 5.5
  2. 2.Best estimate of 3153 ÷ 36? (a) 79 (b) 790 (c) 7900
  3. 3.Best estimate of 6295 ÷ 88? (a) 700 (b) 70 (c) 7000
  4. 4.√76 to 1 decimal place? (a) 8.6 (b) 8.8 (c) 8.7 (d) 8.9
  5. 5.Best estimate of 1262 ÷ 29? (a) 42 (b) 420 (c) 4200
  6. 6.√27 to 1 decimal place? (a) 5.1 (b) 5.0 (c) 5.2 (d) 4.9
  7. 7.Best estimate of 3445 ÷ 83? (a) 430 (b) 4300 (c) 43
  8. 8.√34 to 1 decimal place? (a) 5.9 (b) 5.8 (c) 5.7 (d) 6.0
  9. 9.Best estimate of 2744 ÷ 37? (a) 6900 (b) 69 (c) 690
  10. 10.√92 to 1 decimal place? (a) 9.4 (b) 9.5 (c) 9.6 (d) 9.3
  11. 11.√24 to 1 decimal place? (a) 5.1 (b) 5.0 (c) 4.8 (d) 4.9
  12. 12.√21 to 1 decimal place? (a) 4.4 (b) 4.5 (c) 4.6 (d) 4.3
  13. 13.Best estimate of 2321 ÷ 71? (a) 330 (b) 3300 (c) 33
  14. 14.Best estimate of 2157 ÷ 47? (a) 43 (b) 4300 (c) 430
  15. 15.√26 to 1 decimal place? (a) 5.1 (b) 5.0 (c) 5.2 (d) 4.9
  16. 16.Best estimate of 2362 ÷ 57? (a) 390 (b) 3900 (c) 39
  17. 17.√63 to 1 decimal place? (a) 7.9 (b) 8.2 (c) 8.0 (d) 8.1
  18. 18.√35 to 1 decimal place? (a) 5.9 (b) 6.1 (c) 5.8 (d) 6.0
  19. 19.Best estimate of 2265 ÷ 29? (a) 7600 (b) 760 (c) 76
  20. 20.Best estimate of 731 ÷ 29? (a) 2400 (b) 240 (c) 24
  21. 21.√58 to 1 decimal place? (a) 7.7 (b) 7.5 (c) 7.8 (d) 7.6
  22. 22.√56 to 1 decimal place? (a) 7.7 (b) 7.8 (c) 7.6 (d) 7.5
  23. 23.Best estimate of 1694 ÷ 24? (a) 85 (b) 8500 (c) 850
  24. 24.Best estimate of 543 ÷ 36? (a) 14 (b) 1400 (c) 140
  25. 25.Best estimate of 2289 ÷ 42? (a) 5700 (b) 570 (c) 57
  26. 26.Best estimate of 2715 ÷ 56? (a) 4500 (b) 45 (c) 450
  27. 27.Best estimate of 1429 ÷ 38? (a) 36 (b) 3600 (c) 360
  28. 28.√28 to 1 decimal place? (a) 5.6 (b) 5.5 (c) 5.3 (d) 5.4
  29. 29.√82 to 1 decimal place? (a) 9.0 (b) 9.2 (c) 8.9 (d) 9.1
  30. 30.Best estimate of 2317 ÷ 34? (a) 770 (b) 77 (c) 7700
  31. 31.√32 to 1 decimal place? (a) 5.7 (b) 6.0 (c) 5.9 (d) 5.8
  32. 32.√94 to 1 decimal place? (a) 9.8 (b) 9.5 (c) 9.7 (d) 9.6
  33. 33.Best estimate of 2930 ÷ 51? (a) 590 (b) 5900 (c) 59
  34. 34.Best estimate of 2169 ÷ 43? (a) 54 (b) 540 (c) 5400
  35. 35.Best estimate of 3730 ÷ 72? (a) 530 (b) 5300 (c) 53
  36. 36.Best estimate of 3373 ÷ 36? (a) 84 (b) 8400 (c) 840
  37. 37.√62 to 1 decimal place? (a) 7.8 (b) 7.7 (c) 7.9 (d) 7.6
  38. 38.Best estimate of 1747 ÷ 57? (a) 29 (b) 290 (c) 2900
  39. 39.Best estimate of 2232 ÷ 24? (a) 112 (b) 1120 (c) 11200
  40. 40.√40 to 1 decimal place? (a) 6.3 (b) 6.4 (c) 6.5 (d) 6.2

Answer key

  1. 5.6
  2. 79
  3. 70
  4. 8.7
  5. 42
  6. 5.2
  7. 43
  8. 5.8
  9. 69
  10. 9.6
  11. 4.9
  12. 4.6
  13. 33
  14. 43
  15. 5.1
  16. 39
  17. 7.9
  18. 5.9
  19. 76
  20. 24
  21. 7.6
  22. 7.5
  23. 85
  24. 14
  25. 57
  26. 45
  27. 36
  28. 5.3
  29. 9.1
  30. 77
  31. 5.7
  32. 9.7
  33. 59
  34. 54
  35. 53
  36. 84
  37. 7.9
  38. 29
  39. 112
  40. 6.3

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