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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 39 · 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 3062 ÷ 36? (a) 77 (b) 7700 (c) 770
  2. 2.Best estimate of 2179 ÷ 76? (a) 270 (b) 2700 (c) 27
  3. 3.Best estimate of 3108 ÷ 34? (a) 10400 (b) 1040 (c) 104
  4. 4.√27 to 1 decimal place? (a) 4.9 (b) 5.2 (c) 5.1 (d) 5.0
  5. 5.√62 to 1 decimal place? (a) 7.7 (b) 7.9 (c) 7.8 (d) 8.0
  6. 6.Best estimate of 1158 ÷ 28? (a) 39 (b) 3900 (c) 390
  7. 7.√50 to 1 decimal place? (a) 7.3 (b) 7.2 (c) 7.4 (d) 7.1
  8. 8.Best estimate of 2607 ÷ 48? (a) 52 (b) 520 (c) 5200
  9. 9.Best estimate of 1261 ÷ 43? (a) 320 (b) 32 (c) 3200
  10. 10.Best estimate of 839 ÷ 52? (a) 1700 (b) 170 (c) 17
  11. 11.Best estimate of 2283 ÷ 46? (a) 46 (b) 4600 (c) 460
  12. 12.Best estimate of 3113 ÷ 34? (a) 104 (b) 1040 (c) 10400
  13. 13.√48 to 1 decimal place? (a) 7.0 (b) 7.1 (c) 6.8 (d) 6.9
  14. 14.Best estimate of 1111 ÷ 74? (a) 16 (b) 1600 (c) 160
  15. 15.Best estimate of 5596 ÷ 62? (a) 930 (b) 93 (c) 9300
  16. 16.√43 to 1 decimal place? (a) 6.7 (b) 6.8 (c) 6.9 (d) 6.6
  17. 17.√21 to 1 decimal place? (a) 4.4 (b) 4.7 (c) 4.5 (d) 4.6
  18. 18.Best estimate of 3700 ÷ 88? (a) 410 (b) 4100 (c) 41
  19. 19.Best estimate of 2982 ÷ 53? (a) 6000 (b) 600 (c) 60
  20. 20.√90 to 1 decimal place? (a) 9.7 (b) 9.8 (c) 9.6 (d) 9.5
  21. 21.√66 to 1 decimal place? (a) 8.1 (b) 7.9 (c) 8.2 (d) 8.0
  22. 22.√53 to 1 decimal place? (a) 7.4 (b) 7.2 (c) 7.1 (d) 7.3
  23. 23.√56 to 1 decimal place? (a) 7.6 (b) 7.8 (c) 7.7 (d) 7.5
  24. 24.Best estimate of 5514 ÷ 88? (a) 610 (b) 6100 (c) 61
  25. 25.√40 to 1 decimal place? (a) 6.0 (b) 6.1 (c) 6.3 (d) 6.2
  26. 26.Best estimate of 3263 ÷ 51? (a) 65 (b) 650 (c) 6500
  27. 27.Best estimate of 1047 ÷ 72? (a) 150 (b) 15 (c) 1500
  28. 28.Best estimate of 1850 ÷ 27? (a) 62 (b) 6200 (c) 620
  29. 29.Best estimate of 2065 ÷ 42? (a) 520 (b) 5200 (c) 52
  30. 30.Best estimate of 4472 ÷ 62? (a) 75 (b) 750 (c) 7500
  31. 31.Best estimate of 1742 ÷ 41? (a) 440 (b) 4400 (c) 44
  32. 32.Best estimate of 1193 ÷ 63? (a) 2000 (b) 200 (c) 20
  33. 33.√61 to 1 decimal place? (a) 7.8 (b) 7.9 (c) 8.1 (d) 8.0
  34. 34.√26 to 1 decimal place? (a) 5.1 (b) 4.8 (c) 5.0 (d) 4.9
  35. 35.√30 to 1 decimal place? (a) 5.8 (b) 5.7 (c) 5.5 (d) 5.6
  36. 36.√22 to 1 decimal place? (a) 4.5 (b) 4.8 (c) 4.7 (d) 4.6
  37. 37.Best estimate of 2593 ÷ 39? (a) 65 (b) 6500 (c) 650
  38. 38.Best estimate of 3194 ÷ 57? (a) 5300 (b) 53 (c) 530
  39. 39.Best estimate of 1819 ÷ 29? (a) 610 (b) 6100 (c) 61
  40. 40.√55 to 1 decimal place? (a) 7.4 (b) 7.2 (c) 7.5 (d) 7.3

Answer key

  1. 77
  2. 27
  3. 104
  4. 5.2
  5. 7.9
  6. 39
  7. 7.1
  8. 52
  9. 32
  10. 17
  11. 46
  12. 104
  13. 6.9
  14. 16
  15. 93
  16. 6.6
  17. 4.6
  18. 41
  19. 60
  20. 9.5
  21. 8.1
  22. 7.3
  23. 7.5
  24. 61
  25. 6.3
  26. 65
  27. 15
  28. 62
  29. 52
  30. 75
  31. 44
  32. 20
  33. 7.8
  34. 5.1
  35. 5.5
  36. 4.7
  37. 65
  38. 53
  39. 61
  40. 7.4

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