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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 463 · 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) 5.7 (c) 5.9 (d) 6.0
  2. 2.Best estimate of 2653 ÷ 43? (a) 660 (b) 66 (c) 6600
  3. 3.Best estimate of 1233 ÷ 79? (a) 15 (b) 1500 (c) 150
  4. 4.√98 to 1 decimal place? (a) 9.9 (b) 9.7 (c) 9.6 (d) 9.8
  5. 5.Best estimate of 4206 ÷ 71? (a) 6000 (b) 600 (c) 60
  6. 6.Best estimate of 3616 ÷ 54? (a) 720 (b) 72 (c) 7200
  7. 7.√96 to 1 decimal place? (a) 9.6 (b) 9.9 (c) 9.7 (d) 9.8
  8. 8.Best estimate of 5753 ÷ 72? (a) 82 (b) 820 (c) 8200
  9. 9.√37 to 1 decimal place? (a) 6.1 (b) 6.4 (c) 6.2 (d) 6.3
  10. 10.Best estimate of 1235 ÷ 32? (a) 410 (b) 41 (c) 4100
  11. 11.√58 to 1 decimal place? (a) 7.4 (b) 7.5 (c) 7.6 (d) 7.3
  12. 12.Best estimate of 3499 ÷ 42? (a) 870 (b) 87 (c) 8700
  13. 13.√59 to 1 decimal place? (a) 8.0 (b) 7.7 (c) 7.9 (d) 7.8
  14. 14.Best estimate of 1513 ÷ 88? (a) 1700 (b) 17 (c) 170
  15. 15.√23 to 1 decimal place? (a) 5.0 (b) 4.9 (c) 4.8 (d) 4.7
  16. 16.√85 to 1 decimal place? (a) 8.9 (b) 9.2 (c) 9.0 (d) 9.1
  17. 17.Best estimate of 838 ÷ 37? (a) 210 (b) 2100 (c) 21
  18. 18.√46 to 1 decimal place? (a) 7.0 (b) 6.8 (c) 7.1 (d) 6.9
  19. 19.√48 to 1 decimal place? (a) 6.9 (b) 6.7 (c) 7.0 (d) 6.8
  20. 20.√30 to 1 decimal place? (a) 5.8 (b) 5.5 (c) 5.6 (d) 5.7
  21. 21.Best estimate of 555 ÷ 28? (a) 19 (b) 190 (c) 1900
  22. 22.Best estimate of 1340 ÷ 78? (a) 1700 (b) 17 (c) 170
  23. 23.Best estimate of 2173 ÷ 83? (a) 2700 (b) 270 (c) 27
  24. 24.Best estimate of 2689 ÷ 31? (a) 900 (b) 90 (c) 9000
  25. 25.Best estimate of 824 ÷ 38? (a) 210 (b) 21 (c) 2100
  26. 26.√55 to 1 decimal place? (a) 7.7 (b) 7.6 (c) 7.5 (d) 7.4
  27. 27.√88 to 1 decimal place? (a) 9.4 (b) 9.6 (c) 9.5 (d) 9.7
  28. 28.√56 to 1 decimal place? (a) 7.7 (b) 7.5 (c) 7.4 (d) 7.6
  29. 29.√66 to 1 decimal place? (a) 7.9 (b) 7.8 (c) 8.1 (d) 8.0
  30. 30.Best estimate of 590 ÷ 42? (a) 15 (b) 150 (c) 1500
  31. 31.Best estimate of 1293 ÷ 73? (a) 180 (b) 1800 (c) 18
  32. 32.√32 to 1 decimal place? (a) 5.9 (b) 5.8 (c) 5.7 (d) 6.0
  33. 33.√63 to 1 decimal place? (a) 8.1 (b) 7.8 (c) 8.0 (d) 7.9
  34. 34.Best estimate of 4028 ÷ 84? (a) 500 (b) 50 (c) 5000
  35. 35.√31 to 1 decimal place? (a) 5.4 (b) 5.5 (c) 5.6 (d) 5.7
  36. 36.√41 to 1 decimal place? (a) 6.4 (b) 6.3 (c) 6.2 (d) 6.1
  37. 37.√21 to 1 decimal place? (a) 4.8 (b) 4.5 (c) 4.6 (d) 4.7
  38. 38.Best estimate of 4217 ÷ 64? (a) 700 (b) 7000 (c) 70
  39. 39.Best estimate of 1426 ÷ 49? (a) 290 (b) 2900 (c) 29
  40. 40.√45 to 1 decimal place? (a) 6.9 (b) 6.7 (c) 6.8 (d) 6.6

Answer key

  1. 5.8
  2. 66
  3. 15
  4. 9.9
  5. 60
  6. 72
  7. 9.8
  8. 82
  9. 6.1
  10. 41
  11. 7.6
  12. 87
  13. 7.7
  14. 17
  15. 4.8
  16. 9.2
  17. 21
  18. 6.8
  19. 6.9
  20. 5.5
  21. 19
  22. 17
  23. 27
  24. 90
  25. 21
  26. 7.4
  27. 9.4
  28. 7.5
  29. 8.1
  30. 15
  31. 18
  32. 5.7
  33. 7.9
  34. 50
  35. 5.6
  36. 6.4
  37. 4.6
  38. 70
  39. 29
  40. 6.7

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