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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 346 · 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.√52 to 1 decimal place? (a) 7.1 (b) 7.0 (c) 7.2 (d) 6.9
  2. 2.√21 to 1 decimal place? (a) 4.7 (b) 4.8 (c) 4.9 (d) 4.6
  3. 3.Best estimate of 1517 ÷ 52? (a) 30 (b) 300 (c) 3000
  4. 4.Best estimate of 1536 ÷ 23? (a) 7700 (b) 77 (c) 770
  5. 5.√82 to 1 decimal place? (a) 8.8 (b) 9.0 (c) 8.9 (d) 9.1
  6. 6.Best estimate of 1461 ÷ 43? (a) 3700 (b) 37 (c) 370
  7. 7.√84 to 1 decimal place? (a) 9.1 (b) 9.0 (c) 9.2 (d) 8.9
  8. 8.Best estimate of 1143 ÷ 89? (a) 130 (b) 1300 (c) 13
  9. 9.√98 to 1 decimal place? (a) 10.0 (b) 10.1 (c) 10.2 (d) 9.9
  10. 10.√42 to 1 decimal place? (a) 6.3 (b) 6.5 (c) 6.4 (d) 6.6
  11. 11.Best estimate of 1231 ÷ 27? (a) 410 (b) 41 (c) 4100
  12. 12.√79 to 1 decimal place? (a) 8.9 (b) 9.0 (c) 8.7 (d) 8.8
  13. 13.Best estimate of 2686 ÷ 77? (a) 340 (b) 3400 (c) 34
  14. 14.√63 to 1 decimal place? (a) 7.7 (b) 8.0 (c) 7.8 (d) 7.9
  15. 15.√88 to 1 decimal place? (a) 9.5 (b) 9.4 (c) 9.3 (d) 9.2
  16. 16.Best estimate of 6737 ÷ 73? (a) 960 (b) 9600 (c) 96
  17. 17.Best estimate of 5468 ÷ 88? (a) 610 (b) 6100 (c) 61
  18. 18.√30 to 1 decimal place? (a) 5.6 (b) 5.8 (c) 5.5 (d) 5.7
  19. 19.Best estimate of 2076 ÷ 72? (a) 3000 (b) 30 (c) 300
  20. 20.Best estimate of 2317 ÷ 88? (a) 260 (b) 2600 (c) 26
  21. 21.√87 to 1 decimal place? (a) 9.2 (b) 9.3 (c) 9.0 (d) 9.1
  22. 22.Best estimate of 462 ÷ 38? (a) 120 (b) 1200 (c) 12
  23. 23.√41 to 1 decimal place? (a) 6.4 (b) 6.5 (c) 6.3 (d) 6.6
  24. 24.√67 to 1 decimal place? (a) 8.2 (b) 8.3 (c) 8.1 (d) 8.0
  25. 25.√37 to 1 decimal place? (a) 6.2 (b) 6.3 (c) 6.1 (d) 6.0
  26. 26.√40 to 1 decimal place? (a) 6.3 (b) 6.4 (c) 6.1 (d) 6.2
  27. 27.√38 to 1 decimal place? (a) 6.4 (b) 6.2 (c) 6.5 (d) 6.3
  28. 28.Best estimate of 1011 ÷ 44? (a) 2500 (b) 250 (c) 25
  29. 29.Best estimate of 3288 ÷ 78? (a) 41 (b) 4100 (c) 410
  30. 30.Best estimate of 4577 ÷ 78? (a) 570 (b) 5700 (c) 57
  31. 31.Best estimate of 4440 ÷ 67? (a) 6300 (b) 63 (c) 630
  32. 32.√43 to 1 decimal place? (a) 6.8 (b) 6.6 (c) 6.7 (d) 6.5
  33. 33.√72 to 1 decimal place? (a) 8.4 (b) 8.6 (c) 8.5 (d) 8.3
  34. 34.Best estimate of 1356 ÷ 53? (a) 2700 (b) 270 (c) 27
  35. 35.Best estimate of 1344 ÷ 43? (a) 340 (b) 34 (c) 3400
  36. 36.Best estimate of 3047 ÷ 46? (a) 6100 (b) 61 (c) 610
  37. 37.Best estimate of 1514 ÷ 62? (a) 250 (b) 25 (c) 2500
  38. 38.√66 to 1 decimal place? (a) 8.1 (b) 8.2 (c) 7.9 (d) 8.0
  39. 39.√45 to 1 decimal place? (a) 6.5 (b) 6.7 (c) 6.4 (d) 6.6
  40. 40.Best estimate of 4358 ÷ 46? (a) 87 (b) 8700 (c) 870

Answer key

  1. 7.2
  2. 4.6
  3. 30
  4. 77
  5. 9.1
  6. 37
  7. 9.2
  8. 13
  9. 9.9
  10. 6.5
  11. 41
  12. 8.9
  13. 34
  14. 7.9
  15. 9.4
  16. 96
  17. 61
  18. 5.5
  19. 30
  20. 26
  21. 9.3
  22. 12
  23. 6.4
  24. 8.2
  25. 6.1
  26. 6.3
  27. 6.2
  28. 25
  29. 41
  30. 57
  31. 63
  32. 6.6
  33. 8.5
  34. 27
  35. 34
  36. 61
  37. 25
  38. 8.1
  39. 6.7
  40. 87

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