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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 519 · 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 327 ÷ 27? (a) 110 (b) 1100 (c) 11
  2. 2.Best estimate of 2799 ÷ 62? (a) 470 (b) 4700 (c) 47
  3. 3.Best estimate of 3076 ÷ 66? (a) 44 (b) 440 (c) 4400
  4. 4.√35 to 1 decimal place? (a) 5.8 (b) 5.7 (c) 5.9 (d) 6.0
  5. 5.Best estimate of 3621 ÷ 89? (a) 400 (b) 4000 (c) 40
  6. 6.√69 to 1 decimal place? (a) 8.2 (b) 8.1 (c) 8.0 (d) 8.3
  7. 7.√30 to 1 decimal place? (a) 5.5 (b) 5.3 (c) 5.6 (d) 5.4
  8. 8.Best estimate of 3278 ÷ 51? (a) 66 (b) 660 (c) 6600
  9. 9.Best estimate of 474 ÷ 22? (a) 24 (b) 240 (c) 2400
  10. 10.Best estimate of 2736 ÷ 76? (a) 34 (b) 340 (c) 3400
  11. 11.Best estimate of 1579 ÷ 38? (a) 390 (b) 3900 (c) 39
  12. 12.Best estimate of 5719 ÷ 66? (a) 82 (b) 820 (c) 8200
  13. 13.√29 to 1 decimal place? (a) 5.4 (b) 5.2 (c) 5.1 (d) 5.3
  14. 14.√61 to 1 decimal place? (a) 8.0 (b) 7.9 (c) 7.7 (d) 7.8
  15. 15.√34 to 1 decimal place? (a) 5.5 (b) 5.7 (c) 5.6 (d) 5.8
  16. 16.Best estimate of 3486 ÷ 69? (a) 5000 (b) 500 (c) 50
  17. 17.Best estimate of 6007 ÷ 66? (a) 86 (b) 8600 (c) 860
  18. 18.√47 to 1 decimal place? (a) 6.7 (b) 6.9 (c) 6.8 (d) 7.0
  19. 19.√80 to 1 decimal place? (a) 9.0 (b) 9.1 (c) 9.2 (d) 8.9
  20. 20.Best estimate of 1149 ÷ 37? (a) 290 (b) 2900 (c) 29
  21. 21.Best estimate of 1897 ÷ 57? (a) 320 (b) 3200 (c) 32
  22. 22.√79 to 1 decimal place? (a) 9.2 (b) 9.1 (c) 8.9 (d) 9.0
  23. 23.√75 to 1 decimal place? (a) 8.6 (b) 8.5 (c) 8.7 (d) 8.4
  24. 24.√74 to 1 decimal place? (a) 8.6 (b) 8.8 (c) 8.9 (d) 8.7
  25. 25.√51 to 1 decimal place? (a) 6.9 (b) 7.0 (c) 6.8 (d) 7.1
  26. 26.Best estimate of 1765 ÷ 31? (a) 590 (b) 59 (c) 5900
  27. 27.Best estimate of 1644 ÷ 42? (a) 410 (b) 41 (c) 4100
  28. 28.√84 to 1 decimal place? (a) 9.2 (b) 9.0 (c) 8.9 (d) 9.1
  29. 29.√90 to 1 decimal place? (a) 9.7 (b) 9.5 (c) 9.8 (d) 9.6
  30. 30.Best estimate of 875 ÷ 31? (a) 290 (b) 29 (c) 2900
  31. 31.Best estimate of 2778 ÷ 39? (a) 6900 (b) 690 (c) 69
  32. 32.√66 to 1 decimal place? (a) 8.1 (b) 7.9 (c) 8.2 (d) 8.0
  33. 33.√45 to 1 decimal place? (a) 6.4 (b) 6.7 (c) 6.5 (d) 6.6
  34. 34.Best estimate of 676 ÷ 23? (a) 34 (b) 3400 (c) 340
  35. 35.Best estimate of 2292 ÷ 78? (a) 2900 (b) 290 (c) 29
  36. 36.Best estimate of 3073 ÷ 61? (a) 510 (b) 51 (c) 5100
  37. 37.Best estimate of 1441 ÷ 78? (a) 1800 (b) 18 (c) 180
  38. 38.√43 to 1 decimal place? (a) 6.8 (b) 6.7 (c) 6.9 (d) 6.6
  39. 39.√89 to 1 decimal place? (a) 9.7 (b) 9.5 (c) 9.6 (d) 9.4
  40. 40.√96 to 1 decimal place? (a) 9.6 (b) 9.7 (c) 9.5 (d) 9.8

Answer key

  1. 11
  2. 47
  3. 44
  4. 5.9
  5. 40
  6. 8.3
  7. 5.5
  8. 66
  9. 24
  10. 34
  11. 39
  12. 82
  13. 5.4
  14. 7.8
  15. 5.8
  16. 50
  17. 86
  18. 6.9
  19. 8.9
  20. 29
  21. 32
  22. 8.9
  23. 8.7
  24. 8.6
  25. 7.1
  26. 59
  27. 41
  28. 9.2
  29. 9.5
  30. 29
  31. 69
  32. 8.1
  33. 6.7
  34. 34
  35. 29
  36. 51
  37. 18
  38. 6.6
  39. 9.4
  40. 9.8

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