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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 105 · 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 889 ÷ 27? (a) 3000 (b) 30 (c) 300
  2. 2.√59 to 1 decimal place? (a) 7.9 (b) 7.7 (c) 7.8 (d) 7.6
  3. 3.Best estimate of 2007 ÷ 21? (a) 1000 (b) 10000 (c) 100
  4. 4.Best estimate of 2507 ÷ 43? (a) 630 (b) 63 (c) 6300
  5. 5.√94 to 1 decimal place? (a) 9.8 (b) 9.9 (c) 10.0 (d) 9.7
  6. 6.Best estimate of 2498 ÷ 36? (a) 620 (b) 62 (c) 6200
  7. 7.√53 to 1 decimal place? (a) 7.2 (b) 7.3 (c) 7.1 (d) 7.4
  8. 8.√37 to 1 decimal place? (a) 6.1 (b) 6.3 (c) 6.0 (d) 6.2
  9. 9.Best estimate of 449 ÷ 32? (a) 1500 (b) 150 (c) 15
  10. 10.√45 to 1 decimal place? (a) 6.5 (b) 6.6 (c) 6.4 (d) 6.7
  11. 11.Best estimate of 4744 ÷ 56? (a) 79 (b) 790 (c) 7900
  12. 12.√72 to 1 decimal place? (a) 8.5 (b) 8.2 (c) 8.3 (d) 8.4
  13. 13.√67 to 1 decimal place? (a) 8.4 (b) 8.5 (c) 8.2 (d) 8.3
  14. 14.√84 to 1 decimal place? (a) 9.1 (b) 9.2 (c) 9.3 (d) 9.0
  15. 15.Best estimate of 570 ÷ 26? (a) 1900 (b) 190 (c) 19
  16. 16.√74 to 1 decimal place? (a) 8.7 (b) 8.6 (c) 8.4 (d) 8.5
  17. 17.Best estimate of 2424 ÷ 46? (a) 480 (b) 48 (c) 4800
  18. 18.Best estimate of 1202 ÷ 33? (a) 40 (b) 400 (c) 4000
  19. 19.Best estimate of 2695 ÷ 32? (a) 900 (b) 9000 (c) 90
  20. 20.Best estimate of 3070 ÷ 67? (a) 440 (b) 4400 (c) 44
  21. 21.Best estimate of 467 ÷ 22? (a) 23 (b) 2300 (c) 230
  22. 22.Best estimate of 6690 ÷ 82? (a) 84 (b) 840 (c) 8400
  23. 23.√30 to 1 decimal place? (a) 5.2 (b) 5.3 (c) 5.5 (d) 5.4
  24. 24.Best estimate of 1916 ÷ 33? (a) 64 (b) 640 (c) 6400
  25. 25.√82 to 1 decimal place? (a) 9.2 (b) 9.3 (c) 9.0 (d) 9.1
  26. 26.Best estimate of 6569 ÷ 87? (a) 73 (b) 730 (c) 7300
  27. 27.Best estimate of 5883 ÷ 89? (a) 650 (b) 65 (c) 6500
  28. 28.√40 to 1 decimal place? (a) 6.2 (b) 6.4 (c) 6.1 (d) 6.3
  29. 29.√55 to 1 decimal place? (a) 7.6 (b) 7.4 (c) 7.5 (d) 7.3
  30. 30.Best estimate of 3918 ÷ 63? (a) 650 (b) 6500 (c) 65
  31. 31.Best estimate of 4838 ÷ 79? (a) 600 (b) 60 (c) 6000
  32. 32.Best estimate of 2047 ÷ 38? (a) 5100 (b) 51 (c) 510
  33. 33.Best estimate of 1228 ÷ 46? (a) 25 (b) 2500 (c) 250
  34. 34.Best estimate of 2029 ÷ 68? (a) 290 (b) 29 (c) 2900
  35. 35.Best estimate of 6407 ÷ 72? (a) 920 (b) 9200 (c) 92
  36. 36.√35 to 1 decimal place? (a) 5.8 (b) 5.9 (c) 6.0 (d) 6.1
  37. 37.Best estimate of 1364 ÷ 46? (a) 270 (b) 2700 (c) 27
  38. 38.√42 to 1 decimal place? (a) 6.4 (b) 6.5 (c) 6.2 (d) 6.3
  39. 39.√85 to 1 decimal place? (a) 9.5 (b) 9.4 (c) 9.3 (d) 9.2
  40. 40.√43 to 1 decimal place? (a) 6.5 (b) 6.4 (c) 6.6 (d) 6.7

Answer key

  1. 30
  2. 7.7
  3. 100
  4. 63
  5. 9.7
  6. 62
  7. 7.3
  8. 6.1
  9. 15
  10. 6.7
  11. 79
  12. 8.5
  13. 8.2
  14. 9.2
  15. 19
  16. 8.6
  17. 48
  18. 40
  19. 90
  20. 44
  21. 23
  22. 84
  23. 5.5
  24. 64
  25. 9.1
  26. 73
  27. 65
  28. 6.3
  29. 7.4
  30. 65
  31. 60
  32. 51
  33. 25
  34. 29
  35. 92
  36. 5.9
  37. 27
  38. 6.5
  39. 9.2
  40. 6.6

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