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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 999 · 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 2517 ÷ 47? (a) 50 (b) 500 (c) 5000
  2. 2.Best estimate of 1778 ÷ 84? (a) 22 (b) 2200 (c) 220
  3. 3.Best estimate of 609 ÷ 23? (a) 3000 (b) 300 (c) 30
  4. 4.Best estimate of 3260 ÷ 62? (a) 5400 (b) 54 (c) 540
  5. 5.√51 to 1 decimal place? (a) 6.8 (b) 6.9 (c) 7.0 (d) 7.1
  6. 6.√62 to 1 decimal place? (a) 8.0 (b) 7.8 (c) 8.1 (d) 7.9
  7. 7.√38 to 1 decimal place? (a) 6.3 (b) 6.2 (c) 6.4 (d) 6.1
  8. 8.√87 to 1 decimal place? (a) 9.2 (b) 9.1 (c) 9.3 (d) 9.4
  9. 9.Best estimate of 3964 ÷ 76? (a) 5000 (b) 50 (c) 500
  10. 10.Best estimate of 1792 ÷ 82? (a) 220 (b) 2200 (c) 22
  11. 11.√67 to 1 decimal place? (a) 8.5 (b) 8.4 (c) 8.3 (d) 8.2
  12. 12.√78 to 1 decimal place? (a) 8.9 (b) 8.8 (c) 9.1 (d) 9.0
  13. 13.Best estimate of 1606 ÷ 56? (a) 270 (b) 27 (c) 2700
  14. 14.√45 to 1 decimal place? (a) 6.7 (b) 6.8 (c) 7.0 (d) 6.9
  15. 15.Best estimate of 1917 ÷ 23? (a) 9600 (b) 960 (c) 96
  16. 16.√75 to 1 decimal place? (a) 8.5 (b) 8.7 (c) 8.6 (d) 8.8
  17. 17.Best estimate of 1768 ÷ 27? (a) 5900 (b) 59 (c) 590
  18. 18.Best estimate of 1635 ÷ 78? (a) 20 (b) 200 (c) 2000
  19. 19.Best estimate of 1655 ÷ 66? (a) 24 (b) 2400 (c) 240
  20. 20.√41 to 1 decimal place? (a) 6.1 (b) 6.4 (c) 6.2 (d) 6.3
  21. 21.Best estimate of 1634 ÷ 21? (a) 8200 (b) 820 (c) 82
  22. 22.Best estimate of 3001 ÷ 56? (a) 5000 (b) 50 (c) 500
  23. 23.Best estimate of 7037 ÷ 84? (a) 880 (b) 8800 (c) 88
  24. 24.√98 to 1 decimal place? (a) 9.9 (b) 10.0 (c) 10.1 (d) 10.2
  25. 25.√72 to 1 decimal place? (a) 8.6 (b) 8.8 (c) 8.7 (d) 8.5
  26. 26.Best estimate of 2227 ÷ 56? (a) 37 (b) 370 (c) 3700
  27. 27.Best estimate of 1221 ÷ 47? (a) 240 (b) 24 (c) 2400
  28. 28.Best estimate of 7511 ÷ 81? (a) 940 (b) 9400 (c) 94
  29. 29.Best estimate of 4005 ÷ 44? (a) 1000 (b) 100 (c) 10000
  30. 30.√71 to 1 decimal place? (a) 8.7 (b) 8.6 (c) 8.5 (d) 8.4
  31. 31.Best estimate of 1099 ÷ 64? (a) 18 (b) 1800 (c) 180
  32. 32.√61 to 1 decimal place? (a) 7.8 (b) 7.6 (c) 7.5 (d) 7.7
  33. 33.Best estimate of 3770 ÷ 81? (a) 470 (b) 4700 (c) 47
  34. 34.√79 to 1 decimal place? (a) 8.9 (b) 8.8 (c) 9.0 (d) 9.1
  35. 35.√37 to 1 decimal place? (a) 6.0 (b) 5.9 (c) 6.2 (d) 6.1
  36. 36.Best estimate of 2553 ÷ 89? (a) 28 (b) 280 (c) 2800
  37. 37.√28 to 1 decimal place? (a) 5.3 (b) 5.4 (c) 5.6 (d) 5.5
  38. 38.Best estimate of 3622 ÷ 63? (a) 600 (b) 60 (c) 6000
  39. 39.Best estimate of 1689 ÷ 61? (a) 280 (b) 2800 (c) 28
  40. 40.√40 to 1 decimal place? (a) 6.6 (b) 6.3 (c) 6.5 (d) 6.4

Answer key

  1. 50
  2. 22
  3. 30
  4. 54
  5. 7.1
  6. 7.9
  7. 6.2
  8. 9.3
  9. 50
  10. 22
  11. 8.2
  12. 8.8
  13. 27
  14. 6.7
  15. 96
  16. 8.7
  17. 59
  18. 20
  19. 24
  20. 6.4
  21. 82
  22. 50
  23. 88
  24. 9.9
  25. 8.5
  26. 37
  27. 24
  28. 94
  29. 100
  30. 8.4
  31. 18
  32. 7.8
  33. 47
  34. 8.9
  35. 6.1
  36. 28
  37. 5.3
  38. 60
  39. 28
  40. 6.3

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