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Estimating Square Roots and Division Worksheet

Mental maths lesson 27: Estimate divisions and square roots · Set 126 · 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) 5.5 (d) 5.6
  2. 2.Best estimate of 5605 ÷ 68? (a) 8000 (b) 800 (c) 80
  3. 3.Best estimate of 955 ÷ 21? (a) 4800 (b) 480 (c) 48
  4. 4.Best estimate of 2993 ÷ 47? (a) 6000 (b) 60 (c) 600
  5. 5.√72 to 1 decimal place? (a) 8.4 (b) 8.5 (c) 8.2 (d) 8.3
  6. 6.√70 to 1 decimal place? (a) 8.4 (b) 8.6 (c) 8.5 (d) 8.7
  7. 7.√98 to 1 decimal place? (a) 9.6 (b) 9.9 (c) 9.8 (d) 9.7
  8. 8.√65 to 1 decimal place? (a) 7.8 (b) 8.0 (c) 7.9 (d) 8.1
  9. 9.√30 to 1 decimal place? (a) 5.7 (b) 5.5 (c) 5.6 (d) 5.8
  10. 10.Best estimate of 4007 ÷ 42? (a) 100 (b) 1000 (c) 10000
  11. 11.Best estimate of 1509 ÷ 56? (a) 2500 (b) 250 (c) 25
  12. 12.√28 to 1 decimal place? (a) 5.4 (b) 5.3 (c) 5.5 (d) 5.6
  13. 13.Best estimate of 1246 ÷ 68? (a) 18 (b) 1800 (c) 180
  14. 14.Best estimate of 2898 ÷ 48? (a) 58 (b) 5800 (c) 580
  15. 15.√56 to 1 decimal place? (a) 7.4 (b) 7.3 (c) 7.5 (d) 7.2
  16. 16.Best estimate of 1361 ÷ 29? (a) 45 (b) 450 (c) 4500
  17. 17.Best estimate of 3884 ÷ 52? (a) 780 (b) 78 (c) 7800
  18. 18.√20 to 1 decimal place? (a) 4.8 (b) 4.6 (c) 4.7 (d) 4.5
  19. 19.√53 to 1 decimal place? (a) 7.0 (b) 7.1 (c) 7.3 (d) 7.2
  20. 20.Best estimate of 5217 ÷ 82? (a) 650 (b) 65 (c) 6500
  21. 21.√85 to 1 decimal place? (a) 9.4 (b) 9.2 (c) 9.1 (d) 9.3
  22. 22.Best estimate of 373 ÷ 26? (a) 120 (b) 12 (c) 1200
  23. 23.√96 to 1 decimal place? (a) 10.1 (b) 10.0 (c) 9.9 (d) 9.8
  24. 24.Best estimate of 4341 ÷ 68? (a) 620 (b) 6200 (c) 62
  25. 25.Best estimate of 2502 ÷ 79? (a) 310 (b) 31 (c) 3100
  26. 26.Best estimate of 618 ÷ 27? (a) 210 (b) 2100 (c) 21
  27. 27.√45 to 1 decimal place? (a) 6.7 (b) 6.6 (c) 6.5 (d) 6.4
  28. 28.Best estimate of 2312 ÷ 76? (a) 290 (b) 2900 (c) 29
  29. 29.Best estimate of 1275 ÷ 22? (a) 640 (b) 6400 (c) 64
  30. 30.√22 to 1 decimal place? (a) 4.6 (b) 4.9 (c) 4.7 (d) 4.8
  31. 31.√37 to 1 decimal place? (a) 5.8 (b) 6.1 (c) 5.9 (d) 6.0
  32. 32.√26 to 1 decimal place? (a) 5.0 (b) 5.1 (c) 5.2 (d) 4.9
  33. 33.√21 to 1 decimal place? (a) 4.9 (b) 4.8 (c) 4.6 (d) 4.7
  34. 34.Best estimate of 3611 ÷ 77? (a) 45 (b) 450 (c) 4500
  35. 35.Best estimate of 1957 ÷ 24? (a) 980 (b) 9800 (c) 98
  36. 36.Best estimate of 3923 ÷ 76? (a) 4900 (b) 49 (c) 490
  37. 37.√50 to 1 decimal place? (a) 7.0 (b) 7.1 (c) 6.9 (d) 6.8
  38. 38.√90 to 1 decimal place? (a) 9.7 (b) 9.6 (c) 9.8 (d) 9.5
  39. 39.√62 to 1 decimal place? (a) 7.7 (b) 7.8 (c) 7.9 (d) 7.6
  40. 40.√87 to 1 decimal place? (a) 9.3 (b) 9.5 (c) 9.4 (d) 9.6

Answer key

  1. 5.8
  2. 80
  3. 48
  4. 60
  5. 8.5
  6. 8.4
  7. 9.9
  8. 8.1
  9. 5.5
  10. 100
  11. 25
  12. 5.3
  13. 18
  14. 58
  15. 7.5
  16. 45
  17. 78
  18. 4.5
  19. 7.3
  20. 65
  21. 9.2
  22. 12
  23. 9.8
  24. 62
  25. 31
  26. 21
  27. 6.7
  28. 29
  29. 64
  30. 4.7
  31. 6.1
  32. 5.1
  33. 4.6
  34. 45
  35. 98
  36. 49
  37. 7.1
  38. 9.5
  39. 7.9
  40. 9.3

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